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Fundamentos de Física Moderna - Estudo Geral

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1. sues Instruction Manual ae wa and Experiment Guide Experiment Results for the PASCO scientific WS Model AP 9368 and AP 9369 h e Apparatus and h e Apparatus Accessory Kit 1989 PASCO scientific pad 4 e 0 10101 Foothills Blvd Roseville CA 95747 7100 f waso ses screntific Phone 916 786 3800 FAX 916 786 8905 www pasco com 115 012 04049 h e Apparatus and h e Apparatus Accessory Kit Table of Contents Section Page Copyright Warranty and Equipment Return cc ceceeecesseeseeeteeseeeseeeeensees ii rodu HO a ee E a 1 Backeround Theory eneses a a ee ltd 2 Equipr ntand Setup sisihan anaa eiaei aiii 3 Equipment Listes cisto essen e e a dba a aa la o 3 Installing the Batteries meetan eE e RREN 3 Battery Voltage Check irsinin annir E A loves seodheseesees 3 Equipment Setup noaee n e E S EA A A A EER 4 Using the Accessory Kit Filters eenaa en eas 6 Experiments Experiment 1 Wave Model vs Quantum Model 7 Experiment 2 The Relationship of Energy Wavelength and PreEQUuenCY sessao rteciti o veadieeduttaes sbocedet tavesil 11 Technical Information sanear end apa 13 Theory f Operation essential aetna reet E a E EN 13 Schematic Diagrami ssena nai ii nE a NE AENEA T E Es quado 14 Teacher s Guide s 3 25 ccc otis peices janes te iiiaae dene aan dona AEE EER iA 15 Technical Supports iss sas neste co irs ieni EEE atoa decano Inside Back Cove
2. Observe the two sets of dots on the viewing screen one set from the movable mirror and one set from the adjustable mirror Adjust the position of L until both sets of dots are the same size Adjust the tilt of the adjustable mirror until the two sets of dots coincide Replace lens L in front of the laser Move the viewing screen so it s at least 12 inches from the edge of the interferometer base Fringes should appear in the bright disk of the viewing screen Fine adjustments of L may be necessary to find the fringes A piece of white paper or cardboard can be used in place of the viewing screen A 48 mm FL convex lens may also be used to magnify the projected image of the fringes 18mm FL Rotational component holder 18w s1 MICRON Figure 7 Twyman Green Mode Setup 183 Fabry Perot Mode 1 Align the laser and interferometer base as described in Laser Alignment at the beginning ofthis section The laser beam should be approximately parallel with the top of the base should strike the center of the movable mirror and should be reflected directly back into the laser aperture Mount the adjustable mirror where indicated on the in terferometer base and one component holder in front of the movable mirror See Figure 8 Place the other component holder behind the movable mirror and attach the viewing screen to its magnetic backing You should see several images of the laser beam on
3. equa es do movimento da part cula no referencial S 8 Uma barra com Im de comprimento faz um ngulo de 30 com o eixo x x de S Calcular a velocidade do referencial S em rela o ao referencial S segundo a direc o x x para que a barra fa a um ngulo de 45 relativamente ao eixo x x de S 9 Um cubo tem um volume pr prio de 1 dm Determinar o volume desse cubo medido por um observador O que se move em rela o ao cubo com velocidade 0 8c segundo uma direc o paralela a uma aresta 10 Numa colis o a alta energia de raios c smicos na atmosfera 120 km acima do n vel do mar foi criado um mes o que depois viajou verticalmente No seu sistema pr prio o mes o tem uma vida de 2 5 x 10 s Da terra a sua velocidade v 0 99c Determinar a o tempo de vida do mes o medido da Terra b a altitude a que se d a desintegra o 11 Qual a velocidade de um foguet o para que um observador que nele viaje envelhe a a uma taxa igual a metade da taxa de envelhecimento para um observador na Terra 12 Dois observadores O e O aproximam se um do outro com velocidade de 0 6c Se O registar que inicialmente a sua dist ncia a O igual a 20m calcular o tempo que decorrer at que os dois observadores se encontrem 44 13 Para um observador O dois acontecimentos s o simult neos e ocorrem separados espacialmente de 600 km Qual a diferen a de tempo entre estes dois acontecimen
4. o sobre a dilata o do tempo pode ser encontrada em http faraday physics utoronto ca PVB Harrison SpecRel Flash TimeDilation html Um bonito applet da universidade de Toronto sobre a contra o relativista dos espa os encontra se em http faraday physics utoronto ca PVB Harrison SpecRel Flash Contract Invisible html Em _ http faraday physics utoronto ca PVB Harrison SpecRel Flash Length Contract html ainda se pode encontrar uma simula o e explica o sobre a contrac o relativista dos espa os fazendo a experi ncia com muGes provenientes do espa o e revendo brevemente o fen meno da dilata o do tempo Sobre o paradoxo dos g meos encontra se uma simula o e explica o em _http faraday physics utoronto ca PVB Harrison SpecRel Flash TwinParadox html V rias simula es sobre as transforma es de Lorentz podem ser encontradas em http ankh morpork maths qmul ac uk saha teach lorentz Ainda sobre a teoria da Relatividade Restrita se encontram simula es sobre v rios temas em hitp math ucr edu home baez relativity html Anima es sobre o Efeito Doppler encontram se em http www walter fendt de ph11e dopplereff htm e http faraday physics utoronto ca PVB Harrison Flash Class Mechanics Doppler DopplerEffect html estando incluida neste ltimo endere o uma explica o matem tica da varia o da frequ ncia com a velocidade Em http galileo phys virginia edu classes 109N more stuff Applets nome html
5. 0 061 mm Se a intensidade do feixe incidente for Ip calcular a espessura do material necess ria para reduzir a intensidade do feixe pata I9 3 20 Dois tipos de radia o X de comprimentos de onda e Ap gt Ag com a mesma intensidade atravessam um material para o qual os coeficientes de absor o linear s o gu 0 3 mm e w 0 72 mm Verifica se que a radia o de comprimento de onda menor emergente do material tem intensidade dupla da outra radia o Calcular a espessura do material 21 Usando a conserva o de energia e da quantidade de movimento mostre que um electr o livre em repouso n o pode sofrer efeito fotoel ctrico isto n o pode absorver um fot o E se o electr o livre estiver em movimento 56 Fundamentos de Fisica Moderna Folha 6 Raios X Dualidade onda particula Particula numa caixa Principio de incerteza Decaimento radioactivo 1 Qual a diferen a de potencial que deve ser aplicada a uma ampola de raios X para que sejam emitidos raios X com um comprimento de onda m nimo de 30 pm 2 Electr es s o acelerados em tubos de televis o atrav s de uma diferen a de potencial de 10kV Calcular a frequ ncia mais alta das ondas electromagn ticas emitidas quando estes electr es embatem no ecr do tubo Que tipo de ondas s o estas 3 O ngulo de Bragg mais pequeno para o KCI 28 4 para raios X de A 0 30 nm Calcular a dist ncia entre os planos at micos no KCL 4 A d
6. Dudu nd vu a y a y b g a aw d i Jj 2 2 Se Ja 6 Li i 2 2 _ o AN co Ee 5 com onde a y representa o conjunto das medidas e o constante o erro nas medidas y 172 Anexo E Trabalhos pr ticos de demonstra o Apresentam se nas p ginas seguintes folhas de trabalhos pr ticos gui es e manual com instru es do equipamento a ser usado para os alunos poderem seguir as demonstra es que se far o nas aulas A maioria dos gui es apresentados foram coligidos por colegas do Departamento de F sica 1 Observa o de franjas de interfer ncia no interfer metro de Michelson 175 2 Experi ncia de Franck Her tz seesessseesseessecsseceeceeeccececeeeceseeeaeecseessaeeaeenes 186 3 Experi ncia de Rutherford eee eeeesessecsseceeeceeeeceeeceaeecaeecaeceaceeeeesaeesaeeeeeenee 199 173 174 Observa o de franjas de interfer ncia no interfer metro de Michelson Manual da Pasco incluindo gui o vass Instruction Manual and Ra es us Experiment Guide for the PASCO scientific Models OS 9255A thru OS 9258A PRECISION INTERFEROMETER 1990 PASCO scientific a 4 Or 0 e 10101 Foothills Bivd Roseville CA 95747 7100 waso rl screntific Phone 916 786 3800 FAX 916 786 8905 e www pasco com EZE 175 012 07137A Precision Interferometer Table of Contents Section Page Copyright Warranty and Equipment Return
7. adjusting the rotation of M as needed 16 Adjust the position of M so the beam strikes it ap proximately in the center Again a piece of paper in the beam path will make the beam easier to see 17 With a piece of paper still against the surface of M slide L back and forth along the Optics Bench to focus the beam to the smallest possible point on Mp 18 Adjust the two alignment screws on the back of Mj so the beam is reflected directly back to the center of Mo This step is best performed with two people one adjusting M and one watching the beam posi tion at My 19 Place the polarizers attached to either side of a single Component Holder between the laser and L Begin with the polarizers at right angles to each other than rotate one until the image in the micro scope is bright enough to view comfortably If you can t find the point image there are several things you can try e Vary the tilt of the beamsplitter slightly no more than a few degrees and turn the micrometer knob to vary the transverse position of the microscope until the image comes into view PA SC 85 Loosen the lock screw on the microscope As shown in Figure 13 remove the microscope and place a piece of tissue paper over the tube to locate the beam Ad just the beamsplitter angle and the micrometer knob to center the point image in the tube of the microscope e Slide the Measuring Microscope a centimeter or so in either directi
8. o da constante de Planck 115 6 Difracc o de Electre Soient tessestrnsss or seniasanes LEIA ser da dE NEL entvsentateneioes EKA EEES 129 7 Determina o dos espectros de emiss o de H e Hg 141 61 62 Espectroscopia de Mossbauer e o Paradoxo dos G meos Gui o 1 O efeito de M ssbauer O efeito de M ssbauer envolve a absor o ressonante de fot es emitidos sem recuo dos n cleos Como as larguras das riscas das transi es s o muito pequenas comparadas com as suas energias o processo de absor o ressonante muito sens vel a pequenas varia es na energia dos fot es A resolu o deste efeito tipicamente da ordem de 1 parte em 107 tornando o uma ferramenta poderosa na espectroscopia nuclear e f sica da mat ria condensada 2 Absor o ressonante Quando um fot o emitido numa transi o entre dois n veis de energia a frequ ncia do fot o tem uma largura natural da linha que resulta do tempo de vida finito do estado excitado Se este fot o incidir num sistema similar no estado fundamental prov vel que seja reabsorvido levando o sistema ao estado excitado este o significado de absor o ressonante de fot es Contudo numa transi o a energia n o toda transferida para o fot o Como a quantidade de movimento se conserva alguma da energia perdida do recuo do emissor Da mesma maneira quando o fot o absorvido o absorvente re
9. 2007 9 Einstein s 1934 two blackboard derivation of energy mass equivalence David Topper and Dwight Vincent Am J Phys 75 978 2007 10 How do two moving clocks fall out of sync A tale of trucks threads and twins Daniel F Styer Am J Phys 75 805 2007 11 Using ordinary multiplication to do relativistic velocity addition Alma Teao Wilson Am J Phys 75 799 2007 12 Real Time Relativity Exploratory learning of special relativity C M Savage A Searle and L McCalman Am J Phys 75 791 2007 13 From Newton to Einstein A forgotten relativistic optics of moving bodies Jean Eisenstaedt Am J Phys 75 741 2007 14 A simple derivation of the Lorentz transformation and of the accompanying velocity and acceleration changes J M L vy Am J Phys 75 615 2007 15 Does nature convert mass into energy Ralph Baierlein Am J Phys 75 320 2007 16 Modeling student thinking An example from special relativity Rachel E Scherr Am J Phys 75 272 2007 17 On the differential geometry of time like curves in Minkowski spacetime J B Formiga and C Romero Am J Phys 74 1012 2006 18 An intuitive approach to inertial forces and the centrifugal force paradox in general relativity Rickard M Jonsson Am J Phys 74 905 2006 19 Relativistic addition of parallel velocities from Lorentz contraction and time dilation Aleksandar Gjurchinovski Am J Phys 74 838 2006 20 A co
10. 5 fettos ai sendo os par metros a e b dados pelo sistema de equa es ver eqs 5 i 1 i i aae 0 Le Bwlatbei y 0 Dig dda ig 9 12 Bx 0 Ditiarbm w 0 ad B 55 SD SH 0 cuja solu o 1 Ei Yi t TiYi a ee ree DD 1 Ziyi 1 Ti Yi b KJ 2 2 2 2 2 1 Ti Ti E Da a Be 3 As somas s o sobre todos os pontos medidos A melhor forma de usar estas express es proventura come ar por calcular os v rios somat rios anotar o seu valor e s depois calcular os par metros 171 onde x yi representa o conjunto das medidas e o o erro na medida de y op dada pela matriz de Doar 13 A incerteza na determina o de cada um dos par metros a Fa eb covari ncia 1 x 2 3 242 EN a ay Ca Fa _ 4 Ox OX e x F gt EA 1 443 EA Ce 2 2 ey wi x Ta ba Oh baX X D AR FND Assim 2 1 x 2 1 1 1 xi Oa J 7 Th gt 3 Tab 3 Ne Sa Hr OK NG Os A boa pr tica tem mostrado que conveniente organizar as medidas numa tabela do tipo o 1 amp Ra 2 zy Y a a a a a 1 x E CA ERR DE SE SE dc 1 1 F 1 1 x y x z Dee ey Ve Vs a ISA oz oot e Ajuste a uma recta y x a bx sendo constantes os erros de medida Por vezes os valores medidos t m todos a mesma precis o Nesse caso o o constante ficando as express es anteriores mais simples Dl
11. 7 Additional information particularly advantageous because 8 Protection from rays 9 Experiment literature the diffracted image can be made 10 Technical data directly visible with the help of a 11 Equipment list fluorescent screen and 135 only one simple to operate test instrument is required compact The electron diffraction tube enables the de Broglie principle to be proved experimentally and with considerable accuracy as a basis for wave particle dualism applicable to electrons 2 DESCRIPTION AND MODE OF OPERATION The electron diffraction tube has a mounting to which the necessary power supply units and measuring equipment can be connected In the electron diffraction tube an electron beam is produced which can be controlled as it is dependent on external experimental parameters The electron diffraction tube beam emission system is shown schematically in Fig 2 Thermionic cathode K is heated by a heating coil H The electrons emitted from the cathode are accelerated in an electric field created by the grid system G to Gq Wehnelt cylinder G1 deflects a narrow electron bundle in the direction of the symmetrical axis optical axis The electrons from the Wehnelt cylinder are easily accelerated forward by Grid G2 which has a positive potential Then the electrons flying through the opening at Grid G are accelerated very vigorously because of the strong positive potential at the anode G3 Finally G
12. Beam mirror splitter Adjustable mirror 18mm FL Thumbscrews Micrometer knob Figure 6 Michelson Mode Setup Using the thumbscrews on the back of the adjustable mirror adjust the mirror s tilt until the two sets of dots on the viewing screen coincide The compensator is not needed for producing interfer ence fringes when using a laser light source However if you wish to use the compensator it mounts perpen dicular to the beam splitter as shown Attach the 18 mm FL lens to the magnetic backing of the component holder in front of the laser as shown and adjust its position until the diverging beam is cen tered on the beam splitter You should now see circu lar fringes on the viewing screen If not carefully ad just the tilt of the adjustable mirror until the fringes ap pear Ifyou have trouble obtaining fringes see Trouble Shooting at the end of this section Precision Interferometer 012 07137A Twyman Green Mode 1 Set up the interferometer in the Michelson mode as describedabove Remove the pointer from the rotational componet holder It is recommended to store the pointer washer and thumbscrew in the storage case Place the compo nent holder between the beam splitter and the movable mirror see Figure 7 It attaches magnetically Mount a second 18 mm FL lens L on its magnetic backing and position it Remove the original lens L from in front of the laser
13. The PASCO Thermal Radiation System includes three items the TD 8553 Radiation Sensor the TD 8554A Radiation Cube Leslie s Cube and the TD 8555 Stefan Boltzmann Lamp This manual contains operating instructions for each of these items plus instructions and worksheets for the following four experiments amp Introduction to Thermal Radiation Inverse Square Law Stefan Boltzmann Law at high temperatures Stefan Boltzmann Law at low temperatures The Stefan Boltzmann law states that the radiant energy per unit area is proportional to the fourth power of the temperature of the radiating surface In addition to the equipment in the radiation system several standard laboratory items such as power supplies and meters are needed for most experiments Check the experiment section of this manual for information on required equipment If you don t have all the items of the radiation system read through the operating instructions for the equip ment you do have then check the experiment section to determine which of the experiments you can per form A radiation sensor is required for all the experiments Radiation Sensor The PASCO TD 8553 Radiation Sensor Figure 1 measures the relative intensities of incident thermal radiation The sensing element a miniature thermo pile produces a voltage proportional to the intensity of the radiation The spectral response of the thermopile is essentially flat in the
14. To determine the exact ratio of the Degree Plate to the small Pinion post do the following to calibrate the Degree Plate Rotary Motion Let the post on top of the Pinion rest against the edge of the Degree Plate Sensor Figure 8 Degree Plate onto Base 150 PASC O scientific 012 06575A Educational Spectrophotometer 1 Remove the Light Sensor Arm from the Degree Plate by unscrewing the two small thumbscrews You can store the thumbscrews in the empty threaded holes on the Light Sensor Arm Turn the Degree Plate so the zero degree mark is exactly aligned with the index mark on the arm that extends from the Spectrophotometer Base 2 Start the ScienceWorkshop program See the ScienceWorkshop User s Guide for more information 3 In the ScienceWorkshop program select the Rotary Motion Sensor to be connected to Digital Channels 1 and 2 Set the resolution of the Rotary Motion Sensor to ais Expression for the Angular 1440 Divisions Rotation Position data from the Rotary 4 In the program use the built in Calculator to create a calculation Base the calculation on the Angular Motion Sensor 2n D Experim alculator Position measurement from the Rotary Motion aire e angPos 2 pi Sensor In the calculation divide Angular Posi tion by 27 where 7 is approximately 3 1416 NO
15. bench and the clamp thumbscrew Figure 15 Mounting Clamp onto Optics Bench Adjustable Angle the bench that is closest to the light source you are using To move the holder grasp the holder at the base and push in on the locking clip on one side of the holder Fig 16 Slide the holder along the center section of the bench while squeezing the clip Release the clip to lock the holder firmly in position Snap the Collimating Lens Holder into the Optics Bench between the Collimat ing Slits Holder and the Spectrophotometer Base Position the Collimating Lens Holder about 10 cm from the Collimating Slits Holder Positioning the Collimating Slits and Lens The focal length of the Collimating Lens is about 10 cm so the lens should be positioned about 10 cm from the slits Use the following procedure to position the lens more precisely Set up a light source so that light from the source passes through one of the slits on the Collimating Slits and then through the Collimating Lens Rotate the Light Sensor Arm so the Aperture Bracket and Light Sensor are out of the way and the beam of light can shine onto a distant vertical surface such as a wall Fig 17 Adjust the distance between the Collimating Slits and the Collimating Lens so that the beam of light is neither converging nor diverging i e light rays are parallel The beam of light should light source stay about the same wid
16. by Leybold Didactic GmbH 189 Printed in the Federal Republic of Germany Technical alterations reserved Name Partners Date Visual Quantum Mechanics The Next Generation Collision Excitation of Atoms Franck Hertz Experiment Goal Build inelastic and elastic energy models of collisions between electrons and gas molecules Use the Franck Hertz experiment to investigate atom and electron colli sions in Neon Build a model that describes the excitation of neon atoms and the energy lost by electrons during collisions Measure the excitation energies for neon and mercury Introduction The experiment you will do today was first performed using slightly different equipment by James Franck and Gustav Hertz in 1914 In 1925 Franck and Hertz received the Nobel Prize in physics for their work A Collisions Between Electrons and Atoms In the tutorial on the photoelectric effect we examined photons interacting with atoms ina metal In this tutorial we will look at electrons colliding with gas atoms We will bombard a gas with electrons whose kinetic energy can be varied The collisions between the elec trons and gas atoms can be either elastic or inelastic A 1 Predict the effects elastic and inelastic collisions would have on electrons gas atoms EEE State University 02001 Physics Education Research Group Kansas State University Visual Quantum Mechanics is supported by the National Science Foundation under
17. considerando que no referencial do n cleo a o electr o emitido na mesma direc o e sentido do movimento do n cleo b o electr o emitido na direc o perpendicular do movimento do n cleo 5 Uma part cula move se com velocidade de 0 8c fazendo um ngulo de 30 com o eixo x x no referencial O Qual a velocidade da part cula determinada por um segundo observador O movendo se com velocidade de 0 6c ao longo do mesmo eixo x x 6 Fazer o estudo do efeito Doppler para o som nas seguintes situa es a Fonte em movimento e receptor parado b Fonte parada e receptor em movimento c Fonte em movimento deslocando se com uma velocidade que faz um ngulo 6 com a direc o de propaga o da onda 7 Mostrar que a express o que traduz o efeito Doppler relativista 2 v tee c V Vo I cos 0 c Cont m quer o efeito Doppler longitudinal quer o efeito transversal 8 Obter a express o do efeito Doppler para a luz considerando apenas termos at v c quer para o caso em que a fonte ou o receptor se est a afastar com velocidade v quer para a situa o em que se est a aproximar 9 Determinar qual a varia o registada na frequ ncia de 20x10 Hz do radar da Pol cia de Tr nsito ao detectar um autom vel que circula a 150 km h 48 10 A velocidade de afastamento de uma estrela de 0 005c Calcular a varia o de comprimento de onda da risca D2 A 5890 A emitida pelos
18. foram realizadas com a colabora o de alguns colegas do Departamento de F sica a quem agradecemos vivamente 3 Avaliacao de conhecimentos A avalia o de conhecimentos far se por testes tradicionais com uma parte te rica e outra de problemas Apesar da brevidade do semestre propomos haver duas provas de frequ ncia envolvendo a primeira a Parte I da mat ria e a segunda frequ ncia as restantes partes da mat ria e uma prova de exame final para todos os alunos cobrindo toda a mat ria Os testes ter o um peso de 70 na nota final sendo que os restantes 30 ser o divididos entre o desempenho na resolu o de problemas os problemas que contam para a avalia o ser o resolvidos nas aulas pr ticas e na realiza o dos trabalhos pr ticos indicados A nota final ser a nota mais elevada obtida num dos conjuntos de provas para um aluno que realize os dois Na poca de recurso haver um exame semelhante ao exame final mas que contar 100 por neste caso poderem ser avaliados alunos que n o fizeram avalia o cont nua Os alunos de acordo com as disposi es vigentes podem ainda repetir exames para melhoria de classifica o dentro de um prazo estabelecido Nestes exames recurso e especiais haver quest es relacionadas directamente com os trabalhos pr ticos uma vez que os alunos ter o acesso aos protocolos das experi ncias via p gina da disciplina e aos laborat rios que estar o dispon veis para realiza
19. ii Introduchon asa shane yondiet st Suissa rina rene Mite aed 1 Equipment iss enteresse ii catolianass dose adb la osi a a dheenen does 2 Theory Of Operation sis ai n A NE R a e AE AE EE E sons 4 Michelson Twyman Green Fabry Perot Setupiand Operations ane eE E as E E E ei ce ane iba i 6 Tips on Using the Interferometer innaaeg 9 Sources of Error Troubleshooting Experiments Experiment 1 Introduction to Interferometry 00 0 0 eee 11 Experiment 2 The Index of Refraction of Air oo eee 13 Experiment 3 The Index of Refraction of Glass 15 Suggestions for Additional Experiments nie 17 Maintenance esrudasasparisisasanigratas fedora tin data nn ENEE SE EEEa E 18 Teacher s Guide 20 22 17 e i 176 Precision Interferometer 012 07137A Equipment The OS 9255A Precision Interferometer includes the following equipment 5 ke Base with built in micrometer Adjustable Mirror Movable Mirror Beam Splitter Compensator Plate 2 Component Holder e Viewing Screen Lens 18 mm Focal Length Diffuser Fitted Storage Case Additional Equipment Required Laser OS 9171 Laser Bench OS 9172 NOTE The preceding equipment includes everythingnecded for basic Michelson interferom etry You can produce clear fringes and make precise measurements of the wavelength of your source However to perform the experiments in this manual you will need additional components such as the OS
20. light emitted C 8 Determine the work function of the filament in this experiment C 9 Now that you have collected some data explain why the anode is set at a lower potential compared to the cathode 197 Appendix A Energy levels 21 5 Figure 2 Partial energy diagram of neon 198 Experi ncia de Rutherford Manual da Leybold Atomic and nuclear physics Gm 6 1 3 1 3 The structure of matter Rutherford scattering LE TBOLD MERAEUS Rutherford scattering Measuring the angle dependence N in Rutherford scattering Alpha particles of uniform energy are scattered onto a gold foil The dependence of the scattering rate N and the scattering angle is measured and is compared with Rutherford scattering formula If alpha particles meet on a gold foil they are deflected from their path scattering The majority of alpha particles are scattered by a scattering angleo of Jess than 1 A few particles have a substantially Jargero in the extreme case up to 180 back scattering These initially qualitative observations can only be explained by assuming that the gold atoms have a very smal nucleus containing practically the whole atomic mass and is positively charged On the basis of this idea Rutherford calculated the angular distribution N of the scattering rate This is the number N of a particles which is scattered in a time period of a determined interval do by an
21. o de 61 p 2 Represente graficamente em fun o de 1 p Utilize barras de erro e fa a o ajuste a uma recta utilizando o m todo dos m nimos desvios quadrados Interprete o valor do declive e compare com o valor esperado link para programa de ajuste a uma recta http mars fis uc pt jpinto simulacoes fit linear fit html Discuss o e Conclus es 1 Discuta os resultados obtidos e conclua se estes permitem verificar a rela o de de Broglie 2 Compare a ordem de grandeza dos valores de obtidos com a ordem de grandeza de dj e do Se se tratasse de um feixe de neutr es com uma energia da mesma ordem de grandeza 1 10 KeV esperaria observar a difrac o do feixe de neutr es na amostra de grafite Justifique Estime a ordem de grandeza da energia de um feixe de neutr es para que este seja difractado nos planos dos tomos da grafite 134 Difrac o de Electr es Manual da Phywe PHY WE Electron Diffraction Tube Operating Instructions with mounting 06721 00 CONTENTS 1 PURPOSE 1 Purpose With the electron diffraction tube the 2 Description and mode of operation corpuscular and wave characteristics of 3 Operation electrons can be demonstrated and 4 Diffraction of electrons on graphite studied In comparison with other 5 Electron optic representation of the experiments in the quantum physics of carrier mesh electrons the method of electron 6 Fault levels diffraction on a crystal grid proves
22. o electromagn tica e para part culas A hip tese de de Broglie 12 li o Velocidade de fase e velocidade de grupo de uma onda As experi ncias de Davisson Germer e de Thomson sobre a difrac o de electr es Interpreta o luz da hip tese de de Broglie sobre a natureza ondulat ria das part culas Part cula numa caixa a uma dimens o Fun o de onda e analogia com uma onda estacion ria numa corda Pacote de onda Quantiza o da energia Densidade de probabilidade EE Probabilidade e incerteza Difrac o por uma nica fenda Princ pio de incerteza de Heisenberg Incerteza na energia Interfer ncias em fenda dupla 14 13 li o O modelo at mico de Bohr N veis de energia de um tomo Transi es entre os n veis de energia O espectro do hidrg nio S ries de Lyman Balmer Pashen e Brackett A experi ncia de Franck Hertz Introdu o F sica Nuclear Detec o de radia es ionizantes O contador Proporcional O contador de Geiger O contador de cintila o Efeito das radia es ionizantes Taxa de exposi o Dose absorvida A experi ncia do Espalhamento de Rutherford A difus o de part culas alfa e a descoberta do n cleo 14 li o A f rmula de Rutherford Propriedades do n cleo A for a nuclear Estabilidade nuclear e radioactividade Leis do decaimento radioactivo per odo de decaimento constante de decaimento e vida m dia Actividade de uma fonte radioacti
23. o nos referiremos aqui contagens 8000 5800 5600 5400 5200 5000 4800 4600 4400 0 50 100 150 200 250 canais Um espectro de absor o de M ssbauer do Fe 6 M todo Na espectroscopia de M ssbauer de transmiss o uma amostra s lida exposta a um feixe de radia o gama e um detector mede a intensidade do feixe transmitido 65 atrav s da amostra Os tomos na fonte emissora de raios gama devem ser do mesmo is topo que os tomos na amostra absorvente Se os n cleos emissores e absorventes estiverem em ambientes qu micos id nticos as energias de transi o nucleares ser o exactamente iguais e a absor o ressonante ser observada com ambos os materiais em repouso A diferen a nos ambientes qu micos faz com que os n veis de energia nucleares se desloquem Apesar desses desvios de energia serem muito pequenos s vezes menores que um micro electr ovolt a extremamente estreita largura espectral dos raios gama para alguns nuclidos faz com que pequenos desvios na energia correspondam a largas varia es na absorv ncia Para conseguir resson ncia entre n cleos emissores e absorventes necess rio modificar ligeiramente a energia dos raios gama e na pr tica isto faz se sempre com o efeito Doppler A fonte acelerada numa zona de velocidades usando um motor linear para produzir o efeito Doppler e varrer a energia dos raios gama numa dada faixa Uma gama t pica de velocidades par
24. os alunos dividir se o em grupos de 2 ou 3 elementos e ao longo do semestre realizar o 4 ou 5 experi ncias consoante o n mero total de alunos inscritos na disciplina seguindo um protocolo que lhes fornecido No final ter o de elaborar um relat rio Os alunos poder o voltar ao laborat rio fora do per odo lectivo ap s a aula em que fizeram a experi ncia para a completar ou repetir at data indicada para entrega do relat rio Para avalia o conta o modo como o aluno est no laborat rio e o modo como foi elaborado o relat rio Uma das ltimas aulas ser reservada para discuss o e demonstra es dos trabalhos pr ticos O Departamento de F sica possui dois interfer metros de Michelson bem como um laborat rio de F sica Moderna com v rias experi ncias que podem ser realizadas Numa aula te rica ou te rico pr tica poder ser montada a experi ncia que demonstra a exist ncia do n cleo Espalhamento de Rutherford que por ser demorada propomos deixar a acumular contagens durante a aula e ir vendo os valores de tempos a tempos Propomos tamb m que o professor monte a experi ncia de Franck Hertz e o interfer metro de Michelson para observa o de franjas de interfer ncia e que estes trabalhos sejam de demonstra o uma vez que o n mero de alunos relativamente elevado A escolha dos trabalhos experimentais aqui apresentados assim como a elabora o dos gui es propostos como protocolo para os alunos
25. then continue turning it in the same direction while counting This will almost entirely eliminate er rors due to backlash in the micrometer movement The PASCO interferometer is not designed for large demonstrations However for small demonstrations you can use the 48 mm focal length lens included in the Interferometer Accessories to magnify the fringe pattern Backlash isa slight slippage that always occurs when and project it onto a wall or screen It is helpful to have a you reverse the direction of motion in a mechanical in powerful laserfor large projections strument Turning the micrometer dial clockwise moves the movable mirror toward the right Turning Using the Diffuser the dial counter clockwise moves the mirror toward the left The PASCO micrometer is designed to minimize backlash However by using the technique described above you can practically eliminate all effects ofback lash in your measurements It s sometimes more convenient to view the interference pattern through the diffuser rather than on the viewing screen Just place the diffuser where you would normally place the viewing screen and look through it toward the interferometer 4 Always take several readings and average them for greater accuracy 184 Precision Interferometer 012 07137A Sources of Experimental Error Backlash Although PASCO s carefully designed mirror movement reduces backlash considerably every mechanical system is s
26. 8 Invari ncia do intervalo entre dois acontecimentos 3 9 Diagramas espa o tempo 3 10 Adi o de velocidades segundo a Teoria da Relatividade 3 11 Dedu o das transforma es das velocidades 3 12 Dedu o das express es para o efeito Doppler relativista 4 Din mica Relativista 4 1 Necessidade de redefinir quantidade de movimento 4 2 A equa o fundamental da din mica relativista 4 3 A massa relativista 4 4 A rela o entre massa e energia a equa o E mc 4 5 Energia e quantidade de movimento de um corpo 4 6 Transforma es de Lorentz para a energia e a quantidade de movimento de um corpo 4 7 Transforma es de Lorentz para as componentes de uma for a 5 Introdu o Teoria da Relatividade Geral 5 1 O Princ pio da Equival ncia a curvatura do espa o 5 2 O deslocamento gravitacional para o vermelho Compara o entre previs es relativ sticas e testes no laborat rio utilizando a espectroscopia de M ssbauer 5 3 Buracos negros e raio de Schwarzchild Parte II Introdu o F sica Qu ntica 1 Radia o e radiadores 1 1 Espectros de emiss o e de absor o 1 2 Espectros de radia o t rmica 1 3 Absorvibilidade e emissividade o corpo negro ideal e o espelho ideal 2 Leis do corpo negro 2 1 Lei de Stefan Boltzmann e de Wien 2 2 Fun es de distribui o espectral de Wien e de Planck 2 3 A express o de Rayleigh Jeans 2 4 Dedu o da lei de
27. 85 3 2 14 4 keV 100 ns 1 2 0 26 FE 67 Mossbauer Spectroscopy Periodic Table isotope mass number E Transton energy kev Number of publicabors N gt 1000 100 lt N lt 1000 10 lt N lt 100 N lt t0 Siew RFA Mossbauer Effect Data Center rios rac 40212517 Emai medotuncaedu Wide wewancacdu mede 8 Desvio de Doppler de segunda ordem Quando um n cleo num cristal decai de um estado excitado para o seu estado fundamental por emiss o sem recuo o n cleo perde energia e a sua massa reduzida de 8M E c A quantidade de movimento fica inalterada Contudo a energia cin tica do tomo aumenta com a emiss o do raio gama H uma diminui o da energia do fot o emitido da mesma quantidade Essa diminui o igual a T pe 2 em que lt v gt a velocidade m dia quadr tica do n cleo na rede lt gt r denota a m dia t rmica c a velocidade da luz e E a energia transferida Assumindo que a energia cin tica metade da energia m dia do tomo de acordo com o modelo do s lido de Finstein em que 3hw 1 lt E gt We KT exp Em que wz a frequ ncia caracter stica do s lido Ent o 68 dey eet lt E gt 2 2 onde M a massa do tomo Mossbauer Assim o desvio de temperatura relativista dado por SE _1 lt E gt E 2Mc No limite cl ssico 0 E c 2 aT E Nees em que c o calor espec fico Pound e Rebka em 1960 mostraram que
28. Bel ndez Eur J Phys 24 No 5 497 2003 18 Student understanding of the wave nature of matter Diffraction and interference of particles Stamatis Vokos Peter S Shaffer Bradley S Ambrose and Lillian C McDermott Am J Phys 68 S42 2000 19 Note on group velocity and energy propagation Abraham Bers Am J Phys 68 482 2000 20 Student understanding of the wave nature of matter Diffraction and interference of particles Stamatis Vokos Peter S Shaffer Bradley S Ambrose and Lillian C McDermott Am J Phys 68 S42 2000 21 An investigation of student understanding of single slit diffraction and double slit interference Bradley S Ambrose Peter S Shaffer Richard N Steinberg and Lillian C McDermott Am J Phys 67 146 1999 23 Insights into students understanding of quantum physics visualizing quantum entities Azam Mashhadi and Brian Woolnough Eur J Phys 20 No 6 1999 511 24 Application of high purity germanium HPGe detector to advanced laboratory experiment on the Compton effec Seth A Hieronymus Loraine L Lundquist and David A Cornell Am J Phys 66 836 1998 25 Compton scattering on blackbody photons Lowell S Brown and Ronald S Steinke Am J Phys 65 304 1997 30 26 Development of a computer based tutorial on the photoelectric effect Richard N Steinberg Graham E Oberem and Lillian C McDermott Am J Phys 64 1370 1996 27 An undergraduate experiment on x ray spec
29. Experiment Calculator in ScienceWorkshop to create a calculation of the actual angular position of the Degree Plate If the small post on the top of the Pinion is in contact with the edge of the Degree Plate the Angular Position of the Rotary Motion Sensor must be divided by the ratio of the radius of the Degree Plate PASC z scientific 155 Educational Spectrophotometer 012 06575A and the radius of the small post on the Pinion Expression for the Angular Position Divide by 60 if the small The tioi imately 60 to 1 If the L of the Rotary Motion Sensor post of the Pinion is used or e ratio 18 approximately ol e larger put in the exact value of the diameter section at the bottom of the Pinion is ratio of radii used the Angular Position of the Rotary Motion Sensor must be divided by 15 Fig 22 NOTE The Experiment A Calculator for your version 5 Change the Graph display to show your calcula N Rem ew e ae of SoienceWorkshop may tion of Actual Angular Position on its horizontal EE cotoutatioa name differ in appearance Refer ia E Actual Angular Position to your User s Guide Short Name Units See Calibrating the Degree Plate earlier in the E lengre rea Set Up section for more information on measuring the ratio of the radius of the Degree Plate and the radius of the Pinion Figure 22 Create a Calculation General Information About the L
30. Guide to Spacetime An Introduction to Special Relativity Thomas A Moore Author and Mark M Payne Reviewer Am J Phys 64 668 1996 44 Derivation of relativistic force transformation equations from Lorentz force law Oleg D Jefimenko Am J Phys 64 618 1996 45 The twin paradox and the conventionality of simultaneity Talal A Debs and Michael L G Redhead Am J Phys 64 384 1996 46 Lorentz transformations directly from the speed of light Bernhard Rothenstein and George Eckstein Am J Phys 63 1150 1995 47 Special relativity and length contraction John R Graham Am J Phys 63 637 1995 48 An Equation that Changed the World Newton Einstein and the Theory of Relativity Harald Fritzsch and Hans Christian von Baeyer Am J Phys 63 573 1995 49 Relativistic mass increase at slow speeds Gerald Gabrielse Am J Phys 63 568 1995 50 Lorentz contraction A real change of shape Raymond A Sorensen Am J Phys 63 413 1995 51 Special relativity without clock synchronization B Rothenstein and S Balan Eur J Phys 16 No 1 31 1995 52 Special relativity and the Michelson Morley interferometer Reinhard A Schumacher Am J Phys 62 609 1994 53 On the derivation of the formula for relativistic momentum L Sartori Am J Phys 62 280 1994 54 Relativity Theory Versus the Lorentz Transformations A John Mallinckrodt Am J Phys 61 760 1993 28 55 Relativity Theo
31. If the spot you need to measure is significantly off center you can move it by adjusting the angle of the beamsplitter Enlongated spot with fringes Another common problem is a spot that is stretched with no easily discernible maxima Check first to make sure that this is the spot you need by blocking the beam path between the moving and fixed mirrors If it is then twist L slightly until the image coalesces into a single spot Actual spot Bright band Once the mirror begins to rotate it is safe to look into the microscope without the polarizers You will notice that your carefully aligned pattern has changed now the entire field is covered with a random interference pattern and there is a bright band down the center of the field Ignore the interference pattern there s nothing you can do about it anyway The band is the image of the laser when once each rotation the mirror reflects it into the microscope beamsplitter This is also unavoidable Your actual spot will probably be just to one side of the bright band You can check for it by blocking and unblocking the beam path between the rotating mirror and fixed mirror and watching to see what disappears If you aligned everything perfectly the spot will be hidden by the bright band in this case make sure that you have a spot when the rotating mirror is fixed and is reflecting the laser to the fixed mirror If you do have the correct spot under stationary co
32. against the front of the Light Source Rear Channel of Mercury Light Source housing 3 The Lens Grating Assembly mounts on the support bars of the Light Aperture Assembly Figure 7 Loosen the thumbscrew slip it over the bars and finger tighten the thumbscrew to hold it securely NOTE The grating is blazed to produce the brightest spectrum on one side only During your experiment you may need to turn the Lens Grating Assembly around in order to have the brightest spectrum on a convenient side of your lab table Figure 7 Lens Grating Mounting Detail 4 PAS UM scientific 120 012 04049J h e Apparatus and h e Apparatus Accessory Kit Tum on the Light Source and allow it to warm up for five minutes Check the alignment of the Light Source and the Aperture by looking at the light shining on the back of the Lens Grating assembly If necessary adjust the back plate of the Light Aperture Assembly by loos ening the two retaining screws Figure 8 and sliding the aperture plate left or right until the light shines di rectly on the center of the Lens Grating Assembly Kh Figure 8 Light Aperture Adjustment Insert the Coupling Bar assembly into the lower mounting groove of the Light Source Figure 5 Se cure in place by tightening the thumbscrew against the front of the Light Source housing Remove the screw from the end of the Support Base rod In
33. and reflected rays is just 20 2 0 A This time we label the point where the pulse strikes M as S If we define D as the distance between M and MR then the distance between S and can be calculated S S D 20 20 D 2 0 A0 26 2DAO EQ Figure 2a When M is at angle the Me laser beam is reflected to point S on M Figure 2b When M is at angle 0 the laser beam is reflected to point S on M 0 0440 Figure 2 a b The Reflection Point on M 78 In the next step in the derivation it is helpful to think of a single very quick pulse of light leaving the laser Sup pose M is rotating and this pulse of light strikes M when it is at angle 0 as in Figure 2a The pulse will then be reflected to point S on M However by the time the pulse returns to Mo M will have rotated to a new angle say angle 8 If M had not been rotating but had remained stationary this returning pulse of light would be refocused at point s Clearly since Mp is now in a different position the light pulse will be refocused at a different point We must now determine where that new point will be The situation is very much like that shown in Figure 2b with one important difference the beam of light that is returning to M is coming from point S on ML instead of from point S To make the situation simpler it is conve nient to remove the confusion of the rotating mirr
34. are dy 213 pm and do 123 pm 137 3 The electrons deflected at the graphite have a de Broglie wave length dependent on the anode voltage U3 as follows 7 gt Where U is the anode voltage accelera tion voltage or the potential to earth at Grid G3 Since the anode voltage should not exceed 12 kV the smallest de Broglie wavelength that can be achieved with the electron diffraction tube is Amin 11 2 pm This value is clearly smaller than the grid constants for the structure of graphite Thus there may be interfer ence on the diffraction rings of the individual wave packages Fige 4 In the experiment the additional electric power supply equipment is first of all adjusted to the initial setting The negative voltage at the Wehnelt cylinder Grid Gj is reduced until the strongest possible diffraction rings have formed 4 Fig 4 shows the diffraction image in an experimental example Both rings seen in the image comply with the Bragg definition i E e 1500 kV 2 dy 5 sin 8 255V m a Where GAN 2 represents the angles of diffract Yon of the electron beam dependent on anode voltage U see Fig 5 Ds pa Fig If the relationship between the angles of diffraction 6 and 69 and the anode voltage U is to be studied then the latter must be increased step by step say from Ua 2 kV up to U 12 kV and at the same time the voltage at the Wehnelt cy
35. average angleg The result of the calculation is the Rutherford s scattering formula Except for proportionality factors which are kept constant in our experiment it supplies us with the relationship for the angular dependence of the scattering rate N sin 1 This proportionality is verified in our experiment Because of the very low range of alpha particles in the air this experiment must be carried out in a vacuum Fig 1 shows the geometrical arrangement of the components of the scattering chamber Fig 2 shows the geometry of the experiment The alpha particles emitted from the Am 241 preparation fal through an aperture of 1 mm width onto the gold foil and leave this gold foil with various scattering angles The scattered alpha particles are identified with a detector By swinging the detector in steps of 5 foi example the scattering rate can be determined for al scattering angles from 5 to 60 With the setup we are going to use the detector is not swung but rather the preparation slit and gold foil which are attached on a common swivel arm The a detector is firmly attached to the side wall of the chamber Fig 1 The scattering chamber 1 Preparation 4 Gold foil 2 Holder 5 Arm to swivel end 3 Slit Fig 2 Scattering geometry with preparation collimator slit gold foil and detector D 199 11g 3 Experiment setup for Rutherford scattering e
36. cathode leaving it with a maximum energy of KE in the form of kinetic energy Normally the emitted electrons reach the anode of the tube and can be measured as a photoelectric current However by applying a reverse potential V between the anode and the cathode the photoelectric current can be stopped KE a can be determined by measuring the mini mum reverse potential needed to stop the photoelectrons and reduce the photoelectric current to zero Relating kinetic energy to stopping potential gives the equation Ve max Therefore using Einstein s equation hv Ve W When solved for V the equation becomes V hle v W Je If we plot V vs v for different frequencies of light the graph will look like Figure 2 The V intercept is equal to W e and the slope is A e Coupling our experimental de termination of the ratio h e with the accepted value for e 1 602 x 10 coulombs we can determine Planck s constant A Stopping Potential V Frequency v Figure 2 The graph of V vs v NOTE In experiments with the PASCO h e Ap paratus the stopping potential is measured directly rather than by monitoring the photoelectric current See the Theory of Operation in the Technical Infor mation section of the manual for details 012 04049J h e Apparatus and h e Apparatus Accessory Kit Equipment and Setup Equipment Required Digital voltmeter SE 9589 Filters h e Apparatu
37. de 9 V e Fios e garras crocodilos para liga es e Potenci metro 470 Q e Resist ncia 220 Q e Resist ncia 11 4 KQ e Dois mult metros e Rede de difrac o 1000 linhas mm montada num suporte DADOS Carga elementar e 1 602 x10 C Velocidade da luz no v cuo c 2 998 x10 m s Constante de Boltzmann kB 1 381 x10 J K PRECAUCOES 1 A corrente el ctrica que atravessa o LED n o dever exceder cerca de 50 mA pois este pode danificar se Para protec o do LED a resist ncia de 220 deve estar sempre ligada em s rie com o LED 2 Tenha em aten o as escalas na utiliza o segura dos mult metros como amper metros ou como volt metros A manipula o incorrecta do mult metro poder queimar o seu fus vel interno comprometendo o seu trabalho INFORMA O 1 O potenci metro tem 3 terminais e permite variar a tens o entre o terminal central e uma das extremidades desde 0 at ao valor m ximo fornecido pela pilha 2 S o fornecidos LEDs com as seguintes caracter sticas 110 Tabela 1 LED A nm Azul 470 Verde 2 Vermelho 630 Infravermelho 950 MEDIDAS E AN LISE A COMPORTAMENTO EL CTRICO DOS LEDS Pretende se determinar a curva caracter stica do LED verde ou seja a rela o entre a corrente que o atravessa e a tens o V aplicada aos seus terminais 1 Monte um circuito que permita alimentar o LED verde com uma tens o vari vel em polariza o directa de aco
38. de N equa es E II RS 2 i lI 0 0 5 e S S Este m todo aplic vel qualquer que seja a fun o Pode por m ser complicado resolver algebrica mente o sistemae de equa es sendo ent o prefer vel resolv lo numericamente para obter uma solu o aproximada y fx a b g fi a zo fo 02 X x figura 5 Entende se que o acordo entre as previs es da fun o e as medidas bom se tomando os valores de 4 42 n calculados no ajuste anterior a diferen a f y for em m dia igual imprecis o da medida o De tal facto vai resultar que o valor m nimo de x seja xo M 6 Isto o ajuste bom se o valor de x que se obt m com os par metros que resultam do ajuste x8 for pr ximo do n mero total de pontos medidos M Esta n o por m condi o suficiente devendo sempre analisar se criticamente o acordo entre a previs o dada pela fun o ajustada e os valores medidos Devemos tamb m avaliar o grau de incerteza com que determinado cada um dos par metros A incerteza na determina o do valor de a por ajuste aos dados decorre da incerteza desses mesmos N o analisaremos aqui o caso mais geral em que que se t m em conta as incertezas quer nas abcissas quer nas ordenadas 170 dados A uma varia o de a igual sua incerteza a aj Cap deve corresponder em m dia a varia o de x correspondente incerteza dos dados
39. ee nated E NE tae Ne 1 Measuring the Velocity of Light History 2 Galileo R mer Fizeau Foucault Th Foucault Method vices elit na Mie sine a aa i aed 3 A Qualitative Description A Quantitative Description Equipment ecos Sh ee Ss ia eng ss Bond tia ae ind ASS idas 6 Setup and Alienme nt sasien kaoa ataia tetaki 8 Alignment Summary ea AE a AA attendees 12 Alignment HiMen e a eaten 13 Makins the Measurement arescit 14 Notes on Accuracy and Maintenance scseceeseeeereeneeseseesensearsesessonees 16 PASC Ge i 74 012 07135B Speed of Light Introduction The velocity of light in free space is one of the most important and intriguing constants of nature Whether the light comes from a laser on a desk top or from a star that is hurtling away at fantastic speeds if you measure the velocity of the light you measure the same constant value In more precise terminology the velocity of light is independent of the relative velocities of the light source and the observer Furthermore as Einstein first presented in his Special Theory of Relativity the speed of light is critically important in some surprising ways In particular 1 The velocity of light establishes an upper limit to the velocity that may be imparted to any object 2 Objects moving near the velocity of light follow a set of physical laws drastically different not only from Newton s Laws but from the basic assumptions o
40. es de raios X inicial e difundido 14 Determinar o comprimento de onda final de um fot o cuja energia inicial de 12 MeV que sofre uma colis o de Compton e desviado de 90 por um prot o Para prot es mo C 938 3 MeV 15 Numa colis o de Compton detectam se o fot o e o electr o difundidos Determina se que o electr o tem uma energia cin tica de 75 keV e o fot o uma energia de 200 keV Determinar a o comprimento de onda inicial do fot o b os ngulos de difus o do electr o e do fot o 16 Um fot o de energia E hv hc A colide com um electr o estacion rio O fot o emitido na direc o 6 com energia E hc e o electr o emitido na direc o q Mostrar que h A A 1 cos 0 My C Each pe ni oe i E RRE ee AE Ai ia diin i a e gt lt g oe a 17 Um fot o de 0 0005A produz um par electr o positr o na vizinhan a de um n cleo pesado a Se as part culas tiverem as mesmas energias cin ticas determinar essas energias b Se o positr o tiver uma energia cin tica cinco vezes maior que a energia cin tica do electr o determinar a energia cin tica de cada part cula 55 18 Um electr o com velocidade de 0 8c aniquila se com um positr o em repouso produzindo dois fot es Um dos fot es emergentes observado a mover se na direc o perpendicular do electr o inicial Determinar a energia de cada fot o 19 O coeficiente de absor o de um material
41. geometry for Rutherford scattering S A Dodds and G S Mutchler Am J Phys 64 1295 1996 13 Understanding alpha decay Barry R Holstein Am J Phys 64 1061 1996 14 Specific activities of the elements M P Fewell Am J Phys 62 1043 1994 15 A plane wave approach to particle beam magnetic resonance R Golub R Gahler and T Keller Am J Phys 62 779 1994 16 Experimental verification of the Heisenberg uncertainty principle An advanced undergraduate laboratory P A DeYoung P L Jolivette and N Rouze Am J Phys 61 560 1993 17 The harmonic lattice recoilless transitions and the coherent state David S Bateman Subir K Bose Binayak Dutta Roy and Manoranjan Bhattacharyya Am J Phys 60 829 1992 18 A selective surface solar radiometer Jack Fendley and Michael Hutchins Am J Phys 52 550 1984 19 Population dose due to nucleon decay Carl V Gogolak and Kevin M Miller Am J Phys 52 251 1984 20 A home made pyranometer for solar experiments V Zanetti and A Zecca Am J Phys 51 633 1983 21 Optical and radiation pyrometry in the training laboratory of practical physics at the University Gesamthochschule of Kassel K J Euler R Kirchhof and O Ortelbach Eur J Phys 2 No 3 1981 133 22 Rutherford scattering in two dimensions G Barton Am J Phys 51 420 1983 23 Rutherford Bohr atom J L Heilbron Am J Phys 49 223 1981 24 Statistics of the detection proce
42. grant DUE 965288 Opinions expressed are those of the authors and not necessarily of the Foundation 190 Soon after Bohr presented his atomic model in 1913 Franck and Hertz devised an experi ment to demonstrate that e atoms can be excited by bombardment with electrons e the energy is transferred from the electrons to the atoms in discrete amounts and the amounts of energy transferred are consistent with spectroscopic results The apparatus Franck and Hertz used is shown schematically in Figure 1 In our experiment we will use neon as the gas instead of mercury but the process is the same Filament F Grid G Anode A o Hg atom electron g 1 5V Figure 1 Simplified circuit for the Franck Hertz experiment The original Franck Hertz tube contained droplets of mercury and was baked in an oven so that the mercury vaporized The hot filament F emits electrons thermionically that is the electrons boil off The grid G is at a positive potential with respect to the filament so the electrons are accelerated towards G and their kinetic energy increases The potential of G Vor can be varied A 2 Predict what would happen asV is increased A 3 Examine Figure 1 What is the potential of the anode with respect to the grid 191 A 4 Why do you think the experiment is set up in this way We don t expect a good answer at this stage we will revisit this question after you have collected some data using the app
43. materials that don t block thermal radiation For example do your clothes effectively block the thermal radiation emitted from your body Absorption and Transmission of Thermal Radiation Questions OD What do your results suggest about the phenomenon of heat loss through windows What do your results suggest about the Greenhouse Effect PASCO scientific 99 012 04695D Thermal Radiation System Experiment 2 Inverse Square Law EQUIPMENT NEEDED Radiation Sensor Stefan Boltzmann Lamp Millivoltmeter Power Supply 12 VDC 3 A meter stick Align axes of filament and Sensor Top View Power Supply 13 V MAX Millivoltmeter Meter Stick Align zero point of meter stick with center of filament Figure 2 1 Equipment Setup O Set up the equipment as shown in Figure 2 1 a Tape a meter stick to the table b Place the Stefan Boltzmann Lamp at one end of the meter stick as shown The zero point of the meter stick should align with the center of the lamp filament c Adjust the height of the Radiation Sensor so it is at the same level as the filament of the Stefan Boltzmann Lamp d Align the lamp and sensor so that as you slide the Sensor along the meter stick the axis of the lamp aligns as closely as possible with the axis of the Sensor e Connect the Sensor to the millivoltmeter and the lamp to the power supply as indicated in the figure With
44. meet at any point on the viewing screen therefore depends on the difference in the length of their optical paths in reaching that point Figure 2 Fringes By moving M the path length of one of the beams can be varied Since the beam traverses the path between M and the beam splitter twice moving M 1 4 wavelength nearer the beam splitter will reduce the optical path of that beam by 1 2 wavelength The interference pattern will change the radii of the maxima will be reduced so they now occupy the position of the former minima T M is moved an additional 1 4 wavelength closer to the beam splitter the radii of the maxima will again be reduced so maxima and minima trade positions but this new arrangement will be indistinguishable from the original pattern By slowly moving the mirror a measured distance d and counting m the number of times the fringe pattern is restored to its original state the wavelength of the light A can be calculated as Ifthe wavelength of the light is known the same proce dure can be used to measure d 180 Precision Interferometer NOTE Using the Compensator In Figure 1 notice that one beam passes through the glass of the beam splitter only once while the other beam passes through it three times If a highly co herent and monochromatic light source is used such as a laser this is no problem With other light sources this is a problem The difference in the effective path
45. modo correlacionadas ent o necess rio considerar essa correla o na incerteza de f havendo que considerar explicitamente esses produtos cruzados 169 e AJUSTE DE UMA FUN O PELO M TODO DOS DESVIOS M NIMOS QUADRADOS Seja um conjunto de pares de valores obtidos em medidas f x y que bem descrito pela fun o x m 02 onde ax s o par metros cujos valores pretendemos determinar a partir das medidas Fazem se por hip tese M medidas x y o com 1 M sendo o a incerteza de cada uma das medidas supomos que os valores de x n o t m incerteza ou que ela pode ser desprezada em rela o de y em cada ponto O problema de saber qual o melhor conjunto de valores dos par metros da fun o por forma a que ela descreva o melhor poss vel um conjunto de medidas d normalmente pelo nome de ajuste ou fit em ingl s O m todo mais comum consiste em considerar que a melhor estimativa dos par metros aquela que minimiza a discrep ncia entre os valores previstos pela fun o f r a1 02 e os respectivos valores medidos y 0 No m todo dos desvios m nimos quadrados essa discrep ncia formulada em termos da fun o x M Uai ar ao an yi j 2 2 x a1 d9 i Os melhores valores dos par metros s o aqueles que minimizam a fun o x Onde for o m nimo a fun o x tem derivada nula Por isso na pr tica trata se de resolver o sistema
46. o desvio de temperatura relativista ou desvio de Doppler de segunda ordem no Fe existe Boyle em 1960 mostrou que este Sn Eles verificaram a equa o anterior experimentalmente efeito existe no Simultaneamente a partir de outro ponto de vista Josephson tamb m em 1960 previu este efeito As vibra es dos tomos temperatura ambiente s o da ordem de 10 Hz Logo um ntcleo de Fe no seu estado excitado oscila antes de decair com a ae Ee KT velocidade m dia quadr tica durante este per odo m De acordo com a teoria especial da relatividade um rel gio movendo se com o n cleo mais lento relativamente a outro em repouso no laborat rio pela frac o v 2 Eca 1 Ee a PA y c O centro da energia de uma linha de emiss o de M ssbauer temperatura T tem um desvio negativo da ordem de _ KT 2 C lt P gt E E C O centro da energia de absor o desviado de modo id ntico Como j referido este efeito foi descoberto na experi ncia do desvio gravitacional para o vermelho de Pound e Rebka Eles tiveram especial aten o em manter a fonte e o absorvente mesma temperatura numa frac o de 1 de modo que a diferen a de temperatura n o mascarasse o desvio gravitacional O efeito da temperatura d uma 69 evid ncia clara do paradoxo dos g meos da teoria da relatividade especial e resolve a d vida de se as acelera es envolvidas nas viagens negam a dilata
47. o encontra se numa caixa de largura 0 10 nm que a ordem de grandeza das dimens es at micas Determinar as suas energias permitidas 14 Um prot o numa caixa unidimensional tem energia de 400keV no seu primeiro estado excitado Qual a largura da caixa 15 Uma medida determina a posi o de um prot o com uma precis o de 1 00 x10 m Calcular a incerteza na posi o do prot o passados 1s Considerar v lt lt C 16 Um tomo de hidrog nio tem 53x10 m de raio Estimar a energia m nima que um electr o pode ter neste tomo 17 A posi o e o momento linear de um electr o com energia de 1 00 keV s o determinadas simultaneamente Se a posi o tiver sido determinada com uma incerteza de 0 100 nm qual a percentagem de incerteza no momento linear 18 A actividade de uma amostra de um is topo radioactivo de 115 0 Bq imediatamente ap s a sua forma o na sequ ncia de reac es nucleares num 58 reactor nuclear Decorridas 2h15min verifica se que a actividade desta amostra 82 5 Bq Calcular a a constante de decaimento e o per odo de meia vida deste is topo b O n mero de n cleos radioactivos existentes na atmosfera no instante da sua forma o 19 Entre os produtos radioactivos que se escaparam num acidente nuclear 131 7 5 f Z E 137 encontrava se o 531 cujo per odo de meia vida 8 0 diase o 55Us para o qual o tip 30 anos Foram libertados 10 vezes mais tomos de i
48. para cada valor de determinado pelo valor de V haver diferentes an is para diferentes d Os dois an is de difrac o com raio menor e mais facilmente mensur veis correspondem difrac o de primeira ordem n 1 dos planos da grafite com valor de d mais elevado d e d2 Conhecidos os valores de di d2 e D se medirmos os raios r e r2 dos dois primeiros an is de interfer ncia obtemos duas medidas independentes para cada A d r De A dr D Figura 5 Dist ncias d entre planos de tomos na grafite 131 Sistema Experimental mo e Mito 10 kV G3 graphite its Ee na Biss 3 Oto 300 V Figura 6 Representa o esquem tica do sistema de emiss o focagem acelera o e projec o num alvo do feixe de electr es na ampola O sistema de emiss o e acelera o dos electr es no tubo est esquematizado na Figura 6 O c todo K aquecido atrav s da resist ncia H emitindo electr es Os electr es s o ent o acelerados por um campo el ctrico criado pelo sistema de grelhas G1 G4 O cilindro de Wehlnet G1 vai concentrar o feixe de electr es na direc o do eixo eixo ptico Este feixe ent o acelerado pela grelha G2 a qual est a um potencial positivo e seguidamente pela grelha G3 que est a um potencial ainda mais elevado Finalmente G4 usado para focar o feixe funcionando como uma lente electrost tica Na sua montagem G4 est fixo e igual a 250 V O feixe de electr
49. parte B 11 4 9 i lq B DETERMINACAO DO COMPRIMENTO DE ONDA DO LED VERDE 5 Ligue o LED verde pilha de 9V em s rie com a resist ncia de 220 Q Para determinar o comprimento de onda do LED verde coloque o tubo preto com a rede de difrac o a envolver o LED e verifique visualmente que ocorrem m ximos de intensidade de um lado e do outro da direc o frontal Utilize as folhas A3 para projectar o espectro de difrac o Me a a dist ncia h entre os dois m ximos de primeira ordem e a dist ncia entre a rede de difrac o e o alvo indicando as respectivas incertezas 112 220 Q E Determine a partir de h e 1 o ngulo 01 correspondente difrac o de primeira ordem Determine o comprimento de onda emitido pelo LED verde Apresente o resultado com a respectiva incerteza C DETERMINA O DA CONSTANTE DE PLANCK A 6 Utilizando os dados da tabela obtida em 4 parte A completada com a informa o obtida em B represente graficamente a tens o V em fun o da frequ ncia v da luz emitida pelos LED s Note que de W E E Vem eV hv k ou Polsk E 7 Determine a partir do gr fico o valor da constante de Planck e da respectiva incerteza Comente o resultado O valor tabelado desta constante obtida por m todos muito precisos h 6 626 x10 J s 113 114 Efeito fotoel ctrico e determina o da constante de Planck Manual de instru es da Pasco incluindo gui o
50. pela l mpada de hidrog nio Note que a luz da l mpada de hidrog nio muito menos intensa do que a de merc rio ou s dio Ter que ter mais cuidado com luz parasita e ter que escolher a amplifica o m xima no sensor de luz Seleccione fendas mais largas verifique a focagem e fa a v rios registos com diferentes larguras de fendas at decidir qual o melhor compromisso de intensidade versus resolu o 8 Determine os comprimentos de onda das linhas do hidrog nio Registe os dados e os resultados numa tabela 141 9 As linhas do hidrog nio na regi o do vis vel pertencem s rie de Balmer isto a transi es cujo estado final tem n mero qu ntico principal n 2 Use os comprimentos de onda obtidos para determinar i o n mero qu ntico n do estado inicial para cada linha ii o valor da constante de Rydberg 10 N o se esque a que qualquer resultado tem sempre uma incerteza associada As tabelas e resultados finais devem sempre incluir as incertezas nas medidas e nas grandezas calculadas a partir das medidas 142 Determina o dos espectros de emiss o de H e Hg Manual da Pasco Instruction Manual and o Experiment Guide for the PASCO scientific Model OS 8537 and OS 8539 EDUCATIONAL SPECTROPHOTOMETER ACCESSORY KIT AND EDUCATIONAL SPECTROPHOTOMETER SYSTEM 1998 PASCO scientific B f oy 4 6 10101 Foothills Blvd Roseville CA 95
51. ser encontrada em http Awww colorado edu physics 2000 quantumzone photoelectric html Ai atrav s de um ndice tamb m se encontra muita informa o sobre raios X Ainda sobre a explica o do efeito fotoel ctrico desde a sua descoberta por Hertz teoria de Einstein pode se consultar em http photoelectric effect search ipupdater com Da universidade da Virg nia temos o endere o http rockpile phys virginia edu 252 htm l que nos fornece apontamentos sobre F sica Moderna cobrindo grande parte da mat ria deste curso De um endere o on line http physics nist gov cuu Reference unitconversions html podem se fazer convers es de unidades de v rias grandezas f sicas Datas importantes de descobertas e teorias que fizeram a F sica Moderna podem encontrar se em http musr physics ubc ca jess p200 18 5 2 Applets Pode se visualizar a experi ncia de Michelson Morley no endere o http faraday physics utoronto ca PVB Harrison SpecRel Flash MichelsonMorley MichelsonMo rley html Em http www phy ntnu edu tw ntnujava viewtopic php t 70 pode se simular a rela o espa o tempo em teoria da relatividade e concluir que n o h simultaneidade absoluta Neste endere o pode se conseguir uma explica o detalhada deste conceito a partir dos postulados de Einstein Uma simula o da dilata o do tempo pode ser encontrada em http www walter fendt de ph1 1e timedilation htm Ainda uma explica o e simula
52. the Accessory Kit and Mercury Vapor Light Source 117 h e Apparatus and h e Apparatus Accessory Kit 012 04049J Planck s Quantum Theory By the late 1800 s many physicists thought they had ex plained all the main principles of the universe and discov ered all the natural laws But as scientists continued work ing inconsistencies that couldn t easily be explained be gan showing up in some areas of study Tn 1901 Planck published his law of radiation Tn it he stated that an oscillator or any similar physical system has a discrete set of possible energy values or levels en ergies between these values never occur Planck went on to state that the emission and absorption of radiation is associated with transitions or jumps be tween two energy levels The energy lost or gained by the oscillator is emitted or absorbed as a quantum of radiant energy the magnitude of which is expressed by the equa tion E hv where E equals the radiant energy v is the frequency of the radiation and A is a fundamental constant of nature The constant A became known as Planck s constant Planck s constant was found to have significance beyond relating the frequency and energy of light and became a cornerstone of the quantum mechanical view of the suba tomic world In 1918 Planck was awarded a Nobel prize for introducing the quantum theory of light The Photoelectric Effect In photoelectric emission light strikes a ma
53. the Grating Mount The threaded rod on the bottom of the Grating Mount has a lock washer and a wing nut Remove the lock washer and wing nut from the threaded rod and screw the threaded rod into the short threaded post in the center of the Degree Plate Do not screw the Grating Mount all the way down onto the Light Sensor Arm The Grating Mount must be slightly above the Light Sensor Arm so the Degree Plate can move Use the Light Sensor Arm to rotate the Degree Plate until the zero line on the Degree Plate is aligned with the index mark on the Spectrophotometer Base Turn the Grating Mount so it is aligned with the zero line on the Degree Plate and the label side of the Grating Mount faces away from the sensor on the Light Sensor Arm Put the lock washer and wing nut back onto the threaded rod and tighten the wing nut until the Grating Mount remains in place when the Degree Plate is rotated in either direction Fig 12 Mounting the Spectrophotometer Base on the Optics Bench Align the zero line on the Degree Plate with zero line Fasten the mount with the lock washer and wing nut Screw the mount into the threaded oo cd Grating Mount the index mark Line up the edge of the Grating Mount with the zero line lock washer wing nut Figure 12 Grating Mount onto Rotating Table You can mount the components of the Spectrophotometer on the 1 2 meter Optics Bench that is part of the OS 8515 Ba
54. the lamp OFF slide the sensor along the meter stick Record the reading of the millivolt meter at 10 cm intervals Record your values in Table 2 1 on the following page Average these values to determine the ambient level of thermal radiation You will need to subtract this average ambient value from your measurements with the lamp on in order to determine the contribution from the lamp alone Turn on the power supply to illuminate the lamp Set the voltage to approximately 10 V IZUEN 9 scientific 100 Thermal Radiation System 012 04695D IMPORTANT Do not let the voltage to the lamp exceed 13 V Adjust the distance between the Sensor and the lamp to each of the settings listed in Table 2 2 At each setting record the reading on the millivoltmeter gt IMPORTANT Make each reading quickly Between readings move the Sensor away from the lamp or place the reflective heat shield between the lamp and the Sensor so that the temperature of the Sensor stays relatively constant X Ambient Radiation Level A Rad 1 X Rad Ambient cm mV cm mV cm mV 10 2 5 20 3 0 30 40 3 5 50 4 0 60 45 70 5 0 80 100 7 0 Average Ambient 8 0 Radiation Level 9 0 Table 2 1 19 0 Ambient Radiation Level 12 0 14 0 16 0 18 0 20 0 25 0 30 0 35 0 40 0 45 0 50 0 60 0 70 0 80 0 90 0 Table 2 2 Radiation Level versus Distance 100 0 10 IZEN scien
55. the room tem perature Tm CalculateT for each value of T and record the values in the table Calculate Ts Tu for each value of T and record your results in the table On separate sheet of paper construct a graph of Rad versus TE tame Use Rad as the depen dent variable y axis Questions O What does your graph indicate about the Stefan Boltzmann law at low temperatures Q Is your graph a straight line Discuss any deviations that exist 18 PASCO scientific 107 108 Diodos emissores de luz LED e a constante de Planck Guiao OBJECTIVO Os objectivos desta experi ncia s o Determinar o comprimento de onda da luz emitida por um LED Determinar a constante de Planck INTRODU O Os d odos emissores de luz ou LED de Light Emitting Diode emitem luz quando s o percorridos por uma corrente el ctrica Esta emiss o de luz ocorre quando electr es transitam entre estados de diferentes energias ao passarem na jun o entre os dois tipos n e p do material semicondutor de que feito o d odo A diferen a de energia entre estes estados uma propriedade do material semicondutor Num d odo a passagem de corrente s significativa quando o d odo polarizado no sentido directo corrente el ctrica convencional do lado p para n e nestas condi es ocorre a emiss o de luz Na polariza o directa aplicada uma diferen a de potencial V e para que um electr o atravesse a jun o semicondu
56. the viewing screen Using the thumbscrews adjust the tilt of the adjustable mirror until there is only one bright dot on the screen Now mount the 18 mm FL lens on the front compo nent holder A clear sharp interference pattern should be visible on the viewing screen Ifyou use light with two component wavelengths instead of a laser two sets of fringes can be distinguished on the viewing screen Lens 18mm FL Adjustable mirror Movable mirror PRECISION INTERFEROMETER 7 Z Viewing screen Component holder Component holder Figure 8 Fabry Perot Mode Setup 012 07137A Precision Interferometer Tips on Using the Interferometer Accurate Fringe Counting 5 The slip ring at the base of the micrometer knob adjusts the tension in the dial Before making a measurement be sure the tension is adjusted to give you the best pos sible control over the mirror movement The following techniques can help you make accurate measurements 1 It s not necessary that your interference pattern be per f fectly symmetrical or sharp As long as you can clearly Calibrating the Micrometer distinguish the maxima and minima you can make ac For even more accurate measurements of the mirror curate measurements movement you can use a laser to calibrate the micrometer 2 Its casy to lose track when counting fringes The fol To do this set up the interfer
57. with Aperture Disk and Screen Focusing Lens Grating threaded post lock washer wing nut Quick Start 4 Degree Plate amp Light Sensor Arm Grating Mount Focusing Lens Light Sensor Mount and Light Sensor Educational Spectrophotometer Quick Start 012 06575A Step Five Put the Spectrophotometer Base onto one end of the Optics Bench Optics Bench T slot p square nut Quick Start 5 Put Base onto Optics Bench Step Six Mount the Collimating Slits and Collimating Lens onto the Optics Bench Set up a light source Adjust the Collimating Slits and Collimating Lens to collimate the light beam i Collimating light A Lens source Collimating light ray Slits path Quick Start 6 Setup for Collimation Step Seven Attach the Grating to the mount so the glass side of the Grating faces the light source glass side faces light source Quick Start 7 Attach the Grating CAUTION Avoid touching the Grating surface 146 Step Eight Set up the experiment in the Science Workshop program 1 Select the Light Sensor for Analog Channel A 2 Select the Rotary Motion Sensor for Digital Channels 1 and 2 3 Set the Rotary Motion Sensor to high resolution 1440 Divisions Rotation 4 Create a calculation for Actual Angular Posi tion based on the Angular Position data from the Rotary Mo
58. 0 6 When the thermistor resistance indicates that the temperature is about 12 C above room temperature turn the power down so the temperature is changing slowly Read and record R the ohmmeter reading and Rad the millivoltmeter reading The readings should be taken as nearly simultaneously as possible while briefly removing the heat shield Record these values in Table 4 1 PASC scientific 106 Thermal Radiation System 012 04695D IMPORTANT Make each reading quickly removing the heat shield only as long as it takes to make the measurement Take care that the position of the sensor with respect to the cube is the same for all measurements 6 Replace the heat shield and turn the cube power to 10 When the temperature has risen an additional 12 15 C repeat the measurements of step 5 Repeat this procedure at about 12 15 intervals until the maximum temperature of the cube is reached Data and Calculations Room Temperature R Q Tee SS K Table 4 1 Data Calculations R Rad T T T T To 4 mV CC K Ky K O Using the table on the base of the Thermal Radiation Cube determine To the temperature in degrees Centigrade corresponding to each of your thermistor resistance measurements For each value of T determine T the corresponding value in degrees Kelvin K C 273 Enter both sets of values in Table 4 1 above In the same manner determine
59. 009 2 Radioecology teaching response to a nuclear or radiological emergency R M Anjos Eur J Phys 27 No 2 243 2006 3 Bringing atomic and nuclear physics laboratory data into the classroom Eric B Norman Ruth Mary Larimer Gregory Rech Jeffrey Lee Chue Vue Tholoana Leubane Kenneth Zamvil and Laura Guthrie Am J Phys 72 652 2004 4 Radioecology teaching evaluation of the background radiation levels from areas with high concentrations of radionuclides in soil R M Anjos E Okuno P R S Gomes R Veiga L Estellita L Mangia D Uzeda T Soares A Facure J A P Brage B Mosquera C Carvalho and A M A Santos Eur J Phys 25 No 2 133 2004 5 Short solution of the radioactive decay chain equations Dobromir S Pressyanov Am J Phys 70 444 2002 6 Rutherford simple and multiple scattering by computer simulation J M Paniagua J M S nchez J Moreno A Jim nez and M Rufo Eur J Phys 22 No 2 157 2001 7 Rutherford Scientist Supreme John Campbell Am J Phys 68 873 2000 8 Alpha particle scattering in the Thomson and Rutherford atomic models Marco Zoli Eur J Phys 19 No 2 187 1998 9 The Mossbauer effect explained Guy Vandegrift and Brent Fultz Am J Phys 66 593 1998 10 Proton or prouton Rutherford and the depths of the atom Alfred Romer Am J Phys 65 707 1997 11 Flash of the Cathode Rays A History of J J Thomson s Electron Per F Dahl Eur J Phys 18 No 6 1997 33 12 A novel
60. 1 52 Photoelectric effect Back to basics R A Powell Am J Phys 46 1046 1978 53 Experiments on the photoelectric effect and on the diffusion of electrons in gases G McClellan E M Didwall and Cornel J Rigby Am J Phys 46 832 1978 54 Photoelectric effect revisited or an inexpensive device to determine h e Donald W Boys Mary E Cox and William Mykolajenko Am J Phys 46 133 1978 55 Demonstration of the photoelectric effect with a Geiger counter Harold Brower Am J Phys 44 305 1976 56 On Black Body Radiation and the Attractive Force between Two Metal Plates D J Mitchell B W Ninham and P Richmond Am J Phys 40 674 1972 57 Matter Waves Alan Holden Am J Phys 33 63 1965 58 Compton Effect an Experiment for the Advanced Laboratory A A Bartlett J H Wilson O W Lyle Jr C V Wells and J J Kraushaar Am J Phys 32 135 1964 59 The Scattering of X Rays as Particles A H Compton Am J Phys 29 817 1961 32 60 Introduction to Mechanics Matter and Waves Karl Ingard Am J Phys 29 721 1961 61 Crystals and X Rays Kathleen Lonsdale Am J Phys 18 325 1950 62 The Birth and Early Infancy of X Rays G E M Jauncey Am J Phys 13 362 1945 63 The Discovery of X Rays E C Watson Am J Phys 13 281 1945 Introdu o Fisica Nuclear 1 Rutherford scattering with radiation damping C E Aguiar and F A Barone Am J Phys 77 344 2
61. 1 Detec o de radia es ionizantes 1 1 O contador proporcional O contador Geiger e o contador de cintila o 1 2 Efeitos das radia es ionizantes 1 3 Dosimetria das radia es ionizantes 2 A difus o de particulas alfa e a descoberta do n cleo 2 1 A f rmula de Rutherford 2 2 Propriedades nucleares 2 3 A for a nuclear 10 3 Estabilidade nuclear e radioactividade 3 1 Leis do decaimento radioactivo per odo de deca mento constante de deca mento e vida m dia 3 2 Actividade de uma amostra radioactiva 3 3 Decaimentos alfa beta e gama 3 4 A quantidade de movimento do fot o e o recuo do n cleo na transi o gama o efeito de Mossbauer 3 5 Radioactividade natural 4 2 Sum rios da aulas te ricas 1 li o Apresenta o do programa da disciplina Bibliografia M todos de avalia o O que a F sica Moderna Revis o dos conceitos da Mec nica Cl ssica Referenciais de in rcia Eventos e coordenadas Transforma es de Galileu Invari ncia das leis de Newton quando sujeitas a uma transforma o de coordenadas de Galileu O Princ pio da Relatividade de Galileu 2 li o As ondas electromagn ticas e o ter Propriedades do hipot tico ter A experi ncia de Michelson Morley O interfer metro de Michelson Morley C lculo dos desvios esperados nas franjas de interfer ncia na experi ncia de Michelson Morley Tentativas de preservar o conceito de ter como refe
62. 11 1990 39 Evolution of the modern photon Richard Kidd James Ardini and Anatol Anton Am J Phys 57 27 1989 40 Improved student laboratory on the measurement of Planck s constant using the photoelectric effect J Dean Barnett and Harold T Stokes Am J Phys 56 86 1988 41 One dimensional Bohr atom I Richard Lapidus Am J Phys 56 92 1988 31 42 Some experiments on x ray fluorescence for the student laboratory Mahananda Dasgupta B K Sharma B L Ahuja and Farid M Mohammad Am J Phys 56 245 1988 43 Microphysical objects as potentiality waves C N Villars Eur J Phys 8 No 2 148 1987 44 On the de Broglie waves J Strnad and W Kuhn Eur J Phys 6 No 3 176 1985 45 On reflection and refraction of x rays by ideal mirrors and thin films Ping Lee Am J Phys 53 885 1985 46 Simple demonstration of Compton effect G F Bertsch and J A Nolen Am J Phys 52 183 1984 47 De Broglie s relativistic phase waves and wave groups Harvey R Brown and Roberto de A Martins Am J Phys 52 1130 1984 48 Electron diffraction by macroscopic objects G Anido and D J Miller Am J Phys 52 49 1984 49 The Compton effect a classical treatment J N Dodd Eur J Phys 4 No 4 205 1983 50 Rutherford Bohr atom J L Heilbron Am J Phys 49 223 1981 51 The measurement of Planck s constant using the visible photoelectric effect R G Keesing Eur J Phys 2 No 3 139 198
63. 52 mm L 48 mm Mp focal length focal length Leveling Laser Alignment Leveling Screw Screws Bench em 62 2 cm 82 0 cm 93 0 em Figure 5 Equipment Alignment 8 PASC CH 82 012 07135B Speed of Light __ Alignment Jigs _ Leveling Screws Use to aim the laser beam through the alignment jigs Figure 8 Using the Alignment Jigs to Align the Laser To Set up and Align the Equipment 1 Place the Optics Bench on a flat level surface 2 Place the Laser mounted on the Laser Alignment Bench end to end with the Optics Bench at the end corresponding to the 1 meter mark of the metric scale Use the Bench Couplers and the provided screws to connect the Optics Bench and the Laser Alignment Bench Details are shown in Figure 7 Do not yet tighten the screws holding the Bench Couplers Note that the leveling screws must be removed from the Optics Bench and from the Laser Align ment Bench to attach the Bench Couplers Two of the removed leveling screws are then inserted into the threaded holes in the Bench Couplers and are used for leveling Mount the Rotating Mirror Assembly on the opposite end of the bench Be sure the base of the assembly is flush against the fence of the Optics Bench and align the front edge of the base with the 17 cm mark on the metric scale of the Optics Bench see Figure 8 5 The laser must be aligned so the beam strikes the cen ter of the Rota
64. 747 7100 USA zu s C Phone 916 786 3800 FAX 916 786 8905 web www pasco com 143 012 06575A Educational Spectrophotometer Table of Contents PASC scientific Section Page Copyright Warranty and Equipment Return nenene ii Quick StA iiaeie eerde ee E e ea a ei a e PERA RE 1 Elio A LETONIO EIEEE EE T T 3 Description Set Up Mounting the Rotary Motion Sensor ecran 5 Mounting the Degree Plate and Light Sensor Arm 6 More Information About the Degree Plate wo ieee crete cnn 6 Mounting the Aperture Bracket Light Sensor Mount and Light Sensor 7 Mounting the Grating Mount 8 Mounting the Spectrophotometer Base on the Optics Bench 8 Rod Stand Mounting Clamps 00 00 ccc eee 8 Mounting the Collimating Slits and Lens 9 Positioning the Collimating Slits and Lens 9 Mounting the Grating 10 Mounting and Positioning the Focusing Lens icc ecceeeeeeeceeteeeeeneeees 10 Procedures Turing the Degree Plate ses mesmas a e EE E EE 11 Masking the Light Source or the Spectrophotometer ssssssssssesrerer eressero 11 Using the Science Workshop Program eee 11 General Information About the Light Sensor coe eee eet tenets 12 General Information About Slit Widths Scalining 4 Spec umn yes aciaeh Geass eee aati ahead Calibrating the Grating suonna Ses wek dod ian aut OtherInformation asia e ee Oe SD a eee 13 Activi
65. 8 8514 Laser Adapter Kit OS 9263A High Speed Rotating Mirror Assembly e Alignment Jigs 2 Part Number 648 02230 Fixed Mirror Measuring Microscope OS 9262 Basic Speed of Light Apparatus Ed Fixed Mirror OS 9263A High Speed Rotating Mirror Assembly Measuring Microscope OS 9103 One Meter Optics Bench SE 9367 0 5 mW He Ne Laser 5 Calibrated OS 9133 Lens 48 mm FL and Polarizers 2 08 9135 Lens 252 mm FL OS 8514 Laser Adapter Kit uu He du Alignment OS 9107 OS 9142 Optics Bench Jigs 2 Component Couplers Holders 3 Figure 4 Equipment Included with the OS 9261A Complete Speed of Light Apparatus 6 PASC CH 80 012 07135B Speed of Light About the Equipment 1 High Speed Rotating Mirror Assembly The High Speed Rotating Mirror comes with its own power supply and digital display The mirror is flat to within 1 4 wavelength It s supported by high speed ball bearings mounted in a protective housing and driven by a DC motor with a drive belt A plastic lock screw lets you hold the mirror in place during the alignment procedure An optical detector and the digital display provide measurements of mirror rotation to within 0 1 or 1 rev sec The display and the controls for mirror rotation are on the front panel of the power supply Rotation is reversible and the rate is continuously variable from 100 to 1 000 rev sec In addition holding down the MAX REV SEC butto
66. 81 3 123 40 2 47 87 022 28 30 976 52 12 479 76 5 569 3 100 2 702 7 124 403 0 148 83 124 29 29 756 53 12 043 77 5 395 6 101 2 626 6 125 366 9 149 79 422 30 28 590 54 11 625 78 5 228 1 102 2 553 0 126 331 9 150 75 903 31 27 475 55 11 223 79 5 066 6 103 2 481 7 127 72 560 32 26 409 56 10 837 80 4 910 7 104 2 412 6 128 69 380 33 25 390 57 10 467 81 4 760 3 105 2 345 8 129 2 IZIN scientific 012 04695D Thermal Radiation System Stefan Bolizmann Lamp IMPORTANT The voltage into the lamp should NEVER exceed 13 V Higher voltages will burn out the filament The TD 8555 Stefan Boltzmann Lamp Figure 3 is a high temperature source of thermal radiation The lamp can be used for high temperature investigations of the Stefan Boltzmann Law The high temperature simplifies the analysis because the fourth power of the ambient temperature is negligibly small compared to the fourth power of the high temperature of the lamp filament see Experiments 3 and 4 When properly oriented the filament also provides a good approxima tion to a point source of thermal radiation It therefore works well for investigations into the inverse square law By adjusting the power into the lamp 13 Volts max 2 A min 3 A max filament temperatures up to approxi mately 3 000 C can be obtained The filament temperature is determined by carefully measuring the voltage and current into the lamp The voltage divided by the current gives the resistance
67. 9 8 7 6 5 4 3 2 j 0 0 500 1000 1500 2000 2500 3000 3500 Temperature Kelvin 4 IZEN scientific 96 012 04695D Thermal Radiation System Experiment 1 Introduction to Thermal Radiation EQUIPMENT NEEDED Radiation Sensor Thermal Radiation Cube Window glass Millivoltmeter Ohmmeter NOTES O If lab time is short it s helpful to preheat the cube at a setting of 5 0 for 20 minutes before the laboratory period begins A very quick method is to preheat the cube at full power for 45 minutes then use a small fan to reduce the temperature quickly as you lower the power input Just be sure that equilibrium is attained with the fan off Part and 2 of this experiment can be performed simultaneously Make the measure ments in Part 2 while waiting for the Radiation Cube to reach thermal equilibrium at each of the settings in Part 1 When using the Radiation Sensor always shield it from the hot object except for the few seconds it takes to actually make the measurement This prevents heating of the thermo pile which will change the reference temperature and alter the reading Radiation Rates from Different Surfaces Part 1 OD Connect the Ohmmeter and Millivoltmeter as shown in Figure 1 1 Q Turn on the Thermal Radiation Cube and set the power switch to HIGH Keep an eye on the ohmmeter reading When it gets down to about 40 kQ reset the power switch to 5 0 If the cube is prehe
68. 9256A Interferometer Accessories or a comparable set of your own components The Precision Interferometer is available as acomplete system Please refer to your current PASCO catalog for details 177 Additional Equipment Recommended The OS 9256A Interferometer Accessories includes e Rotating Pointer Vacuum Cell Component Holder Lens 18 mm Focal Length Lens 48 mm Focal Length e Glass Plate e 2 Polarizer Vacuum Pump with Gauge NOTE The OS 9255A Fitted Case also provides storage for these accessory components About Your Light Source We strongly recommend a laser for most introductory applications A spectral light source can be used see the Appendix but that really comprises an experiment in and of itself for beginning students A laser source is easy to use and produces bright sharp fringes The OS 9171 Laser and OS 9172 Laser Alignment Bench are available from PASCO However any low power laser that operates in the visible range will work well Ifyou want to demonstrate the importance of polarization in interferometry a non polarized laser should be used For easy alignment the beam should be approximately 4 cm above the level of the bench top OS 9171 Laser y a OS 9172 LaserAlignment Bench 012 07137A Precision Interferometer Lens Adjustable jeri Mirror Viewing Screen Beam Splitter Diffuser 2 Compo
69. A AQ ss DFB Q3 The angle AO depends on the rotational velocity of M and on the time it takes the light pulse to travel back and forth between the mirrors and Mp a distance of 2D The equation for this relationship is R ag 2Do EQ4 where c is the speed of light and q is the rotational velocity of the mirror in radians per second 2D c is the time it takes the light pulse to travel from Mp to Mp and back Using equation 4 to replace AO in equation 3 gives _ 4AD o EOS DB EQS Equation 5 can be rearranged to provide our final equation for the speed of light _ _4AD o D B As EQS PASC Ci 79 where c the speed of light w the rotational velocity of the rotating mirror Mp A the distance between lens L and lens L minus the focal length of L B the distance between lens L and the rotating mir Tor Mp D the distance between the rotating mirror Mp and the fixed mirror M As the displacement of the image point as viewed through the microscope As s s where s is the position of the image point when the rotating mirror Mp is stationary and s is the position of the image point when the rotating mirror is rotating with angular velocity Equation 6 was derived on the assumption that the image point is the result of a single short pulse of light from the laser But looking back at equations 1 4 the displacc ment of the image point de
70. A varia o de o nos dados faz com que z Gy X eae decorre uma medida da incerteza com que ele determinado pelo ajuste Isto varie em m dia de uma unidade A correspondente varia o do par metro a que da 7 Esta a defini o mais geral da incerteza dos par metros de um ajuste Calculado o m nimo de x x ar Fax XO 1 obtidos os valores para os quais ocorre o m nimo varia se o valor de az at observar um incremento de uma unidade no x nesse ponto estamos em ay Oa A expans o de x em s rie de Taylor em torno do m nimo fica ox ik ox 2 2 x a1 a2 X9 T z Jax s darda ee 8 i gt Jaz lo 2 Jara o ay P onde 5 Es 0 Portanto em face do que acima se disse k 1 Ox l 9 2 darda ip RES 9 Fazendo ap io e Vkj Tapa podemos escrever a igualdade anterior na forma matricial como o produto de duas matrizes Dj ang Veg 1 Isto a V 1 ou V at 2 l 92 2x dada A matriz V conhecida como matriz de covari ncia sendo assim chamada porque os seus elementos 10 t m todas as vari ncias e co vari ncias dos par metros do ajuste i e explicitamente 2 2 2 2 ee Tay Tai az du X A Iaras X Eat Casa Cas 2 9X X 1 Ajuste a uma recta y x a bz sendo diferentes os erros em cada medida Se a fun o representar uma recta y f x a b a bx o ajuste tem solu o anal tica simples 2 Nesse caso x a b
71. Aperture Bracket has two main parts the Light Sensor Mount and the Holder The Holder and thumbscrew are not used and can be put aside An Aperture Disk and Aperture Screen are attached to the front of the Light Sensor Mount The Light Sensor Mount has two holes one hole in the center of the mount and a second hole at the rear of the mount The end of the Light Sensor Arm has three holes two holes along the centerline of the arm and one hole to the side of the centerline Line up the center hole of the Light Sensor Mount with the centerline hole in the Light Sensor Arm that is closest to the Degree Plate Line up the High Sensitivity Light Sensor so the threaded hole in its base is above the center hole of the Light Sensor Mount Use the threaded post included with the Aperture Bracket to fasten the High Sensitivity Light Sensor and Light Sensor Mount to the Light Sensor Arm Fig 11 Aperture Bracket Light Sensor Mount Light Sensor Arm threaded post Figure 11 Sensor and Aperture Bracket onto Light Sensor Arm High Sensitivity Light Sensor PAS CO 7 scientific 151 Educational Spectrophotometer 012 06575A Rotate the Aperture Disk on the front of the Light Sensor Mount so that the narrowest slit is in line with the opening to the sensor Connect one end of the DIN to DIN cable that is included with the High Sensitivity Light Sensor to the DIN connector on the end of the sensor Mounting
72. Boyer Am J Phys 74 742 2006 9 Experimental estimation of the luminosity of the Sun Salvador Gil Mariano Mayochi and Leonardo J Pellizza Am J Phys 74 728 2006 10 Photoelectric effect experiment with computer control and data acquisition Yaakov Kraftmakher Am J Phys 74 941 2006 29 11 Visualizing infrared phenomena with a webcam N A Gross M Hersek and A Bansil Am J Phys 73 988 2005 12 Measurements of K x ray fluorescence parameters A S Bennal P D Shidling N M Badiger S R Thontadarya and B Hanumaiah Am J Phys 73 883 2005 13 Bringing atomic and nuclear physics laboratory data into the classroom Eric B Norman Ruth Mary Larimer Gregory Rech Jeffrey Lee Chue Vue Tholoana Leubane Kenneth Zamvil and Laura Guthrie Am J Phys 72 652 2004 14 Observing the quantum behavior of light in an undergraduate laboratory J J Thorn M S Neel V W Donato G S Bergreen R E Davies and M Beck Am J Phys 72 1210 2004 15 Observing the quantum behavior of light in an undergraduate laboratory J J Thorn M S Neel V W Donato G S Bergreen R E Davies and M Beck Am J Phys 72 1210 2004 16 A novel empirical study of the photoelectric effect in thin gold films G D Earle B L Copp J H Klenzing and R L Bishop Am J Phys 71 766 2003 17 An analysis of the classical Doppler effect C Neipp A Hern ndez J J Rodes A Marquez T Bel ndez and A
73. Introduction Optics Bench for more information et Uh base s Collimating Rotary Motion 2 Ifthe light source has a large open Lens Sensor ing mask the opening so it trans Figure 1 2 Equipment Setup mits a narrow 0 5 to 1 0 cm beam to the Collimating Slits Put a cloth hood over the light source and attach the edge of the hood to the plate on the Collimating Slits 3 Turn on the light source Once it is warmed up adjust the light source Collimating Slits Collimating Lens and Focusing Lens so clear images of the central ray and the first order spectral lines appear on the Aperture Disk and Aperture Screen in front of the High Sensitivity Light Sensor Turn the Aperture Disk so the smallest slit on the disk is in line with the central ray 4 Connect the ScienceWorkshop interface to the computer turn on the interface Start Science Workshop 5 Connect the High Sensitivity Light Sensor cable to Analog Channel A Connect the Rotary Motion Sensor cable to Digital Channels 1 and 2 Experiment Setup Select the Sensors Set the Sample Rate and Create a Calculation Refer to the User s Guide for your version of ScienceWorkshop for detailed information on selecting sensors changing the sample rate and creating a calculation 1 Inthe ScienceWorkshop program select the Rotary Motion Sensor and connect it to Digital Channels 1 and 2 and select the Light Sensor and connect it to Analog Channel A 2 Inthe program set up the Rotary M
74. John Willey Publisher 1989 Pouco extenso na parte da Teoria da Relatividade Aprofunda com muito pormenor as partes da F sica Qu ntica a um n vel que pode ser tratado em cursos avan ados Jeremy I Pfeffer e Shlomo Nir Modern Physics An Introductory Text Imperial College Press 2000 Bom livro de consulta para a disciplina Embora nao aborde todos os temas escolhidos para a disciplina f lo com profundidade naqueles que trata Num cap tulo de Aplica es Seleccionadas tem o efeito de M ssbauer muito bem tratado de uma forma j um pouco avan ada para este n vel e com aplica o ao desvio gravitacional e buracos negros Michael Podesta Understanding the Properties of Matter University College London 1996 Livro com uma abordagem muito interessante e intuitiva no que diz respeito apresenta o de conceitos fundamentais da F sica Qu ntica sobretudo em temas de F sica do estado S lido Ray Skinner Relativity for Scientists and Engineers Dover Publications Inc New York 1982 24 Livro que embora nao se adeque a parte da Teoria da Relatividade da disciplina que apresentamos aconselhavel para consulta Lawrence S Lerner Modern Physics Jones and Barlett Publishers 1996 Livro interessante mas demasiado conciso e com uma abordagem que n o suficiente para os alunos alvo desta disciplina 6 3 Artigos sobre did tica da F sica Moderna Teoria da
75. Maria Benilde Faria de Oliveira e Costa Programa conte do e m todos de ensino da disciplina Fundamentos de F sica Moderna Relat rio apresentado Universidade de Coimbra no mbito das Provas de Agrega o em F sica Coimbra Abril 2011 INDICE 1 Intr du o eS cick sevcccssecestounzassdccntecus a Loctzans bosana haces ese osedoudcestenosteonansuastenedomseess 4 2 Estrutura da disciplina e metodologia erre 5 3 Avalia o de conhecimentos e rrerereeeeeeenerenearan a 7 4 Conte dos ua arena aa a a A a vce eda o NOR A E cette Ga CCR da 7 4 1 Programa da disciplina 2 0 ee eeeeeseceseceeeeceeeceeeceseecseecsaecsaeceaceseeesaeeeaeeeeeenee A 4 2 Sum rios das aulas te ricas e eeeseeseeeeessssssresresressessrssrsrresesssssresresrresessssresee 11 4 3 Sum rios das aulas te rico pr ticas errar 15 5 Aplica es inform ticas dispon veis na Internet 20 0 0 eeeeeeeeeeeeeeneeeeeeeneees 17 5 1 Apontamentos e problemas de disciplinas afins de outras universidades 17 Sa2 CADDICISS E N aan E E E EE AE E 19 6 Bibliografian aai e sha E E a cae E A EN E 21 6 1 Oo EE S EE A a ieatbens 21 6 2 Livros de consulta nrnna eene a e a i A A a coke es 23 6 3 Artigos sobre did tica da F sica Moderna eeseeeeeeeeseeeereseessrsreerrerrssrrsresreses 25 Anexo A Folhas de Exerc cios eeeeeereeeessessresresresressessrssrerresressessessrerresressse 37 Anexo B Folhas de Trabalhos
76. NOTE For some apparatus the stopping poten tial will temporarily read high and then drop down to the actual stopping potential voltage The Variable Transmission Filter consists of computer generated patterns of dots and lines that vary the intensity not the frequency of the incident light The relative trans mission percentages are 100 80 60 40 and 20 122 012 04049J h e Apparatus and h e Apparatus Accessory Kit Experiment 1 The Wave Model of light vs the Quantum Model According to the photon theory of light the maximum kinetic energy KE of photoelectrons depends only on the frequency of the incident light and is independent of the intensity Thus the higher the frequency of the light the greater its energy In contrast the classical wave model of light predicted that KE would depend on light inten sity In other words the brighter the light the greater its energy This lab investigates both of these assertions Part A selects two spectral lines from a mercury light source and investigates the maximum energy of the photoelectrons as a function of the intensity Part B selects different spectral lines and investigates the maximum energy of the photoelectrons as a function of the frequency of the light Setup Set up the equipment as shown in the diagram below Focus the light from the Mercury Vapor Light Source onto the slot in the white reflective mask on the h e Apparat
77. PASCO scientific Model TD 8553 8554A 8555 THERMAL RADIATION SYSTEM TD 8554A Radiation Cube Leslie s Cube TD 8555 STEFAN BOLTZMAN LAMP CAUTION 1 CAUTION HOT ON a E TD 8555 Stefan Boltzman Lamp TD 8553 Radiation Sensor 1988 PASCO scientific 5 00 BD A 0 o etter fz 10101 Foothills Blvd e Roseville CA 95747 7100 screntific Phone 916 786 3800 FAX 916 786 8905 www pasco com 91 012 04695D Thermal Radiation System Table of Contents SECTION o cacccacsssssscetseasenssesssinesscisevesassddessscisiconmssdcesssoiscsoeasadsecseniscsseesdssensend Page Copyright and Warranty Equipment Return ii Tntrod ct giiia a E id sh ae bed eli 1 Radiation SENSO ia ss 5s cass ara U MORNAS Lad dass ria sa dentes siga casais parana 1 Thermal Radiation Cube Leslie s Cube cccccccccccceseeseesceeeceeeeseeseeneeeeneees 2 Stefan Boltzmann AMPs eeke Aba eae a A anii 3 Experiments Experiment 1 Introduction to Thermal Radiation sseseeeseeeeeieeeeeeeeeeee 5 Experiment 2 Inverse Square Law ester 9 Experiment 3 Stefan Boltzmann Law high temperature 13 Experiment 4 Stefan Boltzmann Law low temperature 17 Teacher S QUIdE a tai RE Me oS oak E a i Secs a 19 Technical Support ecne ka iene keene ets Inside Back Cover PASC Ue i scientifre 92 012 04695D Thermal Radiation System Introduction
78. Planck os quanta de Planck 2 5 Algumas aplica es das leis do corpo negro o efeito estufa e estimativa da temperatura da Terra 3 A teoria qu ntica da radia o electromagn tica 3 1 A natureza ondulat ria da radia o electromagn tica 3 2 A natureza corpuscular da radia o electromagn tica O efeito fotoel ctrico leis experimentais do efeito fotoel ctrico a teoria de Einstein O fot o 3 3 O efeito de Compton para a radia o X Comprimento de onda de Compton 3 4 A produ o e aniquila o de pares electr o positr o O positr nio 3 5 Absor o de fot es 3 6 Produ o de raios X e suas caracter sticas Espectros de raios X caracter sticos 3 7 Electr es Auger 3 8 Fluoresc ncia de raios X 3 9 Difrac o de raios X por um cristal Lei de Bragg 4 Ondas de mat ria 4 1 A dualidade onda part cula para a radia o electromagn tica e para a mat ria 4 2 A hip tese de de Broglie 4 3 Velocidades de grupo e de fase de uma onda 4 4 Exper ncias de Davisson Germer e de Thomson 4 5 Leis da reflex o e refrac o 4 6 Princ pio de Huygens Fresnel Experi ncia de Young 4 7 Quantiza o da energia 4 8 Princ pio de incerteza de Heisenberg 5 O modelo at mico de Bohr 5 2 N veis de energia de um tomo 5 3 Transi es entre os diversos n veis 5 4 O espectro do Hidrog nio 5 5 Experi ncia de Franck Hertz Parte III Introdu o F sica Nuclear
79. Pr ticos eeeeeseseeeesesressessrssresresressessrssrerresresssse 61 Anexo C Instru es para a elabora o de um relat rio eseese 167 Anexo D Notas sobre An lise de Dados re 197 Anexo E Trabalhos Pr ticos de Demonstra o ooo eee eeeeeeseceseceesceeeceesseeeseeeseeeaes 173 1 Introdu o Iremos come ar por enquadrar a disciplina de Fundamentos de F sica Moderna no plano curricular Esta disciplina frequentada por alunos do 1 ano dos cursos de F sica e Engenharia F sica sendo uma disciplina do 2 semestre Anteriormente t m uma disciplina de F sica Geral I onde rev em os conceitos de Mec nica Cl ssica A prepara o f sica e matem tica dos alunos suficiente excepto no que respeita a temas como derivadas parciais e equa o de propaga o de ondas electromagn ticas A escolaridade de uma aula te rica por semana com dura o de duas horas e uma aula te rico pr tica semanal tamb m com dura o de duas horas A F sica uma ci ncia experimental que tem as suas origens nos m todos experimentais aplicados Mec nica por Galileo s c XVID At ao fim do s culo XIX enquadrava se fundamentalmente nas reas cl ssicas Mec nica Termodin mica ptica e Electromagnetismo e atingiu um auge na segunda metade do s culo XIX com as equa es de Maxwell Contudo por volta dos fins do s culo XIX foram descobertos v rios fen menos f sicos que abriram novas ideias para o de
80. Relatividade Restrita 1 Student experiences of virtual reality A case study in learning special relativity Dominic McGrath Margaret Wegener Timothy J McIntyre Craig Savage and Michael Williamson Am J Phys 78 862 2010 2 Einstein on mass and energy Eugene Hecht Am J Phys 77 799 2009 3 Experimental special relativity with a meter stick and a clock M Lund and U I Uggerhgj Am J Phys 77 757 2009 4 Illustrating some implications of the conservation laws in relativistic mechanics Timothy H Boyer Am J Phys 77 562 2009 5 Momentum energy change in elastic relativistic binary collisions V J Menon R K Dubey M Mishra and B K Patra Am J Phys 77 447 2009 6 Three vector and scalar field identities and uniqueness theorems in Euclidean and Minkowski spaces Dale A Woodside Am J Phys 77 438 2009 7 Mass versus relativistic and rest masses L B Okun Am J Phys 77 430 2009 5 Energy and momentum in special relativity Gregory S Adkins Am J Phys 76 1045 2008 6 Relativistic transformation of perpendicular velocity components from the constancy of the speed of light Ben Yu Kuang Hu Am J Phys 76 691 2008 7 A trip to the end of the universe and the twin paradox T M ller A King and D Adis Am J Phys 76 360 2008 25 8 On some applications of Galilean electrodynamics of moving bodies M de Montigny and G Rousseaux Am J Phys 75 984
81. TE The Experiment Calculator for your version of ScienceWorkshop may differ in appearance Refer Label your calculation Ratio of Radii Fig 9 a EO RR O RD i jour User s Guide Calculation Name 5 In the program select a Graph display and set it to Ta Ratio af Radii show the calculation Ratio of Radii on its E N label for the vertical axis calculation 6 Start recording data Turn the Degree Plate in one Figure 9 Calculation for Ratio of Radii direction slowly and continuously for exactly one complete rotation Stop recording data 7 In the Graph display use the built in Statistics tools to find the maximum value of the Ratio of Radii i e the maximum of y see Fig 10 This value is the exact ratio of the Degree Plate 0 1000 y 0 0000 x 49 1000 y 59 6639 e NOTE The Graph display in your version of ScienceWorkshop may differ in appearance Refer to your User s Guide radius to the small Pinion post radius Note This value should be close to 60 maximum y value Ratio o f Radii Time Record the actual ratio DEC Ratio of Radii Figure 10 Sample Degree Plate Calibration Data 8 Replace the Light Sensor Arm on the Degree Plate and fasten it to the plate with the two small thumbscrews Mounting the Aperture Bracket Light Sensor Mount and Light Sensor The
82. a o Fe por exemplo 10 mm s Imm s 48 075 neV No espectro resultante a intensidade dos raios gama representada em fun o da velocidade da fonte Para velocidades correspondentes aos n veis de energia ressonantes da amostra uma parte dos raios gama absorvida o que resulta numa queda da intensidade medida e num pico para baixo no espectro O n mero posi o e intensidade dos picos fornecem informa o sobre o ambiente qu mico dos n cleos absorventes e podem ser usados para caracterizar a amostra colimador detector amostra Esquema de um espectr metro em geometria de transmiss o 66 7 Escolha da fonte adequada A espectroscopia de Mossbauer limitada pela necessidade de uma fonte de raios gama adequada Habitualmente esta consiste num parente radioactivo que decai para o is topo desejado Por exemplo a fonte de Fe consiste em Co que decai por captura electr nica para um estado excitado do Fe o qual decai para o estado fundamental emitido o desejado raio gama Idealmente o is topo parente ter uma meia vida suficientemente longa para ser til mas tamb m ter de ter uma boa taxa de decaimento para se obter uma boa intensidade de radia o A energia do raio gama dever ser relativamente baixa para que o recuo n o seja grande porque isto faz com que a rela o sinal ru do seja m e sejam necess rios longos tempos de medida 57 57 Co 270d EC L 5 2 136 keV
83. age and observe changes in the neon tube As you increase the voltage you should see the neon begin to glow However the neon does not glow all the way through the tube The glow begins at a certain distance from the cathode B 1 Think about how the accelerating electrons gain energy and explain why the tube does not glow uniformly As you increase the accelerating voltage further you will see the glowing region increase Look carefully and you should be able to see a dark band in the middle of the glowing region B 2 Explain this observation in terms of the energies of the electrons and the neon gas Depending on the values of the various currents and voltages you may be able to see a second dark band Try it although it may be difficult to achieve B 3 Dial through the accelerating voltage and describe what happens to the current as you increase the voltage B 4 How are the changes in current related to the onset or changes in the light emitted by the neon gas 193 For the next part of the experiment set the power supply to the ramp option On the oscilloscope voltage is the horizontal axis while current is displayed vertically B 5 Sketch below what you see on the screen Be sure to include values for the current and voltage Adjust the accelerating voltage oven temperature and gain so you can see the maximum number of peaks B 6 Record the peak number for several different voltages in the table below Pea
84. alignment Fig 5 This prevents the a particies from losing too much energy after the scattering process by having too long a path in the gold foil Fig 6 Fig 5 Position of the preparation slit foil and detector during the measurement for large scattered angles In the shown example 60 202 If the 4 mm pin of the preparation is bent the preparation turns in a circle when it is pushed in and then it turns around its longitudinal axis a constant error of the angle can appear In this case it is necessary to displace the theoretical curve also parallel to the abscissa of the measuring diagram Fig 4 so that the curves f sin 4 e 2 and the measured points coincide Fig 6 The path of the a particles in the gold foil with a scattering around 60 without the movement of slit and foil shown in Fig
85. ance s characteristic pattern of absorption and transmission To set up the Spectrophotometer and cuvette for measuring an absorption spectrum do the following 1 Unscrew the threaded post that holds the Light Sensor and Light Sensor Mount onto the Light Sensor Arm cuvette High Sensitivity 2 Move the Light Sensor back so its threaded hole is lined up with Aperture Disk Light Sensor the rear centerline hole on the Light Sensor Mount Use the threaded post to reattach the Light Sensor and Light Sensor Mount to the Light Sensor Arm 3 Place the empty cuvette in front of the opening to the Light Sensor between the sensor and the backside of the Aperture Disk Make sure that the cuvette is turned so that the smooth sides are in line with the Light Sensor Fig 25 Light Si A ante teem threaded post 4 Scan the spectrum from an incandescent light source such as a bulb powered by a regulated DC power supply p 3 Ed Fi 25 tte with Light 5 Fill the cuvette with the liquid to be tested and then rescan the igure 25 Curve with Light Sensor spectrum of the incandescent light that is transmitted through the liquid Other Information The material on the front of the Aperture Disk may fluoresce under ultraviolet UV light It may produce a faint violet color when UV light shines on it This faint violet color might be seen on the Aperture Disk when you use a mercury light source for example T
86. and higher order spectra The higher order spectra are broader and less bright than the first order ay L spectra and may overlap N The Grating is blazed so one side of the spectrum is much brighter than the other Light Source Collimating Lens Collimating Slit Rotary Motion Sensor Diffraction Grating Grating Mount Light Sensor Arm Degree Plate Pinion High Sensitivity Light Sensor Figure 3 Spectrophotometer System Top View This part of the manual describes how to set up the Spectrophotometer System see Fig 3 Mounting the Rotary Motion Sensor This describes how to mount the Rotary Motion Sensor to the hinge on the side of the Spectrophotom eter Base The top of the Spectrophotometer Base has a short threaded post for centering the circular Degree Plate and for holding the Grating Mount It also has a magnetic pad for holding the Degree Plate and a magnetic pad Pinion hinge mef eb al large thumbscrew o small index thumbscrews threaded post Spectrophotometer Base Figure 4 Spectrophotometer Base Top View triangular shaped index marker One side of the base has a post upon which the Pinion can be stored when it is not in use The other side has a spring loaded hinge and two small thumbscrews for mounting the Rotary Motion Sensor included in the Spectrophotometer System On both sides of the base are
87. aratus B The Experiment Equipment An electron gun apparatus contained in a glass tube with neon a specialized power supply and an oscilloscope Hints In this experiment it is possible to boil off so many electrons that the current be comes too great for the electronics to handle You will see this happening if the line on the oscilloscope becomes flat at the top If this happens just turn down the heater The Gain setting on the upper left of the power supply amplifies the current You may need to adjust it to keep it from overwhelming the electronics In this experiment you can control the energy of the accelerated electrons by controlling the accelerating voltage dial marked U You can also measure the current through the tube As you increase the accelerating voltage you will see an increase in the current because the electrons are increasing their kinetic energy Thus more of them are passing through the wires each second However if the electrons lose energy the current will decrease The oscilloscope is measuring and plotting the accelerating voltage on the horizontal axis and the electron current on the vertical axis The power supply has a switch in the middle of the panel with two options illustrated and a The first allows you to manually adjust the voltage and the second automatically ramps through the voltage Select the manual option 192 Gradually increase the accelerating volt
88. arth has moved 76 farther away the light must now travel a longer distance to reach the astronomer The astronomer therefore sees an eclipse that lasts longer than the actual geometrical eclipse Similarly when the Earth is moving toward Jupiter the astronomer sees an eclipse that lasts a shorter interval of time From observations of these eclipses over many years R mer calculated the speed of light to be 2 1 x 10 m sec This value is approximately 1 3 too slow due to an inaccurate knowledge at that time of the distances involved Nevertheless R mer s method provided clear evidence that the velocity of light was not infinite and gave a reasonable estimate of its true value not bad for 1675 Fizeau The French scientist Fizeau in 1849 developed an ingenious method for measuring the speed of light over terrestrial distances He used a rapidly revolving cogwheel in front of a light source to deliver the light to a distant mirror in discrete pulses The mirror reflected these pulses back toward the cogwheel Depending on the position of the cogwheel when a pulse returned it would either block the pulse of light or pass it through to an observer Fizeau measured the rates of cogwheel rotation that allowed observation of the returning pulses for carefully measured distances between the cogwheel and the mirror Using this method Fizeau measured the speed of light to be 3 15 x 10 m sec This is within a few percent of th
89. ase In this case the combined field will always be a maximum and a bright spot will be seen At another point the light from the beams may be continually out of phase and a minima or dark spot will be seen Thomas Young was one of the first to design a method for producing such an interference pattern He allowed a single narrow beam of light to fall on two narrow closely spaced slits Opposite the slits he placed a viewing screen Where the light from the two slits struck the screen a regular pattern of dark and bright bands appeared When first performed Young s experiment offered important evidence for the wave nature of light Young s slits can be used as a simple interferometer If the spacing between the slits is known the spacing of the maxima and minima can be used to determine the wave length of the light Conversely if the wavelength of the light is known the spacing of the slits could be determined from the interference patterns 179 The Michelson Interferometer In 1881 78 years after Young introduced his two slit experiment A A Michelson designed and built an interfer ometerusinga similar principle Originally Michelson designed his interferometer as a means to test for the existence of the ether a hypothesized medium in which light propagated Due in part to his efforts the ether is no longer considered a viable hypothesis But beyond this Michelson interferometer has become a widely used instr
90. at absolute zero temperature it would produce a voltage directly proportional to the intensity of the radiation that strikes it How ever the detector is not at absolute zero temperature so it is also radiating thermal energy According to the Stefan Boltzmann law it radiates at a rate R tet a sT gt The voltage produced by the Wt sensor is proportional to the radia tion striking the detector minus the radiation leaving it Mathemati cally the sensor voltage is propor tional toR Rpa 7 Rie s T To As long as you are careful to shield the Radiation Sensor from the Radiation Cube when measure ments are not being taken T rf will be very close to room temperature TJ Ohmmeter Heat Shield reflective side toward cube Millivoltmeter Procedure Figure 4 1 Equipment Setup OD Set up the equipment as shown in Figure 4 1 The Radiation Sensor should be pointed directly at the center of one of the better radiating surfaces of the cube the black or white surface The face of the Sensor should be parallel with the surface of the cube and about 3 to 4 cm away Q With the Thermal Radiation Cube off measure Rw the resistance of the thermistor at room temperature Enter this data in the space on the following page Shield the sensor from the cube using the reflecting heat shield with the reflective side of the shield facing the cube 4 Turn on the Radiation Cube and set the power switch to 1
91. ated just set the switch to 5 0 When the cube reaches thermal equilibrium the ohmmeter reading will fluctuate around a relatively fixed value use the Radiation Sensor to measure the radiation emitted from each of the four surfaces of the cube Place the Sensor so that the posts on its end are in contact with the cube surface this ensures that the distance of the measurement is the same for all surfaces Record your measurements in the appropriate table on the following page Also measure and record the resistance of the ther mistor Use the table on the base of the cube to determine the corresponding temperature Millivoltmeter 4 Increase the power switch setting first to 6 5 then to 8 0 then to HIGH At each setting wait for the cube to reach thermal equilibrium then repeat the measurements of step 1 and record your results in the appropriate table Figure 1 1 Equipment Setup PASC O 5 scientific 97 Thermal Radiation System 012 04695D Part 2 Use the Radiation Sensor to examine the relative magnitudes of the radiation emitted from various objects around the room On a separate sheet of paper make a table summarizing your observations Make measurements that will help you to answer the questions listed below Absorption and Transmission of Thermal Radiation Place the Sensor approximately 5 cm from the black surface of the Radiation Cube and record the reading Place a pi
92. ation by switching the direction switch on the power supply to CCW Allow the mirror to come to a complete stop before reversing the direction Then repeat your measurement as in step 3 NOTES When the mirror is rotated at 1 000 rev sec or more the image point will widen in the direction of displacement Position the microscope cross hair in the center of the resulting image The micrometer on the Measuring Microscope is graduated in increments of 0 01 mm for the beam deflections PA SC 89 5 The following equation was derived earlier in the manual c 4AD o D B As When adjusted to fit the parameters just measured it becomes _ 8TAD Rev sec Rev sec D BYS ay i S cen Use this equation along with the diagram in Figure 15 to calculate c the speed of light To measure A measure the distance between L and L then subtract the focal length of L 48 mm gt NOTES This equation is the same as the original equation in step 5 but with two differences The rotational velocity is expressed in rad s The CCW rotational velocity is expressed as a negative number reflecting the direction of ro tation 44D 0 Oy DF BMS m S con 90 Radia o t rmica Manual de instru es da Pasco incluindo gui o 012 04695D 03 99 Includes Tectershoes Instruction Manual and ewerinenfesuts Experiment Guide for the
93. aw is perfectly true only for ideal black body radiation A black body is any object that absorbs all the radiation that strikes it Is the filament of the lamp a true black body What sources of thermal radiation other than the lamp filament might have influenced your measurements What affect would you expect these sources to have on your results a 45x 10 K Ta oom temperature K K C 273 R filament resistance at T_ ref ref Q Table 3 1 Data Calculations v Volts Amps mV R Ohms T K Tt K5 1 00 2 00 3 00 4 00 5 00 6 00 7 00 8 00 9 00 10 00 11 00 12 00 IZUEN scientific 105 012 04695D Thermal Radiation System Experiment 4 Stefan Bolizmann Law low temperature EQUIPMENT NEEDED Radiation Sensor Thermal Radiation Cube Millivoltmeter Ohmmeter Introduction In experiment 3 you investigated the Stefan Boltzmann Law R sT for the high temperatures attained by an incandescent filament At those high temperatures approxi mately 1 000 to 3 000 K the ambient temperature is small enough that it can be neglected in the analysis In this experiment you will investigate the Stefan Boltzmann relationship at much lower temperatures using the Thermal Radiation Cube At these lower temperatures the ambient temperature can not be ignored If the detector in the Radiation Sensor were operating
94. bindo o seu car cter ondulat rio ii verificar a rela o de de Broglie h p onde o comprimento de onda do feixe de electr es p a sua quantidade de movimento e h a constante de Planck Material ampola de difrac o de electr es fontes de alimenta o craveira Introdu o No interior do tubo de difrac o existe um filme de grafite constitu do por micro cristais cuja orienta o no espa o aleat ria O tubo cont m tamb m um c todo que emite electr es e grelhas de acelera o atrav s das quais aplicado um campo el ctrico Os electr es acelerados por uma diferen a de potencial V que varia num intervalo de cerca de 1 a 10 kV incidem na grafite atravessam na e s o depois projectados sobre um cran fluorescente Figura 1 Representa o esquem tica do tubo de difrac o de electr es G representa a amostra de grafite e o feixe de electr es e E o cran fluorescente Tratando se de part culas esperar se ia a forma o de uma mancha no ecr com a forma do filme de grafite Em seu lugar por m observa se um padr o de interfer ncia com an is circulares correspondentes a m ximos e m nimos tal como t pico de uma onda Os electr es comportam se afinal como ondas que se difractam nos planos de tomos de carbono que constituem a grafite O seu comprimento de onda pode ent o ser determinado se conhecermos a estrutura da grafite e se medirmos o di metro dos an is que se
95. bright than the spectral lines on the other side Figure 19 Position Focusing Lens P PASCA scientific 154 012 06575A Educational Spectrophotometer Grounding 1 If you use an AC powered spectral light source plug the power cord for the light source into a different outlet than the outlet used for your ScienceWorkshop interface and computer 2 Fora very dim light source you may need to use the 100 GAIN setting on the High Sensitivity Light Sensor and the 100x Sensitivity setting in the ScienceWorkshop program If so connect a wire from the Spectropho tometer Base to an earth ground in order to reduce electrical noise You can use one of the small thumb screws from the Light Sensor Arm to connect a ground wire not included to the threaded hole on the side of the Spectrophotometer Base opposite to the Rotary Motion Sensor Turning the Degree Plate The spring in the hinge on the Spectrophotometer Base is strong enough to keep the Pinion in contact with the edge of the Degree Plate as you move opaque cloth binder clips the Light Sensor Arm to turn the plate If the small diameter post on the Pinion slips rather than turns make sure that the thumbscrews that hold the Rotary Motion Sensor onto the hinge are tight You may need to loosen the screws and then push the Rotary Motion Sensor so it is as close to the Base as possible before re tightening the screws Masking the Light Source or the Spectrophot
96. button release it and observe approximately how much time is re quired to return to the recorded voltage 3 Move the Variable Transmission Filter so that the next section is directly in front of the incoming light Record the new DVM reading and approximate time to recharge after the discharge button has been pressed and released Repeat Step 3 until you have tested all five sections of the filter Repeat the procedure using a second color from the spectrum Color 1 Transmission Stopping Potential Approx Charge name Time 100 80 60 40 20 Color 2 Transmission Stopping Potential Approx Charge name Time 100 80 60 40 20 8 1 Ffeto 124 012 04049J h e Apparatus and h e Apparatus Accessory Kit Part B 1 You can easily see five colors in the mercury light spectrum Adjust the h e Apparatus so that only one of the yellow colored bands falls upon the opening of the mask of the photodiode Place the yellow colored filter over the White Reflective Mask on the h e Apparatus 2 Record the DVM voltage reading stopping potential in the table below 3 Repeat the process for each color in the spectrum Be sure to use the green filter when measur ing the green spectrum Analysis 1 Describe the effect that passing different amounts of the same colored light through the Vari able Transmission Filter has on the stopping potential and thus the maximum energy of the pho
97. ca em MeV e a quantidade de movimento do electr o para cada observador 51 7 Um mes o 2 mo 264 2 moe decai em apenas dois fot es e tem uma vida m dia de 2x10 s quando em repouso c Se um destes mes es fosse produzido num n cleo de um tomo que velocidade m nima deveria ter para sair do tomo durante uma vida m dia raio do tomo 10 m d Na situa o da al nea anterior e admitindo que o mes o e os dois fot es se propagam segundo o eixo x x calcular a energia dos dois fot es medida por dois observadores A e B colocados no eixo x x A est para a direita no eixo e B est para a esquerda 8 Um objecto de massa m 80 kg move se com velocidade igual a 90 da velocidade da luz a Calcular o valor da sua energia cin tica b Considerando que este objecto emite um fot o de comprimento de onda 50 nm segundo um ngulo igual a 0 relativamente a um observador em repouso determinar o valor do comprimento de onda medido pelo observador 52 Fundamentos de Fisica Moderna Folha 5 Radia o e interac o da radia o com a mat ria Qual a frequ ncia comprimento de onda e momento linear de um fot o cuja energia igual energia de repouso dum electr o Ege 511 keV Calcular o comprimento de onda a energia e o momento linear de um fot o de frequ ncia 106 Hz Qual a massa efectiva de um fot o de A 5000 A Uma esta o de r dio opera a uma frequ nc
98. cm 82 0 cm 93 0cm Screws Bench Leveling Screw Figure 14 Equipment Alignment 12 PASC CN 86 012 07135B Speed of Light CAUTION Do not look through the micro scope until the polarizers have been placed between the laser and the beamsplitter 6 Position M at the chosen distance from Mp 2 15 meters so the reflected image from MR strikes the center of Mp 7 Adjust the position of L to focus the beam to a point on My 8 Adjust M so the beam is reflected directly back onto Mp 9 Insert the polarizers between the laser and the beam splitter 10 Focus the microscope on the image point 11 Remove polarizers Alignment Hints Once you have the microscope focused it may still be difficult to obtain a good spot There may be several other lights visible in the microscope besides the spot reflected from the fixed mirror tray interference pattern Off center spot Stray spot The most common of these are stray interference patterns These are caused by multiple reflections from the surfaces of the lenses and may be ignored If necessary you may be able to eliminate them by angling the lenses 1 2 Stray Spots are most often caused by reflections off the window of the rotating mirror housing To determine which spot is the one you must measure block the beam path between the rotating mirror and the fixed mirror The relevant spot will disappear PA SC 87
99. creases to zero and the anode to cathode volt age stabilizes This final voltage between the anode and cathode is therefore the stopping potential of the photoelectrons To let you measure the stopping potential the anode is connected to a built in amplifier with an ultrahigh input impedance gt 10 Q and the output from this amplifier is connected to the output jacks on the front panel of the apparatus This high impedance unity gain Vout Vin 1 amplifier lets you measure the stopping potential with a digi tal voltmeter 128 Due to the ultra high input impedance once the capacitor has been charged from the photodiode current it takes a long time to discharge this potential through some leak age Therefore a shorting switch labeled PUSH TO Zero enables the user to quickly bleed off the charge However the op amp output will not stay at O volts after the switch is released since the op amp input is floating Due to variances in the assembly process each appara tus has a slightly different capacitance When the zero switch is released the internal capacitance along with the user s body capacitance coupled through the switch is enough to make the output volatge jump and or os cillate Once photoelectrons charge the anode the input voltage will stabilize Difrac o de electr es Gui o Objectivos ii Verificar que electr es com energias da ordem de 1 10 keV s o difractados por um filme de grafite exi
100. cua As distribui es das energias de emiss o e de absor o s o assim separadas pelo dobro da energia de recuo A probabilidade da absor o ressonante proporcional sobreposi o destas distribui es No caso das transi es at micas as energias de recuo s o pequenas comparadas com as larguras naturais das linhas H ent o uma grande probabilidade de absor es ressonantes nas transi es at micas No caso das transi es nucleares as 63 energias dos fot es s o muito maiores do que as energias de recuo e do que as larguras naturais das linhas Por isso h pouca ou nenhuma sobreposi o das transi es de energia Resulta da que a absor o ressonante n o muito prov vel para transi es nucleares 3 Emiss o sem recuo Quando se determina a energia de um n cleo que faz parte de um s lido a interac o com toda a estrutura da rede do s lido deve tamb m ser considerada Aumentando a massa efectiva do sistema que recua a energia de recuo diminui O n cleo transmite energia para a rede por excita o vibracional de estados atrav s da cria o de fon es Se n o for produzido nenhum fon o a mec nica qu ntica permite o ent o toda a energia da transi o vai para o fot o emitido isto que significa a emiss o sem recuo A frac o da emiss o a zero fon es dada pelo factor de Debye Waller fun o da temperatura de Debye da energias dos raios gama e das temperaturas do e
101. d earlier the small diameter post of the Pinion will make contact with the edge of the Degree Plate The shaft of the Rotary Motion Sensor will rotate approximately 60 times for every rotation of the Degree Plate or 360 One rotation of the Rotary Motion Sensor shaft represents approximately 6 of angular displacement of the Degree Plate The maximum resolution of the Rotary Motion Sensor is 1440 divisions per rotation Since one PASCO if scientific 157 Educational Spectrophotometer 012 06575A rotation is 6 the angular resolution is 6 divided by 1440 or one quarter of a minute 0 25 or fifteen seconds of arc This translates to a wavelength resolution of 2 nm given a grating line spacing of approximately 1666 nm for the Diffraction Grating included with the Spectrophotometer If the Rotary Motion Sensor is fastened to the upper set of holes on the hinge the larger diameter part of the Pinion will make contact with the edge of the Degree Plate The shaft of the sensor will rotate 15 times for every rotation of the Degree Plate The maximum angular resolution is one minute or sixty seconds of arc This trans lates to a wavelength resolution of 8 nm given a grating line spacing of approximately 1666 nm Cuvettes The Educational Spectrophotometer Accessory Kit includes two plastic cuvettes These flat sided containers can hold about five milliliters of liquid You can use the Spectrophotometer and a cuvette to measure a subst
102. da energia com a velocidade Din mica relativista 1 A energia de uma part cula o dobro da sua energia em repouso Calcular a sua velocidade 2 Calcular as raz es das massas de repouso de um electr o e de um prot o que partindo do repouso atravessam uma diferen a de potencial de 10 V Calcular as respectivas velocidades 3 Uma part cula tem energia cin tica de 65 MeV e momento linear de 335 MeV c Calcular a sua massa em repouso e a sua velocidade 4 A vida m dia dos mes es u em repouso 2 3x10 s e a massa de repouso 207 me Uma medida de laborat rio fornece nos um valor para a vida m dia desses mes es de 6 9x 10 s Considerando mec 0 511 MeV m 9 109x107 kg determinar a avelocidade dos mes es no laborat rio b a massa efectiva dos mes es quando se movem a velocidade determinada na al nea anterior c a sua energia cin tica d A sua quantidade de movimento 5 Uma part cula com velocidade de repouso mo que se move com velocidade 0 6c colide e fica unida a uma part cula id ntica inicialmente em repouso Qual a massa de repouso e velocidade da part cula composta 6 Um electr o est a ser estudado por um observador ligado ao laborat rio e por outro que se move velocidade de 0 5c relativamente ao laborat rio A velocidade do electr o em rela o ao laborat rio de 0 8c Considerando mo 9 109x10 kg Eo 0 511 MeV q 1 602x10 C calcular a energia cin ti
103. determine cube temperature Figure 2 Radiation Cube Leslie s Cube 94 Table 1 Resistance versus Temperature for the Thermal Radiation Cube Therm Temp Therm Temp Therm Temp Therm Temp Therm Temp Therm Temp Res O CC Res Q CO Res CO Rs CO Res CO Res CO 207 850 0 66 356 34 24 415 58 10 110 82 4 615 1 106 2 281 0 130 97 560 1 63 480 35 23 483 59 9 767 2 83 4 475 0 107 2 218 3 31 87 840 2 60 743 36 22 590 60 9 437 7 84 4 339 7 108 2 157 6 132 78 650 3 58 138 37 21 736 61 9 120 8 85 4 209 1 109 2 098 7 133 69 950 14 55 658 38 20 919 62 88160 86 4 082 9 110 2 041 7 134 61 730 5 53 297 39 20 136 63 8 522 7 87 3 961 1 111 9864 135 53 950 6 51 048 40 19 386 64 8 240 6 88 3 843 4 112 9328 136 46 580 Te 48 905 4 18 668 65 7 969 1 89 3 729 7 113 3880 9 137 39 610 8 46 863 42 17 980 66 7 707 7 90 3 619 8 114 7830 5 138 33 000 9 44 917 43 17 321 67 7 456 2 91 3 513 6 115 781 7 139 26 740 20 43 062 44 16 689 68 7 214 0 92 3 411 0 116 734 3 40 20 810 21 41 292 45 16 083 69 6 980 6 93 3 311 8 117 6884 141 15 190 22 39 605 46 15 502 70 6 755 9 94 3 215 8 118 643 9 142 09 850 23 37 995 47 14 945 A 6 539 4 95 3 123 0 119 600 6 143 04 800 24 36 458 48 14 410 72 6 330 8 96 3 033 3 120 558 7 144 00 000 25 34 991 49 13 897 73 6 129 8 97 2 946 5 121 5180 145 95 447 26 33 591 50 13 405 74 5 936 1 98 2 862 5 122 478 6 146 91 126 27 32 253 51 12 932 75 5 749 3 99 2 7
104. distance between M and Mp e the magnification of L which depends on the focal length of L and also on the distances be tween L L and Mye Each of these variables will show up in the final expres sion that we derive for the speed of light Speed of Light 012 07135B To begin the derivation consider a beam of light leaving the laser It follows the path described in the qualitative description above That is first the beam is focused to a point at s then reflected from Me to M and back to My The beam then returns through the beamsplitter and is refocused to a point at point s where it can be viewed through the microscope This beam of light is reflected from a particular point on M As the first step in the derivation we must determine how the point of reflection on M relates to the rotational angle of M Figure 2a shows the path of the beam of light from the laser to Mp when My is at an angle In this case the angle of incidence of the light path as it strikes M is also 8 and since the angle of incidence equals the angle of reflection the angle between the incident and reflected rays is just 20 As shown in the diagram the pulse of light strikes M at a point that we have labeled S Figure 2b shows the path of the pulse of light if it leaves the laser at a slightly later time when M is at an angle 6 0 AO The angle of incidence is now equal to 6 6 AO so that the angle between the incident
105. do do eixo x x com velocidade v 0 8c No instante t 1s parte de um ponto do eixo x x de coordenada 6x 10 km uma segunda nave B tamb m na direc o e sentido do mesmo eixo mas com velocidade v 0 2c a Determinar a velocidade da nave A medida pelo piloto da nave B depois de ambas terem partido b Calcular a velocidade de um observador O relativamente a O que determina que a partida das duas naves simult nea c Sabendo que as origens dos dois sistemas o sistema S e o sistema em que se encontra O cujo tempo pr prio coincidem para t t 0 determinar a posi o x da nave A em fun o de 3 Num dado sistema inercial S duas naves A e B s o enviadas a partir de um dado ponto O com a mesma velocidade em m dulo v 0 8c mas seguindo traject rias perpendiculares a Qual a velocidade de cada uma das naves relativamente outra b A nave tem 100m de comprimento e quando a parte da frente desta nave passa por um observador em S o piloto colocado nesse mesmo ponto envia um sinal luminoso em direc o retaguarda Que tempo leva o sinal luminosos a tingir a cauda da nave medido 1 pelo piloto ii pelo observador S 47 4 Um n cleo radioactivo que se desloca em rela o ao laborat rio com velocidade constante de grandeza 0 5c decai emitindo um electr o com velocidade 0 9c relativamente ao n cleo Calcular a velocidade desse electr o no referencial do laborat rio
106. dos s o demasiado extensos para serem dados num curso semestral Dividimos estes livros em duas sec es livros base e outros livros de consulta 6 1 Livros de base Arthur Beiser Concepts of Modern Physics McGraw Hill 6 edition 2003 Bom livro que cobre praticamente todos os assuntos da disciplina embora no que diz respeito parte de F sica Qu ntica f lo com pormenor mais extenso do que 21 poss vel leccionar numa disciplina do primeiro ano A parte da relatividade n o t o aprofundada como o que fazemos neste curso mas aborda assuntos modernos Este livro tem muitos exemplos de resolu o de exerc cios que ilustram os temas tratados Paul A Tippler e Ralph A Llewellyn F sica Moderna LTC 3 edi o 2006 Livro em portugu s bastante completo e moderno que aborda muitos temas por exemplo da Teoria da Relatividade tratados no R Resnick em sec es chamadas Explorat rias ou de Leitura Suplementar mas que fazem parte deste curso um livro muito esquem tico com Sum rio em cada cap tulo e Notas sobre acontecimentos referidos no tempo relacionados com os temas de cada cap tulo Efeito de Mossbauer claramente tratado de maneira muito acess vel numa sec o explorat ria do cap tulo de F sica Nuclear Robert Resnick Introduction to Special relativity John Willey Publisher 1968 Apesar de antigo consideramos o melhor livro de estudo
107. duzir a experi ncia para verifica o dessas conclus es O relat rio deve em consequ ncia seguir algumas regras b sicas que permitam a sua elabora o com clareza A estrutura do relat rio a apresentar dever ser a seguinte e Cabe alho T tulo nomes dos autores e data da realiza o da experi ncia e Sum rio Descri o muito sucinta do trabalho Deve indicar os objectivos que se pretendem alcan ar o m todo seguido para os atingir e os resultados obtidos N o deve ocupar mais do que 4 ou 5 linhas e Introdu o Desenvolvimento simples da teoria subjacente ao trabalho Deve indicar as equa es e os princ pios f sicos em que se baseia a experi ncia mas n o necess rio deduzir as equa es apresentadas N o deve ser simplesmente copiada do protocolo e M todo Experimental Descri o do m todo e material utilizado Sempre que poss vel incluir um esquema da montagem utilizada com uma legenda elucidativa e Resultados Devem ser apresentados os dados obtidos os c lculos efectuados com incertezas e o resultado final obtido Devem ser inclu das tabelas e figuras todas com legenda com os resultados obtidos e Discuss o e conclus es Esta a parte mais importante do relat rio aqui que se devem apresentar as vossas pr prias conclus es acerca do trabalho realizado e dos objectivos alcan ados ou n o bem como a discuss o do m todo comentando os resultados com valores conhecidos se for poss v
108. e currently accepted value Foucault Foucault improved Fizeaw s method using a rotating mirror instead of a rotating cogwheel Since this is the method you will use in this experiment the details will be discussed in considerable detail in the next section As mentioned Michelson used Foucault s method to produce some remarkably accurate measurements of the velocity of light The best of these measurements gave a velocity of 2 99774 x 108 m sec This may be compared to the presently accepted value of 2 99792458 x 10 misec I PASC ON 012 07135B Speed of Light The Foucault Method Me Fixed Mirror Beamsplitter Rotating Mirror Laser Measuring Microscope Figure 1 Diagram of the Foucault Method A Qualitative Description In this experiment you will use a method for measuring the speed of light that is basically the same as that developed by Foucault in 1862 A diagram of the experi mental setup is shown in Figure 1 above With all the equipment properly aligned and with the rotating mirror stationary the optical path is as follows The parallel beam of light from the laser is focused to a point image at point s by lens L Lens L is positioned so that the image point at s is reflected from the rotating mirror M and is focused onto the fixed spherical mirror M M reflects the light back along the same path to again focus the image a
109. e agora que colocada uma folha de alum nio muito fina de emissividade igual a 0 1 entre as duas superf cies Considere que atingido o estado estacion rio ficando ambas as faces da folha de alum nio mesma temperatura b Qual a temperatura a que se encontra a folha de alum nio c Qual agora a taxa de perda de calor da superf cie mais quente 10 O potencial de corte para fotoelectr es emitidos de uma superf cie por luz de 4910 0 71V Qual o comprimento de onda da radia o incidente quando se encontra para este potencial um valor de 1 43V 11 Luz de comprimento de onda 2000 incide numa placa de alum nio No alum nio s o necess rios 4 2 eV para retirar um electr o a Qual a energia cin tica do fotoelectr o emitido mais r pido E a do fotoelectr o emitido mais lento b Qual o potencial de paragem c Qual o comprimento de onda limite para o alum nio d Se a intensidade da luz incidente for de 2 Wim qual o n mero m dio de fot es por unidade de tempo e por unidade de rea que atinge a superf cie 12 Se a fun o trabalho do pot ssio for 2 21 eV quando iluminado por luz ultravioleta de 2500 qual a energia cin tica m xima dos fotoelectr es emitidos 54 13 Um electr o que sofre uma colis o frontal com um fot o de raios X tem um potencial de paragem de 70kV Se o electr o estava inicialmente em repouso quais s o os comprimentos de onda dos fot
110. e corresponding gap or line in the first order on the other side of the central ray 3 Determine the difference between the angles and use one half of the difference as the angle 8 to determine the wavelength of that gap or dark line If you did not calibrate the Diffraction Grating assume d 1666 nm A dsin6 4 Repeat the process for the other gaps if any in the first order spectral pattern PASCO r scientific 165 Educational Spectrophotometer 012 06575A Data Table Record your data here Dark Line 9 8 AO 0 49 2 A dsin6 Questions 1 What color corresponds to the wavelength for each dark line in your absorption spectrum 2 How does the color or colors that are absorbed out of the continuous spectrum compare to the naked eye color of your liquid sample Extensions Repeat the process for a different liquid sample such as chlorophyll extracted from a spinach leaf 22 IPASCQ scientific 166 Anexo C Instru es para a elabora o de um relat rio Esta forma de apresentar um relat rio n o deve ser entendida como nica mas sim como um guia geral de elabora o de um relat rio e dever ser a seguida nesta disciplina A redac o do relat rio deve permitir a qualquer pessoa n o sendo da rea entender a finalidade o objectivo do trabalho o que foi feito e como foi executado de maneira a entender os resultados obtidos e as conclus es decorrentes O leitor deve poder repro
111. e n o aprofunda muito certos temas visto os alunos serem apenas do primeiro ano Ser feita uma ponte entre a F sica Cl ssica e a Moderna e as ferramentas necess rias para o estudo dos temas propostos ser o fornecidas sempre que se verifique que os alunos ainda n o as possuam Os alunos de Engenharia F sica n o ter o mais nenhuma disciplina onde abordem a Teoria da Relatividade Por esta raz o d se um peso maior Relatividade no programa da disciplina 2 Estrutura da disciplina e metodologia Como j dissemos a disciplina de Fundamentos de F sica Moderna est enquadrada no 2 semestre do 1 ano dos cursos de F sica e Engenharia F sica Segundo a Ficha de Unidade Curricular a escolaridade de uma aula te rica por semana com dura o de duas horas e uma aula te rico pr tica semanal tamb m com dura o de duas horas tendo 4 5 cr ditos ECTS Embora o semestre tenha uma dura o oficial de 15 semanas a ocorr ncia de feriados e toler ncias de ponto fazem com que o n mero de aulas te ricas e de te rico pr ticas seja em m dia de 14 aulas cada uma As aulas te ricas ser o expositivas e as dedu es feitas no quadro negro por considerarmos que assim a interac o com os alunos maior O recurso a acetatos ou informa o em Powerpoint ser feito no caso de apresenta o de figuras gr ficos ou tabelas Este recurso a um ensino mais tradicional o reflexo de considerarmos que embora a expos
112. ece of window glass between the Sensor and the bulb Does window glass effectively block thermal radiation Remove the lid from the Radiation Cube or use the Stefan Boltzmann Lamp and repeat the measurements of step 1 but using the bare bulb instead of the black surface Repeat with other materials Radiation Rates from Different Surfaces Data and Calculations Power Setting 5 0 Power Setting 6 5 Power Setting 8 0 Power Setting 10 0 Therm Res Q Therm Res Q Therm Res Q Therm Res Q Temperature C Temperature C Temperature ne Temperature Ke Sensor Sensor Sensor Sensor Surface Reading Surface Reading Surface Reading Surface Reading mv anv anv mV Black Black Black Black White White White White Polished Polished Polished Polished Aluminum Aluminum Aluminum Aluminum Dull Dull Dull Dull Aluminum Aluminum Aluminum Aluminum IZUN scientific 98 012 04695D Thermal Radiation System Questions Part 1 List the surfaces of the Radiation Cube in order of the amount of radiation emitted Is the order independent of temperature Itis a general rule that good absorbers of radiation are also good emitters Are your measure ments consistent with this rule Explain Questions Part 2 Do different objects at approximately the same temperature emit different amounts of radiation Can you find materials in your room that block thermal radiation Can you find
113. een the two matching spectral lines The angle 0 is one half of the angle between the two lines Use mA d sin O and let the order m be 1 to calculate the wavelength of the chosen spectral line If a dim spectral line only appears on one side of the central ray zeroth order calculate where the central ray is using a brighter spectral line that is visible on both sides of the central ray Then determine the angle from the central ray to the dim line to find the angle 0 for that spectral line Tig 24 Calibrating the Grating The number of grating lines on the Grating is approximately 600 lines per millimeter This translates to a Grating line spacing of d 1666 nm 1 666 x10 m To find the exact Grating line spacing use a sodium lamp to calibrate the Grating The average wavelength A of the yellow sodium doublet is 589 3 nm Solving mA d sin for the line spacing d assuming m 1 for the first order gives d Asin 6 where is the known wavelength of the sodium doublet To determine the angle 0 find the difference in angle between the two first order yellow lines and divide by two Using the calibrated Grating line spacing d the wavelength of any spectral line in any other spectrum can be more accurately determined using mA d sin O where the order m is 0 1 2 Angular Resolution When the Rotary Motion Sensor is fastened to the lower set of holes on the hinge on the Spectrophotometer Base as describe
114. eight times higher counting rate was measured with the 5 mm slit than with the 1 mm slit The scattering rates for gt 30 must then be divided by 8 in order to convert them to 1 mm slit conditions The corrected measured values and those for e lt 30 are shown in Fig 4 in floating point notation In order to compare the measured values with the theoretically predicted sint 6 dependence of the scattering rate the curve f a sin7 5 is plotted on a second sheet of logarithmic paper with the same division of the axes The measured points and the theoretical curves must be made to coincide by displacement parallel to the ordinate This parallel displacement corresponds to multiplication of the overal function with a corresponding proportionality constant observe the logarithmic division of the axes As can be concluded from Fig 4 the measured points can easily be made to coincide with the theoretical curves Note If we remove the preparation from the scattering chamber and darken the chamber the digital counter does not register anything even after several hours 201 False counts can occur when electrical devices e g the pump are turned on or off during a measurement and interfering impulses from the power source influence the digital counter Measurements of angles over 30 turn out especially well when the holder with the foil and the 5 mm slit is turned by 30 beyond the 90
115. el discutindo m todos alternativos e respondendo a quest es pertinentes que tenham surgido durante a experi ncia 167 e Bibliografia Devem apresentar toda a bibliografia que consultaram N o aceit vel utilizarem s o protocolo Os endere os da Internet n o devem ser gen ricos e g www google com Notas As legendas das figuras colocam se imediatamente abaixo delas e as legendas das tabela por cima delas O relat rio n o deve exceder duas p ginas excepto quando o n mero de figuras ou tabelas o exigir 168 Anexo D Notas sobre An lise de Dados Notas sobre an lise de dados J Pinto da Cunha Departamento de Fisica Universidade de Coimbra Setembro de 2006 e F RMULA DE PROPAGA O DE ERROS Seja f uma fun o bem comportada de N par metros vari veis f 01 02 4n Como sabido N 9 f df da k 1 N 1 gt Jaz eg 1 h 1 sendo N o n de vari veis e da uma varia o infinitesimal de ap Isto quando as vari veis v o de ar ak day fun o varia de f f df Assim na pr tica pequenas varia es 6 nos valores dos par metros a quando ak ap daz fazem com que f gt f df sendo N af s a ie 2 k l Para al m disso N N aI af af l o dar o gt dando A 3 Se os valores de far forem o resultado de medidas directas ou indirectas esses valores estar o afectados de flutua es estat sticas devidas a m ltiplas causas por hi
116. ensor to slowly and continuously scan the spectrum in one direction Scan all the way through the first order spectral pattern on one side of the central ray through the central ray itself and all the way through the first order spectral pattern on the other side of the central ray 4 Stop recording data Record Data Cuvette with Liquid Sample 1 Remove the cuvette and fill it three quarters full with the liquid sample you are testing Cap the cuvette and replace it in front of the sensor 2 Start recording data 3 Push on the threaded post under the light sensor to slowly and continuously scan the spectrum in one direction Scan all the way through the first order spectral pattern on one side of the central ray through the central ray itself and all the way through the first order spectral pattern on the other side of the central ray 4 Stop recording data Analyze the Data Refer to the User s Guide for your version of Science Workshop for detailed information on using ScienceWorkshop for data analysis 1 Use the Graph display to compare the plot of Light Intensity versus Actual Angular Position for the first run of data empty cuvette to the plot of Light Intensity versus Actual Angular Position for the second run of data cuvette plus liquid sample 2 Use the built in analysis tools of the program to find the angle of the first gap or dark line in the absorption spectrum of the liquid sample Find the angle of th
117. erimental consequences of time variations of the fundamental constants J Rich Am J Phys 71 1043 2003 32 Apparatus to measure relativistic mass increase John W Luetzelschwab Am J Phys 71 878 2003 33 Relativistic causality and conservation of energy in classical electromagnetic theory A Kislev and L Vaidman Am J Phys 70 1216 2002 34 A comparison between the Doppler and cosmological redshifts Maria Luiza Bedran Am J Phys 70 406 2002 35 The origins of length contraction I The FitzGerald Lorentz deformation hypothesis Harvey R Brown Am J Phys 69 1044 2001 36 Student understanding of time in special relativity Simultaneity and reference frames Rachel E Scherr Peter S Shaffer and Stamatis Vokos Am J Phys 69 24 2001 37 Two novel special relativistic effects Space dilatation and time contraction J H Field Am J Phys 68 367 2000 38 Introduction to the Relativity Principle Gabriel Barton Eur J Phys 21 No 3 May 2000 277 278 27 39 Relativistic contraction of an accelerated rod Hrvoje Nikoli Am J Phys 67 1007 1999 40 Lorentz transformations of the electromagnetic field for beginners Rafael Ferraro Am J Phys 65 412 1997 41 Paradoxical twins and their special relatives Richard H Price and Ronald P Gruber Am J Phys 64 1006 1996 42 Direct calculation of time dilation Oleg D Jefimenko Am J Phys 64 812 1996 43 A Traveler s
118. erns in the back ground of the main fringe pattern These background patterns normally do not move when the mirror is moved and have no impact on measurements made using the main interference pattern 4 Convection Currents If the fringe pattern ap pears to wave or vibrate check for air currents Even a slight breeze can effect the fringes 5 Vibration Under normal conditions the interferometer base and mirror mounts are stable enough to provide a vibration free setup However if the experiment table is vibrating sufficiently it will effect the interference pattern 10 185 gt IMPORTANT If the movable mirror doesn t move when you turn the micrometer dial see Micrometer Spacer Replacement in the Maintenance section at the end of this manual Component Specifications Interferometer Mirrors 3 175 cm in diameter 0 635 0 012 cm thick flat to 1 4 wavelength on both sides coated on one side for 80 reflectance and 20 transmission Beam Splitter 3 175 cm in diameter 0 635 0 012 cm thick flat to 1 4 wavelength on both sides coated on one side for 50 reflectance and 50 transmission Compensator Identical to the beam splitter but uncoated Movable Mirror movement is controlled by the micrometer that is built into the interferometer base turning the dial clockwise moves the mirror toward the right looking from the micrometer side 25 microns per micrometer dial revolution 41 nea
119. ers on the Reflective Mask of the h e Apparatus when you measure the yellow and green spectral lines 3 Move to the second order and repeat the process Record your results in the table below Analysis Determine the wavelength and frequency of each spectral line Plot a graph of the stopping potential vs frequency Determine the slope and y intercept Interpret the results in terms of the h e ratio and the W e ratio Calculate A and W In your discussion report your values and discuss your results with an interpretation based on a quantum model for light First Order Wavelength Frequency Stopping Potential Color nm x10 Hz volts Yellow Green Blue Violet Ultraviolet Second Order Wavelength Frequency Stopping Potential Color nm x10 Hz volts Yellow Green Blue Violet Ultraviolet 127 012 04049J h e Apparatus and h e Apparatus Accessory Kit Technical Information Theory of Operation In experiments with the h e Apparatus monochromatic light falls on the cathode plate of a vacuum photodiode tube that has a low work function Wo Photoelectrons ejected from the cathode collect on the anode The photodiode tube and its associated electronics have a small capacitance which becomes charged by the photo electric current When the potential on this capacitance reaches the stopping potential of the photoelectrons the current de
120. es in front of any of the spectral lines in the second order High Sensitivity Light Sensor Scan slowly and In the ScienceWorkshop program begin continuously in one recording data Then scan the spectrum Figure 23 Scan the Spectrum direction continuously but slowly in one direction by pushing on the threaded post to rotate the Degree Plate Scan all the way through the first order spectral lines on one side of the central ray zeroth order through the central ray and all the way through the first order spectral lines on the other side of the central ray Fig 23 The angle of a particular line in the spectral pattern is one half of the difference of the angle between the chosen spectral line in the first order on one side of the central ray and the matching spectral line in the first order on the ag PASCO scientific 156 012 06575A Educational Spectrophotometer Mercury spectrum For example measure the difference in angle between these two lines One half of the difference is the angle 9 to use for calculating the wavelength 2 29 25 z 20 central ray 050 Run 2 Actual Angular Position rad Figure 24 Measure the Angles for Both First Order Spectral Patterns other side of the central ray Use the built in analysis tools in the ScienceWorkshop Graph display to find the angle betw
121. es a continuous spec trum of wavelengths Light produced by an d grating line electric discharge in a rarefied gas of a ee single element contains a limited number of discrete wavelengths an emission or bright line spectrum The pattern of colors n AIN in an emission spectrum is characteristic of the element The individual colors appear in the shape of bright lines because the light Theory path difference d sin 6 8 angle of diffraction Ray A light rays Grati that is separated into the spectrum usually es passes through a narrow slit illuminated by Figure 1 1 Ray diagram for first order diffraction pattern the light source A grating is a piece of transparent material on which has been ruled a large number of equally spaced parallel lines The distance between the lines is called the grating line spacing d Light that strikes the transparent material is diffracted by the parallel lines The diffracted light passes through the grating at all angles relative to the original light path If diffracted light rays from adjacent lines on the grat ing interfere and are in phase an image of the light source can be formed Light rays from adjacent lines will be in phase if the rays differ in path length by an integral number of wavelengths of the light The first place that an image can be formed is where the path length between two adjacent light rays differs by one wavelength However the difference
122. es vai ent o incidir na amostra que est fixa no eixo do tubo A amostra consiste numa rede de cobre na qual se encontra um filme de grafite policristalina Quando os electr es incidem na amostra s o difractados com diferentes ngulos projectando uma imagem no ecr fluorescente A corrente no nodo n o deve exceder significativamente 1 mA A limita o de corrente pode ser obtida usando uma resist ncia de cerca de 10 MW ou atrav s de um circuito limitador de corrente inclu do na pr pria fonte A intensidade e contraste dos an is pode ser controlada com a tens o G1 A mancha luminosa central correspondente a electr es que atravessaram o cristal sem sofrer desvio intensa e pode danificar a camada fluorescente do tubo Para o evitar reduza a intensidade da luz ap s cada leitura Execu o 1 Ajuste a tens o de acelera o dos electr es para V 8 kV V U4 na figura 6 V n o deve exceder 8 kV Ajuste a tens o G1 de forma a que a imagem de difrac o seja n tida 2 Mega os di metros 2rl e 2r2 dos dois an is de difrac o de menor raio com o aux lio de uma craveira Estime as incertezas O2r1 02 associadas a cada medida e anote esses valores 132 3 Repita o procedimento anterior para um conjunto de valores de V inferiores a 8 kV Note que espera que A h p h 2 me V 12 ou seja espera que vi Uma vez que n o varia linearmente com V a escolha de intervalos regulares de V n o a mais adeq
123. experi ncia do Espalhamento de Rutherford e de part culas alfa por um n cleo e a pr pria f rmula de Rutherford Tem v rias refer ncias de livros sobre o assunto e conceitos relacionados Do g nero do endere o anterior http hyperphysics phy astr gsu edu hbase nuclear crosec html c1 que explica o conceito de sec o eficaz relacionando o tamb m com a experi ncia do Espalhamento de Rutherford O endere o da Universidade de Toronto http Avww upscale utoronto ca Generalinterest Key relspec htm tem apontamentos sobre a Teoria da Relatividade Restrita que cobrem os temas escolhidos no programa desta disciplina Em http www aip org history einstein voice1 htm temos a explica o do pr prio Einstein sobre a Equival ncia entre Energia e Massa onde se pode ouvir a sua voz a explicar a f rmula E me Em hitp Awww motionmountain net text html pode se fazer o download de um livro de F sica muito interessante que cobre algumas partes da mat ria escolhida para esta disciplina sobretudo a Relatividade Restrita No endere o http Ayww mhhe com physsci astronomy applets Blackbody frame htm l pode se aceder a v rias quest es sobre a radia o do corpo negro e a luminosidade das estrelas O endere o tem desde a explica o do que um corpo negro at exerc cios sobre radia o do corpo negro e as respectivas solu es A explica o de assuntos como o efeito fotoel ctrico os quanta de Planck e a energia de um fot o pode
124. f human intuition PASC OH 15 With this in mind it s not surprising that a great deal of time and effort has been invested in measuring the speed of light Some of the most accurate measurements were made by Albert Michelson between 1926 and 1929 using methods very similar to those you will be using with the PASCO Speed of Light Apparatus Michelson measured the velocity of light in air to be 2 99712 x 10 m sec From this result he deduced the velocity in free space to be 2 99796 x 10 m sec But Michelson was by no means the first to concern himself with this measurement His work was built on a history of ever improving methodology Speed of Light 012 07135B Measuring the Velocity of Light History Galileo Through much of history those few who thought to speculate on the velocity of light considered it to be infinite One of the first to question this assumption was the great Italian physicist Galileo who suggested a method for actually measuring the speed of light The method was simple Two people call them A and B take covered lanterns to the tops of hills that are separated by a distance of about a mile First A uncovers her lantern As soon as B sees A s light she uncovers her own lantern By measuring the time from when A uncovers her lantern until A sees B s light then dividing this time by twice the distance between the hill tops the speed of light can be determined However the s
125. formam no ecr Por outro lado a quantidade de movimento p dos electr es que colidem com a grafite pode ser determinada a partir da diferen a de potencial el ctrico V a que s o sujeitos atrav s da rela o eV p 2m Assim para cada valor da tens o de acelera o V podemos determinar o comprimento de onda e a quantidade de movimento p dos electr es repetindo as 129 medidas para um conjunto de valores V obtemos um conjunto de pares de valores p e podemos verificar a validade da rela o de de Broglie A hp Note se que tal como em qualquer figura de difrac o h uma frac o do feixe que atravessa o alvo sem sofrer desvio e produz uma mancha no centro do tubo Se diminuirmos a tens o de acelera o o di metro dos an is aumenta e o di metro da mancha central aumenta tamb m Focando a imagem torna se evidente que essa mancha central associada a electr es que n o sofreram desvio de facto a uma imagem da grafite tal como esperar amos para um feixe de part culas mesmo poss vel reconhecer a forma dos parafusos de suporte do filme de grafite Como podemos determinar o comprimento de onda dos electr es A amostra de grafite composta por cristais que t m um arranjo regular de tomos de carbono ver Fig 2 Os planos desses tomos separados por uma dist ncia d actuam como uma rede de difrac o tal como est esquematizado na Fig 3 A condi o de interfer ncia construtiva dos feixes emerge
126. g mask the opening so it trans Figure 2 2 Equipment Setup for Absorption Spectrum mits a narrow 0 5 to 1 0 cm beam to the Collimating Slits Adjust the Collimating Slits slide so the number 2 slit is in line with the light source Put a cloth hood over the light source and attach the edge of the hood to the plate on the Collimating Slits 4 Turn on the light source Once it is warmed up adjust the light source Collimating Slits Collimating Lens and Focusing Lens so clear images of the central ray and the first order spectral pattern appear on the Aperture Disk and Aperture Screen Turn the Aperture Disk so the second smallest slit on the disk is in line with the central ray 5 Connect the ScienceWorkshop interface to the computer turn on the interface Start Science Workshop 6 Connect the High Sensitivity Light Sensor cable to Analog Channel A Connect the Rotary Motion Sensor cable to Digital Channels 1 and 2 Experiment Setup Select the Sensors Set the Sample Rate and Create a Calculation Refer to the User s Guide for your version of ScienceWorkshop for detailed information on selecting sensors changing the sample rate and sensitivity and creating a calculation 1 Inthe ScienceWorkshop program select the Rotary Motion Sensor and connect it to Digital Channels and 2 and select the Light Sensor and connect it to Analog Channel A 2 Inthe program set up the Rotary Motion Sensor for high resolution 1440 D
127. gnment procedure in the preceding section see Figure 14 for approximate component placement 1 Align the laser so the laser beam strikes the center of Cleaning Up the Image M use the alignment jigs 22 In addition to the point image you may also see in 2 Adjust the rotational axis of M so it is perpendicular terference fringes through the microscope as well as to the beam i e as M rotates there must be a posi the extraneous beam images mentioned above These tion at which it reflects the laser beam directly back fringes cause no difficulty as long as the point image into the laser aperture is clearly visible However the fringes and extraneous 3 Insert L to focus the laser beam to a point Adjust L beam images can sometimes be removed without los so the beam is still centered on M ing the point image This is accomplished by turning yi care L2 slightly askew so it is no longer quite at a right 4 Insert L and adjust it so the beam is still centered on angle to the beam axis see Figure 12 Mg 5 Place the Measuring Microscope in position and again be sure that the beam is still centered on Mp Earlier units with the microscope offset to the right of center on its base should be set at 81 0 cm Measuring A A E Optics Bench Rotating I ie Microscope p poani L 252 mm L 48 mm Ma f it Laser focal length focal length Leveling Laser Alignment 17 em 62 2
128. he violet line of color appears to be a part of the spectral pattern when the light falls on the disk but disappears when the light falls only on the Aperture Screen The High Sensitivity Light Sensor cannot measure ultraviolet light The ScienceWorkshop program interprets the starting position of the Rotary Motion Sensor as the zero angular or linear position For some measurements it may be important to put a mark or stop on the edge of the Degree Plate for reference so you can begin each trial of measurement from the same position The Degree Plate has several threaded holes near its outer edge You can put one of the small thumbscrews that are stored on the Light Sensor Arm into one of these threaded holes to use as a reference point for beginning or ending a scan M PASCO scientific 158 012 06575A Educational Spectrophotometer Activity 1 Emission Bright Line Spectrum EQUIPMENT NEEDED Spectrophotometer System OS 8539 or Spectrophotometer Kit OS 8537 High Sensitivity Light Sensor CI 6604 Rotary Motion Sensor CI 6538 Basic Optics Bench part of OS 8515 Aperture Bracket OS 8534 and Mercury Vapor Light Source OS 9286 Large Rod Stand ME 8735 2 Rod 45 cm ME 8736 2 Introduction The purpose of this activity is to determine the wavelengths of the colors in the spectrum of a mercury vapor light An incandescent source such as a hot solid metal filament produc
129. i o da mat ria seja mais lenta os alunos apreendem na melhor uma vez que a dedu o do racioc nio feita passo a passo mais interactiva e suscita mais interroga es aos alunos Ali s do contacto que temos tido com os alunos ao longo dos anos conclu mos que este tipo de ensino tem maior receptividade da sua parte Por outro a exist ncia das novas ferramentas inform ticas permite a utiliza o no ensino de t cnicas de simula o computacional como o caso dos diversos applets que a mais adiante nos referiremos As aulas te rico pr ticas ser o de discuss o realiza o de problemas e de realiza o demonstra o de trabalhos pr ticos Discutir se o exerc cios sobre a mat ria exposta nas aulas te ricas que os alunos devem autonomamente resolver fora da sala de aulas Tentar se que cada exerc cio acabe por ser completamente resolvido no quadro preferencialmente por um aluno uma vez que a disciplina do primeiro ano e os conceitos s o quase sempre novos Ser o elaboradas folhas de exerc cios dos quais alguns ser o os que os alunos resolvem autonomamente e se discutem nas aulas Outros ficar o para os alunos resolverem em casa consolidando a mat ria apreendida nas aulas Outros ainda ter o a sua solu o apresentada na p gina da disciplina na Internet Alguns exerc cios ser o resolvidos nas aulas individualmente pelos alunos o que contar para avalia o Para a realiza o de trabalhos pr ticos
130. ia de 103 7 MHz com uma pot ncia de sa da de 200 keV Determinar a taxa de emiss o dos quanta da esta o Uma esta o emissora de F M considerar f 100 MHz com uma pot ncia m dia de 10kW est na Louz a 20km de dist ncia da Universidade de Coimbra Quantos fot es s o recebidos por m na Universidade Um filamento de carbono que pode ser considerado um radiador corpo negro aquecido sucessivamente a 500 C 1000 C 1500 C e 2500 C Calcular os correspondentes comprimentos de onda para os quais a intensidade da radia o emitida m xima a estas temperaturas Supondo que as superf cies estelares se comportam como corpos negros calcular a temperatura da superf cie do sol e a da estrela polar supondo que o comprimento de onda para o qual a radi ncia espectral atinge o seu m ximo 5100A e 3500 respectivamente A emissividade do tungst nio aproximadamente igual a 0 35 Uma esfera deste material com lcm de raio est suspensa num vasilhame de raio muito maior estando este vasilhame a uma temperatura de 300K Qual a pot ncia requerida 53 para manter a esfera a uma temperatura de 3000K despreze a condu o t rmica ao longo do suporte 9 Duas superf cies muito extensas e pr ximas uma da outra s o mantidas temperatura de 200K e 300K respectivamente Considere as superf cies como corpos negros ideais a Qual a taxa de perda de calor da superf cie mais quente Consider
131. ield Turn the power switch ON Rotate the h e Apparatus about the pin of the Coupling Bar Assembly until one of the colored maxima in the first order shines directly on the slot in the white reflective mask Rotate the h e Apparatus on its support base so that the same spectral maxima that falls on the opening in the White Reflec tive Mask also falls on the window in the photodi ode mask NOTE The white reflective mask on the h e apparatus is made of a special fluorescent material This allows you to see the ultraviolet line as a blue line and it also makes the violet line appear more blue You can see the actual colors of the light if you hold a piece of white non fluorescent material in front of the mask The palm of your hand works ina pinch although it fluoresces enough that the UV line will still be visible When making measurements it is important that only one color falls on the photodiode window There must be no overlap from adjacent spectral maxima h e Apparatus and h e Apparatus Accessory Kit 012 04049J Green amp Yellow Spectral lines in 3rd Order are not Visible Color Frequency Hz Wavelength nm All values except wavelength for yellow line are from Handbook of Chemistry and Physics 46th ed Yellow pp RO LZR EM e The wavelength of the yellow was determined ex Green 5 48996E 14 546 074 perimentally using a 600 line mm grating Blue 6 87858E 14 435 835 NOTE The ye
132. ight Sensor The High Sensivitiy Light Sensor has a GAIN amplification select switch on the top with three settings 1 10 and 100 When you measure a spectrum start with the lowest GAIN setting to measure the brightest lines Then switch to the next setting and re scan the spectrum to measure the dimmer lines Then re scan again at the highest GAIN setting to measure the dimmest lines It is also possible to amplify the signal from the Light Sensor using the ScienceWorkshop program The normal Sensitivity setting is Low 1x The other settings are Medium 10x and High 100x In general you will record better data if you increase the GAIN setting on the Light Sensor before you increase the Sensitivity setting in the ScienceWorkshop program General Information About Slit Widths There are five slits on the Collimating Slits slide and six slits on the Aperture Disk You can select wider slits in order to increase the amount of light that passes through the Grating and into the Light Sensor but this will make a wider spectral pattern and decrease the accuracy of your measurements first order spectral lines Scanning a Spectrum Diffraction Grating To scan a spectrum use the threaded post under the Light Sensor to move the Light Sensor Arm so the Light Sensor is beyond the central ray zeroth order far end of the first order spectral lines but not first order spectral lin
133. in path length for two adjacent light rays also depends on the grating line spacing d and the angle 9 at which the two light rays were diffracted by the grating The relationship between the wavelength of the light the grating line spacing d and diffraction angle 0 is as follows A dsin6 In the diagram Fig 1 1 the path length for Ray A is one wavelength longer than the path length of Ray B PASC E scientific 159 Educational Spectrophotometer 012 06575A Procedure In this activity the High Sensitivity Light Sensor measures the relative intensity of colors of light in an emission spectrum produced by light from a mercury vapor light source passing through a grating The Rotary Motion Sensor measures the angle 0 of each band or bright line of color The ScienceWorkshop program records and displays the light intensity and the angle You can use the program s built in data analysis tools to find the angle for each color and then you can determine the wave length A of each color Equipment Setup Collimating Focusing Lens 1 Set up the Spectrophotometer next Slits cloth xe High Sensitivity oa mene vapor light source as hood binder Grating Light Sensor shown Fig 1 2 If needed use the s Rod Stand Mounting Clamps two i rods and two bases to raise the f Spectrophotometer to the same aces level as the opening to the light 4 source Refer to the
134. infrared region from 0 5 to 40 um and the voltages produced range from the micro volt range up to around 100 millivolts A good millivolt meter is sufficient for all the experiments described in this manual See the current PASCO catalog for recommended meters The Sensor can be hand held or mounted on its stand for more accurate positioning A spring clip shutter is opened and closed by sliding the shutter ring forward or back During experiments the shutter should be closed when measurements are not actively being taken This helps reduce temperature shifts in the thermopile reference junction which can cause the sensor response to drift NOTE When opening and closing the shutter it is possible you may inadvertently change the sensor position Therefore for experiments in which the sensor position is critical such as Experiment 3 two small sheets of opaque insulating foam have been provided Place this heat shield in front of the sensor when measurements are not actively being taken PASC scientific 93 The two posts extending from the front end of the Sensor protect the thermopile and also provide a reference for positioning the sensor a repeatable distance from a radiation source Specifications Temperature Range 65 to 85 C Maximum Incident Power 0 1 Watts cm Spectral Response 6 to 30um Signal Output Linear from 10 to 10 Watts em Thumbscrew Loosen to reposition Se
135. ing and recording data Darken the room Examine the spectrum closely Determine which of the two first order spectral patterns is brightest In the Data Table list the colors you see in order starting with the color that appears farthest from the central ray Use the Light Sensor Arm on the Spectrophotometer to turn the Degree Plate until the light sensor is beyond the last line in the brightest first order spectral pattern Record Data 5 Set the GAIN select switch on top of the Push on the threaded post under the light Stop recording data Set the GAIN select switch on top of the High Sensitivity Light Sensor to 1 Start recording data sensor to slowly and continuously scan the spectrum in one direction Scan all the way through the first order spectral lines on one side of the central ray through the central ray itself and all the way through the first order spectral lines on the other side of the central ray Fig 1 4 first order spectral lines SS SG Grating first order spectral lines central ray zeroth order light sensor to 10 Put the light sensor back at its starting point Repeat the data High Sensitivity collection procedure Light Sensor Scan slowly and continuously in one Figure 1 4 Scan the Spectrum direction PASCO j scientific 161 Educational Spectrophotometer 012 06575A 6 Setthe GAIN select switch on top of the light sensor to 100 and
136. ist ncia entre planos at micos adjacentes na calcite CaCO3 de 0 300 nm Calcular o ngulo de Bragg mais pequeno para raios X de 0 030 nm 5 Um fot o e uma part cula t m o mesmo comprimento de onda Comparar os seus momentos lineares e a energia do fot o com a energia total da part cula Qual a rela o entre a energia do fot o e a energia cin tica da part cula 6 Um electr o parte do repouso numa regi o onde existe uma diferen a de potencial de 100 V Qual o seu comprimento de onda de de Broglie 7 Calcular o comprimento de onda de de Broglie de um gr o de areia com 1 mg de massa empurrado pelo vento com uma velocidade de 2x10 m s 8 Um electr o e um prot o t m a mesma velocidade Comparar os comprimentos de onda e velocidades de fase e de grupo das suas ondas de de Broglie 57 9 A velocidade de fase das ondas do oceano Jg 1 27 onde g a acelera o da gravidade Calcular a velocidade de grupo das ondas do oceano 10 Calcular as velocidades de fase e de grupo de ondas de de Broglie de um electr o com energia cin tica de 500 eV 11 Qual o efeito de se aumentar a energia do electr o no ngulo de espalhamento na experi ncia de Davisson Germer 12 Um feixe de electr es com energia de 50 eV incide num cristal e os electr es difractados s o detectados num ngulo de 50 relativamente ao feixe incidente Qual o espa amento dos planos at micos do cristal 13 Um electr
137. ivisions per Rotation and set the sample rate to 20 Hz or 20 measurements per second 3 Set the Sensitivity for the High Sensitivity Light Sensor to 10x 4 Use the Calculator to create a calculation of Actual Angular Position based on the Angular Position measure ment made by the Rotary Motion Sensor and the ratio of the radius of the Spectrophotometer s Degree Plate to the radius of the small post on the Pinion Refer to the Introduction for more information Select the Display Refer to the User s Guide for your version of ScienceWorkshop for detailed information on displays 1 Select a Graph display 2 Set the axes of the Graph display so Light Intensity is on the vertical axis and Actual Angular Position is on the horizontal axis Prepare to Record Data Refer to the User s Guide for your version of ScienceWorkshop for detailed information on monitoring and recording data 20 PASCO scientific 164 012 06575A Educational Spectrophotometer 1 Darken the room Examine the spectrum closely Determine which of the two first order spectral patterns is brightest 2 Use the Light Sensor Arm on the Spectrophotometer to turn the Degree Plate until the light sensor is beyond the last color in the brightest first order spectral pattern Record Data Empty Cuvette 1 Set the GAIN select switch on top of the High Sensitivity Light Sensor to 10 2 Start recording data 3 Push on the threaded post under the light s
138. k Number Accelerating Voltage Table 1 DataTable of Peak Number and Accelerating Voltages 194 C Analysis Putting It All Together C 1 Using your observations of the glowing neon the sketch you made and the table of peak voltages describe what is happening when the electrons collide with the neon gas You should refer to the predictions you made in questions A 1 and A 2 and resolve any differences C 2 What does the minima in electron current mean Describe how these minima are related to the quantized energy levels in the neon atom C 3 The dips occur regularly in a plot of current versus voltage Using your sketch and the table of values determine the excitation energy of the neon gas 195 C 4 C 5 C 6 The dips in the oscilloscope plot of current versus voltage are not perfectly sharp Why is this the case Why is the first peak at about 30V instead of 19V Using the energy diagram provided in Appendix A determine the most likely transi tions resulting from the collision excitation of neon 196 Below is a table showing the peak number and the accelerating voltage for a typical Franck Hertz tube using mercury vapor instead of the neon you used here Peak number Accelerating voltage V 1 6 7 2 11 5 3 16 5 4 21 25 5 26 25 Table 2 Table of Typical Results Using a Mercury Vapor Tube C 7 Calculate the excitation energy of mercury and the corresponding wavelength of
139. lectr es Verifica se que um dos electr es sai com velocidade 0 6c e que outro sai com velocidade 0 7c mas em sentido oposto Obter de acordo com a regra cl ssica de adi o de velocidades a velocidade de um dos electr es medido no referencial que acompanha o outro 3 Num autom vel descapot vel que se desloca velocidade constante de 90 km h viaja uma crian a que num determinado instante atira verticalmente para cima uma bola com velocidade de 6 m s Escrever a equa o de movimento da bola para um observador no autom vel e para um observador parado na berma da estrada 4 Uma pessoa viaja num barco em direc o a Este com uma velocidade de 5 m s No instante em que o barco passa pelo cais uma crian a atira do cais uma pedra em direc o a Norte e a pedra cai a 50 m do cais 6 segundos depois Determinar as coordenadas do ponto em que caiu a pedra medidas pela pessoa que vai no barco 39 5 a Um rapaz que viaja num comboio atira uma bola segundo a orienta o do seu deslocamento e com uma velocidade de 20 km h O comboio desloca se com uma velocidade de 80 km h Qual a velocidade da bola calculada por um observador em terra Um condutor numa plataforma de caminho de ferro sincroniza o seu rel gio com o maquinista na parte da frente de um comboio circulando a 100 km h O comboio tem 300 m de comprimento Dois minutos depois da dianteira do comboio passar a plataforma um homem na traseira acende um ciga
140. lectrical connection Apparatus 1 Rutherford scattering chambers 559 56 1 Pump S 1 5 220 V 50 Hz 101 01 1 Vacuum rubber hose 2 m 307 68 1 Digital counter E 575 59 1 Discriminator preamplifier 2 559 93 1 Power supply unit plug in 9 2 V 530 88 2 HF cables sccveccccccccccvee seessess 501 02 1 Americum AM 241 preparation 333 kBq ICI cccveiacecvscedcccesesdseaetes 559 82 1 Saddle base eeeeeee 300 11 1 Stop clock avessas ces ata OD A Never touch the gold foil Air the scattering chamber very carefully see operating instructions 559 56 otherwise you may destroy the sensitive gold foil Set up and connect the instruments as shown in Fig 3 Turn the potentiometer on the discriminator preamplifier all the way to the left Air the scattering chamber and take off the lid Set the digital counter to AS Preparing the scattering chamber Fig 1 Tnsert the preparation into the 4mm socket of the swiveling holder Place the 1 mm slit and the plastic sheet containing the gold foil on top of one another and insert them both into the holder so that the slit points towards the preparation Swing the holder for swinging in not needed during this measurement to the top of the cover Make sure the aperture slit of the detector on the inner wall of the chamber is perpendicular with the mark at the top Close the chamber and evacuate it fof e e o 2 Carrying out the e
141. lei do deslocamento de Wien Dedu o da express o de Rayleigh Jeans para a radia o t rmica do corpo negro e a chamada cat strofe do ultravioleta 9 li o Teoria de Planck da radia o do corpo negro Dedu o da express o de Planck para o espectro do corpo negro e sua adequa o aos resultados experimentais Obten o da lei de Stefan e da lei de Wien a partir da lei de Planck Consequ ncias do postulado de Planck Algumas aplica es das leis do corpo negro o radi metro o efeito de estufa e a estimativa da temperatura da Terra 13 10 li o Introdu o Teoria Qu ntica da Radia o Electromagn tica A natureza ondulat ria e a natureza corpuscular da radia o electromagn tica O efeito fotoel ctrico A sua descoberta por Hertz As tr s leis experimentais do efeito fotoel ctrico A teoria qu ntica de Einstein sobre o efeito fotoel ctrico O fot o Fun o trabalho O efeito Compton A experi ncia e an lise dos resultados Interpreta o baseada na natureza corpuscular da luz Comprimento de onda de Compton Produ o e aniquila o de pares electr o positr o O positr nio Absor o de fot es 11 li o Produ o de raios X Radia o de Bremstralung Linhas espectrais Kg Kg La Lp Efeito Auger Fluoresc ncia de raios X Riscas K e Kg Difrac o de raios X por um cristal Lei de Bragg Ondas de mat ria A dualidade onda part cula para a radia
142. length of the separated beams is increased thereby decreasing the coherence of the beams at the viewing screen This will obscure the interference pattern A compensator is identical to the beam splitter but without the reflective coating By inserting it in the beam path as shown in Figure 1 both beams pass through the same thickness of glass eliminating this problem The Twyman Green Interferometer The Twyman Green Interferometer is a variation of the Michelson Interferometer that is used to test optical components A lens can be tested by placing it in the beam path so that only one of the interfering beams passes through the test lens see Figure 3 Any irregularities in the lens can be detected in the resulting interference pattern In particular spherical aberration coma and astigmatism show up as specific variations in the fringe pattern Figure 3 Twyman Green Interferometer Precision Interferometer 012 07137A The Fabry Perot Interferometer In the Fabry Perot Interferometer two partial mirrors are aligned parallel to one another forming a reflective cavity Figure 4 shows two rays of light entering such a cavity and reflecting back and forth inside At each reflection part of the beam is transmitted splitting each incident ray into a series of rays Since the transmitted rays are all split froma single incident ray they have a constant phase relationship assuming a sufficientl
143. lers Then recheck the alignment of the laser Align the Rotating Mirror Mp must be aligned so that its axis of rotation is vertical and also perpen dicular to the laser beam To accomplish this remove the second alignment jig and then rotate M so that the laser beam reflects back toward the hole in the first alignment jig Figure 9 Be sure to use the re flective side of the mirror It helps to tighten the lock screw on the rotating mirror assembly just enough so M holds its position as you adjust its rotation If needed use pieces of paper to shim between the Rotating Mirror Assembly and the Optics Bench so that the laser beam is reflected back through the hole in the first jig 10 Remove the first alignment jig 11 Mount the 48 mm focal length lens L on the Optics Bench so that the center line of the Component Holder is aligned with the 93 0 cm mark on the met ric scale of the bench Without moving the Compo nent Holder slide L as needed on the holder to cen ter the beam on Me see Figure 10 Notice that L has spread the beam at the position of Mp 12 Mount the 252 mm focal length lens L on the Op tics Bench so the center line of the Component Holder aligns with the 62 2 cm mark on the metric scale of the bench As for L in step 11 adjust the position of L on the Component Holder so that the beam is again centered on My 84 10 13 14 Place the Measuring Microscope on the Optics Bench sotha
144. ley 39 Folha 2 Postulados de Einstein da Teoria da relatividade Transforma es de Lorentz E suas CONSEQU NCIAS sizes iii dain MEM a dian SAR ISSA e ATA 43 Folha 3 Transforma es de velocidades Efeito Doppler 47 olha 4 Varia o da energia com a velocidade Din mica relativista 51 Folha 5 Radia o e interac o da radia o com a mat ria 2 0 eee eeeeseeeeeeeseeeeeeeeeees 53 Folha 6 Raios X Dualidade onda part cula Part cula numa caixa Princ pio de incerteza Decaimento radioactivo rir re eae e ea aaene seara aerea 57 37 38 Fundamentos de Fisica Moderna Folha 1 Transforma es de Galileu Experi ncia de Michelson Morley 1 Um passageiro de um comboio que se desloca velocidade de 30 m s passa por um homem que est de p na plataforma da esta o no instante t t 0 Vinte segundos mais tarde o homem na plataforma verifica que um p ssaro que voa altura de 50 m paralelamente linha e no sentido do movimento do comboio est a 800 de dist ncia de si a Calcular as coordenadas do p ssaro no referencial do passageiro b Cinco segundos depois da primeira observa o o homem da plataforma verifica que o p ssaro est agora a 850 m Determinar a velocidade constante da ave em rela o ao homem da plataforma e em rela o ao passageiro do comboio 2 Uma amostra de material radioactivo em repouso no laborat rio emite e
145. linder must be adjusted so that the diffraction image is as clear as possible when increasing the Wehnelt voltage the anode voltage pre viously set will always drop slightly because there is increasing load on the HV supply unit Angles of diffraction 6 62 can be determined from the definitive equa tion 1 2r 8 gt arc sin 1 2 1 2 q D using the appropriate diffraction ring diameters 2 rj and 2 Yo The ring diameters can best be measured with a slide rule noting that the rule should be aligned with the maximum intensity of the rings Relatively accurate results can be obtained if the diameter is measured from the edges of the rings in each case and the position of maximum intensity calculated by finding mean values D is the greatest distance of the graphite layer the diffraction sub stance from the wall of the glass sphere The nominal dimension to be used in the calculation is D 127 mm The graphs in Fig 6 show the relation ship found between angles of diffraction 61 and 89 and the anode voltage Vg ina measuring example 1 Fig 6 138 The values of 4 2 sin 91 9 are accord ing to Fig 7 mostly identical to the values of the grid level distances dy and do 212 sin nd pm 250 200 150 100 50 eee os 6 7 8 9 10 u Fig 7 5 ELECTRON OPTIC REPRESENTATION OF THE CARRIER MESH If the electron bundle that hits the sample is expanded sufficiently the copper mesh
146. llow line is actually a doublet Violet 7 40858E 14 404 656 with wavelengths of 578 and 580mm Ultraviolet 8 20264E 14 365 483 Figure 10 The Three Orders of Light Gradients 14 Press the PUSH TO ZERO button on the side panel Using the Filters of the h e Apparatus to discharge any accumulated po The AP 9368 h e Apparatus includes three filters one tential in the unit s electronics This will assure the Ap Green and one Yellow plus a Variable Transmission Filter paratus records only tie potential OF Wie lieht yet ait The filter frames have magnetic strips and mount to the out measuring Note that the output voltage will drift with side of the White Reflective Mask of the h e Apparatus the absence of light on the photodiode Use the green and yellow filters when you re using the green and yellow spectral lines These filters limit higher frequencies of light from entering the h e Apparatus This prevents ambient room light from interfering with the lower energy yellow and green light and masking the true results It also blocks the higher frequency ultraviolet light from the higher order spectra which may overlap with lower orders of yellow and green 15 Read the output voltage on your digital voltmeter It is a direct measurement of the stopping potential for the photoelectrons See Theory of Operation in the Tech nical Information section of the manual for an expla nation of the measurement
147. m ar a Determinar o intervalo de tempo gasto pelo mes o a atravessar o tubo medido num referencial ligado ao mes o b No instante em que o mes o entra no tubo emite um sinal luminoso Calcular o tempo que o sinal demorou a atravessar o tubo medido por um observador ligado Terra e por outro ligado ao mes o 45 17 A estrela Arcturus dista 36 anos luz da Terra 1 ano luz 9 463x10 m distancia que a luz percorre num ano a Qual deve ser a velocidade de uma nave relativamente a Terra para que a dist ncia medida pelo sistema de refer ncia da nave seja apenas 1 ano luz b Qual o tempo que a nave demora da Terra estrela medido por um rel gio na nave c Aplicando a relatividade Galileana qual a velocidade da nave se a viagem demorar um ano 46 Fundamentos de Fisica Moderna Folha 3 Transformacoes de velocidades Efeito Doppler 1 Um observador S move se em rela o a um observador S segundo o eixo comum x x com velocidade constante de 0 6c O observador S dispara um proj ctil de 20cm de comprimento medido no sistema de repouso do proj ctil com uma velocidade de 0 2c segundo uma direc o que faz um ngulo de 60 com o eixo x x Calcular a a velocidade em m dulo e direc o do proj ctil em rela o ao observador S b o comprimento do proj ctil medido por S 2 Da origem de coordenadas O de um sistema de in rcia S parte no instante t 0 uma nave A na direc o e senti
148. meter allows you to view and measure the spectral pattern spectrum produced by a light source The Collimating Slits and Collimating Lens produce a narrow beam of parallel light rays The Grating disperses the beam of light into a spectrum with different colors at different angles but with all of the light of a given color in a parallel beam The Focusing Lens focuses these parallel beams of color into spectral lines see Fig 2 The narrow slit on the Aperture Disk part of the Aperture Bracket allows light of a single color to enter the High Sen sitivity Light Sensor The High Sensitivity Light Sensor included with the Spectrophotometer System measures the intensity of the light while the Rotary Motion Sensor included with the Spectrophotometer System measures the angle to which the light is diffracted by the Grating 8 Light Source Collimating Lens Diffraction Grating You can find the wavelength of each color of light using the measured angle and the Grating Not spacing d 7 N mA dsin0 m 0 1 2 Collimating Slit E E i Focusing Lens where d is the distance between the rulings on the Grating m is the order of the particular spectral line principal maximum is the angle of the Figure 2 Grating Spectrometer diffracted light and is the wavelength A PASC scientific 148 012 06575A Educational Spectrophotometer The Grating disperses the beam of light into a first order spectrum Optics Bench
149. missor e do absorvente Devido quantifica o da excita o vibracional h alguma n o pequena probabilidade de que uma dada transi o n o transfira energia para a rede emiss o sem recuo 4 Desvio Doppler Quando um emissor se move em rela o a um absorvente a energia dos fot es sofre um desvio de Doppler Para velocidades n o relativistas AE hAv Bhvo onde B v c e vo a frequ ncia de um fot o emitido a partir de um tomo em repouso Este o Desvio Doppler de primeira ordem e v lido para v lt lt c De acordo com esta rela o a varia o na energia do fot o proporcional velocidade relativa Variando a velocidade relativa do emissor poss vel varrer as energias do fot o numa gama de valores Na espectrometria de Mossbauer a taxa de absor o medida em fun o da velocidade da fonte Usando a f rmula de Doppler pode 64 converter se velocidade em desvio de energia A an lise dos picos de absor o observados revela detalhes sobre n veis de energia nuclear 5 Interac es observ veis Uma vez que os n veis de energia dos n cleos dependem de alguns factores externos poss vel obter informa o sobre a estrutura at mica e molecular de materiais a partir de espectros de Mossbauer Dependendo da natureza das interac es pode haver uma separa o ou desvio dos n veis nucleares No espectro de M ssbauer tr s interac es poss veis s o observadas a que n
150. mpact apparatus for muon lifetime measurement and time dilation demonstration in the undergraduate laboratory Thomas Coan Tiankuan Liu and Jingbo Ye Am J Phys 74 161 2006 21 An undergraduate experiment to test relativistic kinematics using in flight positron annihilation Jerzy Dryzek Douglas Singleton Takenori Suzuki and Runsheng Yu Am J Phys 74 49 2006 22 Relativity energy flow and hidden momentum Timothy H Boyer Am J Phys 73 1184 2005 26 23 The Minkowski metric in non inertial observer radar coordinates E Minguzzi Am J Phys 73 1117 2005 24 Differential aging from acceleration An explicit formula E Minguzzi Am J Phys 73 876 2005 25 How special relativity determines the signs of the nonrelativistic Coulomb and Newtonian forces S Deser Am J Phys 73 752 2005 26 Conventions and inertial reference frames Alberto A Martinez Am J Phys 73 452 2005 27 c is the speed of light isn t it George F R Ellis and Jean Philippe Uzan Am J Phys 73 240 2005 28 Relativistic velocity and acceleration transformations from thought experiments W N Mathews Jr Am J Phys 73 45 2005 29 Special Relativity and Motions Faster than Light Moses Fayngold Author and John G Cramer Reviewer Am J Phys 72 1134 2004 30 Kinematic subtleties in Einstein s first derivation of the Lorentz transformations Alberto A Martinez Am J Phys 72 790 2004 31 Exp
151. n on the motor If the image was not in sharp focus adjust the microscope You should also turn L slightly askew about 1 2 to improve the image To get the best image you may need to adjust the micro scope and L several times Let the motor warm up at about 600 revolutions sec for at least 3 minutes 2 Slowly increase the speed of rotation Notice how the beam deflection increases 3 Use the ADJUST knob to bring the rotational speed up to about 1 000 revolutions sec Then push the MAX REV SEC button and hold it down When the rotation speed stabilizes rotate the micrometer knob on the microscope to align the center of the beam im age with the cross hair in the microscope that is per pendicular to the direction of deflection Record the speed at which the motor is rotating turn off the motor and record the micrometer reading Fixed Mitror Rotating Mirror Measuring Microscope Figure 15 Diagram of the Foucault Method 14 PASC CH 88 012 07135B Speed of Light NOTE When reversing the direction of movement of the micrometer carriage there will always be some movement of the micrometer knob before the carriage responds Though this source of error is small it can be eliminated Just adjust the initial position of the micrometer stage so that you always turn the micrometer knob in the same direction as you adjust it Reverse the direction of the mirror rot
152. n will bring the rotation speed quickly to its maximum value at approximately 1 500 rev sec CAUTION Before turning on the motor for the rotating mirror carefully read the cautionary notices in the section of this manual entitled Making the Measurement 2 Measuring Microscope The 90X microscope is mounted on a micrometer stage for precise measurements of the displacement of the image point Measurements are most easily made by visually centering the image point on the microscope cross hairs before and after the displacement By noting the change in the micrometer setting the displacement can be resolved to within 0 005 mm To focus the cross hairs slide the eyepiece up or down in the microscope To focus the microscope loosen the lock screw on the side of the mounting tube and slide the microscope up or down within the tube With the lock screw loosened the microscope can also be removed from the mounting tube This can be helpful when you are trying to locate the image point A piece of lissue paper placed over the tube provides a screen that allows you to view the point without focusing the micro scope In addition to the microscope and micrometer the micrometer stage also contains the beamsplitter The lever on the side of the stage is used to adjust the angle of the beamsplitter When the lever points directly down the beamsplitter is at a forty five degree angle 1 PASC OH 81 3 Fixed Mi
153. na parte da Relatividade Cont m muitos exerc cios que podem ajudar os alunos a consolidar a mat ria Dado que os alunos de engenharia F sica e de alguns ramos da F sica nunca mais abordarem a Teoria da relatividade conv m escolher um livro como este com uma abordagem com rigor apropriado para alunos do primeiro ano nomeadamente no que diz respeito dedu o das transforma es de Lorentz Keneth S Krane Modern Physics 2 edition John Willey Publisher 1996 Livro actualizado bastante completo para um curso do primeiro ano de F sica ou de Engenharia F sica ou mesmo para outros cursos de Engenharia embora aconselhado mais no aspecto da F sica Qu ntica especialmente em F sica Nuclear N o aprofunda o suficiente a parte da Relatividade Ronald Gautreau e William Savin Modern Physics Schaum s Outline Series Mc Graw Hill 2 edition 1999 22 Tem muitos exercicios resolvidos e nao resolvidos Livro aconselhado aos alunos para problemas nas aulas te rico pr ticas embora tenha tamb m em cada capitulo uma introdu o te rica bastante Util Trata com suficiente pormenor a Teoria da Relatividade bem como a F sica Qu ntica Hugh D Young e Roger A Freedman F sica IV ptica e F sica Moderna 10 edi o Pearson Addison Wesley 2004 Livro muito completo que cobre tanto a parte da Teoria da Relatividade embora com pouca profundidade como a da Teoria Qu ntica Cont m mui
154. ncandescent light Then the sensor measures the relative intensity of colors of light in an absorption spectrum produced when light from the incandescent source passes through a liquid sample The Rotary Motion Sensor measures the angle 0 of each part Figure 2 1 Continuous Spectrum and of the continuous spectrum and then the absorption spec Absorption Spectrum trum absorption Cuvette with Sample The ScienceWorkshop program records and displays the light intensity and the angle You can use the program s built in data analysis tools to find the angle for each gap or dark line in the absorption spectrum and then you can determine the wavelength Equipment Setup 1 Set up the Spectrophotometer next to a DC powered incandescent light source as shown Move the High Sensi tivity Light Sensor to the second position on the Light Sensor Arm so there is room for a cuvette between the back of the Aperture Disk and the opening to the sensor Refer to the Set Up section for more information PASCO a scientific 163 Educational Spectrophotometer 012 06575A 2 Put an empty cuvette in front of the High Sensitivity Light Sensor cioth hood binder Cuvette between the sensor and the back of Light Source E High Sensitivity the Aperture Disk Make sure that i Light Sensor the smooth sides of the cuvette are in line with the opening to the sensor Fig 2 2 3 Ifthe light source has a large open SSS in
155. nditions then misalign the fixed mirror very slightly 0 004 or less around the horizontal axis This will bring the actual spot out from under the bright band Speed of Light 012 07135B Making the Measurement The speed of light measurement is made by rotating the mirror at high speeds and using the microscope and micrometer to measure the corresponding deflection of the image point By rotating the mirror first in one direction then in the opposite direction the total beam deflection is doubled thereby doubling the accuracy of the measurement gt Important to Protect the Rotating Mirror Assembly Before turning on the motor be sure the lock screw for the rotating mirror is completely loos ened so the mirror rotates freely by hand Whenever the speed of the motor is accelerated the red LED on the front panel of the motor con trol box will light up As the speed stabilizes this light should go off If it does not turn off the mo tor Something is interfering with the motor rota tion Check to be sure the lock screw for M is fully loosened Never run the motor with the MAX REV SEC button pushed for more than one minute at a time and always allow about a minute between runs for the motor to cool off 1 With the apparatus aligned and the beam image in sharp focus see the previous section set the direction switch on the rotating mirror power supply to CW and tur
156. nent Com jpensator Holder Plate OS 9255A Precision Interferometer Component Holder OS 9256A Interferometer Accessories 2 Polarizer Rotating Pointer Vacuum Pump with Gauge Vacuum Cell 178 Precision Interferometer 012 07137A Theory of Operation Interference Theory A beam of light can be modeled as a wave of oscillating electric and magnetic fields When two or more beams of light meet in space these fields add according to the principle of superposition That is at each point in space the electric and magnetic fields are determined as the vector sum of the fields of the separate beams Ifeach beam of light originates from a separate source there is generally no fixed relationship between the electro magnetic oscillations in the beams At any instant in time there will be points in space where the fields add to produce amaximum field strength However the oscilla tions of visible light are far faster than the human eye can apprehend Since there is no fixed relationship between the oscillations a point at which there is a maximum at one instant may have a minimum at the next instant The human eye averages these results and perceives a uniform intensity oflight If the beams of light originate from the same source there is generally some degree of correlation between the frequency and phase of the oscillations At one point in space the light from the beams may be continually in ph
157. nit The Light Sensor Arm is attached to the circular Degree Plate with two small thumbscrews The hole in the center of the Degree Plate fits over the short threaded post on the top of the Spectrophotometer Base Hold the Rotary Motion Sensor slightly away from the base so the small diameter post on top of the Pinion is not in the way of the edge of the Degree Plate Position the hole in the plate over the short threaded post on the top of the base Place the Degree Plate onto the Spectrophotom eter Base Let the small diameter post on the top of the Pinion rest against the edge of the Degree Plate see Fig 8 More Information About the Degree Plate 012 06575A Spectrophotometer Base Remove the Pinion Remove the thumbscrews Put the Pinion on the shaft Use the thumbscrews to attach the sensor Rotary Motion Sensor The ratio between the radius of the Degree Plate and the radius of the small post on the top of the Pinion is designed to be 60 to 1 In other words the Pinion rotates 60 times for one rotation of the Degree Plate This assumed ratio of 60 to 1 is included in a calcula Pinion tion for the actual angular displacement of the Degree Plate as it turns during the measurement of a spectrum see Using the ScienceWorkshop Program in the Procedure section Using the exact ratio of the Degree Plate to the small Pinion post can slightly improve the accuracy of measurement
158. nly for getting good results but for getting Tor kroperAlignment any results at all Please follow this alignment procedure carefully Allow yourself about three Laser and Laser Alignment Bench hours to do it properly the first time Once you have set up the equipment a few times you may find that the alignment summary at the end of this section is a helpful guide Optics Bench For reference as you set up the equipment Figure 5 Top shows the approximate positioning of the components View with respect to the metric scale on the side of the Optics TT Four leveling TT screws from Optics Bench Bench The exact placement of each component depends Pour scrawe cee and Laser on the position of the Fixed Mirror Mp and must be included with TT Alignment determined by following the steps of the alignment Bench Couplers Bench use procedure described below two save two All component holders the Measuring Microscope and the Rotating Mirror Assembly should be mounted flush against the fence of the Optics Bench Figure 6 This will insure that all components are mounted at right angles to the beam axis Bench Couplers Figure 7 Coupling the Optics Bench and the Laser Alignment Bench Earlier units with the microscope offset to the right of center on its base should Measuring be set at 81 0 cm Microscope Optics Bench Polarizers Rotating Mirror Assembly L 2
159. nsforma es de coordenadas de Galileu 11 A figura representa em esquema o interfer metro de Michelson Morley com um dos bra os paralelo ao vento do ter Mostrar que rodando o sistema de 90 se deveria observar um deslocamento na figura de interfer ncia correspondente a um n mero de franjas dado por 2 v AN ae ba l Ether wind Mirror B ai v g fod 7 c E me ae N Mirror A Source Telescope 12 Na experi ncia original Michelson e Morley usaram um interfer metro de bra os iguais com J lg 11m e luz de s dio de comprimento de onda 5900 A A sensibilidade do aparelho usado na experi ncia permitia detectar valores de AN at 0 005 Calcular o valor limite para a velocidade da Terra atrav s do ter consistente com os resultados da experi ncia 41 42 Fundamentos de Fisica Moderna Folha 2 Postulados de Einstein da Teoria da relatividade Transforma es de Lorentz e suas consequ ncias 1 Dois acontecimentos ocorrem a iguais dist ncias de um observador Suponha que ele adopta a seguinte defini o de simultaneidade de acontecimentos equidistantes Os dois acontecimentos s o simult neos se os sinais de luz emitidos de cada acontecimento me atingirem ao mesmo tempo Mostrar que de acordo com esta defini o se o observador determinar que dois acontecimentos s o simult neos ent o outro observador que se mova em rela o a ele determina em geral que os aco
160. nsor or to remove Sensor from stand Shutter Ring Slide forward to open shutter Shutter Banana Connectors Connect to millivolt meter Figure 1 Radiation Sensor Thermal Radiation System 012 04695D Thermal Radiation Cube Leslie s Cube The TD 8554A Radiation Cube Figure 2 provides four different radiating surfaces that can be heated from room temperature to approximately 120 C The cube is heated by a 100 watt light bulb Just plug in the power cord flip the toggle switch to ON then turn the knob clockwise to vary the power Measure the cube temperature by plugging your ohmmeter into the banana plug connectors labeled THERMISTOR The thermistor is embedded in one corner of the cube Measure the resistance then use Table 1 below to translate the resistance reading into a temperature measurement An abbreviated version of this table is printed on the base of the Radiation Cube NOTE For best results a digital ohmmeter should be used See the current PASCO catalog for recommended meters IMPORTANT When replacing the light bulb use a 100 Watt bulb Bulbs of higher power could damage the cube CAUTION Cube may be HOT Flip toggle switch to ON to turn on power CAUTION HOT Turn knob clockwise to increase temperature Banana Connectors Measure thermistor resistance Use table on back to
161. nt para meters we recommend using a two channel oscilloscope However note that at a frequency of the acceleration voltage Uz such as is required for producing a stationary oscilloscope pattern capacitances of the Franck Hertz tube and the holder become significant The current required to reverse the charge of the electrode causes a slight shift and distortion of the Franck Hertz curve An XY recorder is recommended for recording the Franck Hertz curve a Manual measurement Set the operating mode switch to MAN and slowly in crease U2 by hand from 0 V to 30 V Read voltage U2 and current fa from the display use the selector switch to toggle between the two quantities for each voltage b Representation on the oscilloscope Connect output sockets U2 10 to channel II 0 5 V DIV and output sockets Up to channel 2 V DIV of the oscillo scope Operate the oscilloscope in XY mode Set the operating mode switch on the Franck Hertz supply unit to Sawtooth Set the Y position so that the top section of the curve is displayed completely c Recording with the XY recorder Connect output sockets U2 10 to input X 0 2 V cm CAL and output sockets UA to input Y 1 V cm CAL of the XY recorder Set the operating mode switch on the Franck Hertz supply unit to RESET LEYBOLD Physics Leaflets P6 2 4 1 Adjust the zero poin
162. ntecimentos n o s o simult neos 2 Uma barra move se da esquerda para a direita Quando a extremidade esquerda passa por uma m quina fotogr fica tira se uma fotografia juntamente com uma r gua estacion ria Depois de revelada a fotografia v se que a extremidade esquerda coincide com o zero e a direita com 0 90 m da r gua Se a barra se mover a 0 8c relativamente m quina fotogr fica calcular o verdadeiro comprimento da barra so Uma fonte luminosa localizada a 30 km de um observador emite um flash que detectado pelo observador uma da tarde Qual o instante em que o flash foi emitido 4 Verificar que a equa o de uma onda electromagn tica 2 2 2 2 26 96 DP 19 79 4 dx dy dz e at invariante sob as transforma es de coordenadas de Lorentz 5 Uma part cula que se move com velocidade 0 8c no laborat rio decai ap s ter percorrido 3m Quanto tempo existiu essa part cula antes de decair 43 6 Um flash emitido no ponto x 100 km y 10 km z 1 kmet 5x 10 s Determinar as coordenadas x y z t deste acontecimento para um observador O que se move relativamente a O com velocidade v 0 8c 1 7 Uma part cula move se relativamente a O com velocidade constante c 2 no plano x y fazendo a sua traject ria num ngulo de 60 com o eixo x Sabendo que O se move relativamente a O com velocidade 0 6c na direc o x x obter as
163. ntes dada pela lei de Bragg n 2dsin6 comn 1 23 onde 9 o ngulo entre o feixe de electr es e os planos da rede 4 d 7 Figura 2 Planos de tomos na grafite Figura 3 Os feixes difractados pelos dois associados aos primeiros dois aneis de planos de tomos est o interfer ncia em fase e interferem construtivamente se a distancia ABC 2 d sin for igual a um n mero inteiro de comprimentos de onda isto se nA 2dsin 8 A amostra de grafite policristalina estando os diferentes cristais orientados de forma aleat ria O ngulo de Bragg O pode ser determinado a partir do ngulo de desvio amp do feixe ver Figuras 4 e 6 sendo o 2 0 130 plano de tomos a Figura 4 O ngulo de Bragg o ngulo entre o feixe de electr es e um plano tomos em condi es de interfer ncia construtiva o ngulo de desvio a correspondente a um m ximo de interfer ncia o dobro do ngulo de Bragg o 2 0 Da fig 6 temos sin 20 r R 2r D onde D 127 mm a dist ncia nominal entre a amostra de grafite e a parede do tubo onde se encontra o ecr fluorescente Para ngulos pequenos sin 20 2 sing 2 sin 2 0 4 sing Assim nA dr D A grafite tem uma estrutura hexagonal na qual poss vel encontrar v rias dist ncias interplanares d ver Fig 5 Os dois valores de d mais elevados s o d 0 213 nm e dz 0 123 nm representados na Fig 2 Para cada ordem n de difrac o e
164. o das mesmas ou apenas para observa o dos aparelhos envolvidos nos trabalhos pr ticos 4 Conte dos 4 1 Programa da disciplina Parte I Introdu o Teoria da Relatividade Restrita 1 Revis o das leis da Mec nica Newtoniana 1 1 Refer nciais de in rcia 1 2 Transforma o de coordenadas de Galileu 1 3 Invari ncia das leis de Newton 1 4 Princ pio da relatividade de Galileu 1 5 Electromagnetismo e relatividade Newtoniana 2 Os postulados de Einstein 2 1 O espa o absoluto e o ter 2 2 A experi ncia de Michelson Morley 2 3 Tentativa de preservar o conceito de ter hip tese da contrac o dos espa os hip tese do arrastamento do ter A aberra o das estrelas A experi ncia de Fizeau 2 4 Os postulados de Einstein e a origem da Teoria da Relatividade 3 Cinem tica Relativista 3 1 Sincronismo e simultaneidade 3 2 Dedu o das transforma es de Lorentz para as coordenadas do espa o e do tempo de um acontecimento 3 3 Consequ ncias das transforma es de Lorentz invari ncia das equa es do Electromagnetismo relatividade do intervalo de tempo entre dois acontecimentos e do conceito de simultaneidade 3 4 Medidas relativistas de comprimentos a contrac o dos espa os 3 5 Medidas relativistas de tempos a dilata o do tempo 3 6 O paradoxo dos g meos 3 6 O conceito de espa o tempo 3 7 O espa o tempo de Minkowski como espa o euclideano a 4 dimens es 3
165. o do tempo sofrida pelos rel gios em movimento 9 Realiza o da experi ncia Coeficiente de temperatura das linhas Mossbauer e o paradoxo dos g meos O efeito de temperatura um desvio na frequ ncia de resson ncia de uma linha de absor o devido ao efeito de Doppler de segunda ordem que se relaciona com o atraso de um rel gio at mico numa amostra aquecida devido ao movimento t rmico relativo ao rel gio de refer ncia no laborat rio De acordo com a teoria da relatividade esse efeito da ordem de 10 como referido anteriormente pequeno mas acess vel espectroscopia de Mossbauer A estrat gia da experi ncia a seguinte a operar o espectr metro em muito alta dispers o e calibr lo medindo a separa o entre os dois picos centrais do Fe b medir o desvio fraccional na posi o AE E do pico nico do a o inox entre a temperatura ambiente Te T AT c comparar o resultado com a teoria de Josephson Material a utilizar 1 folha de ferro met lica 2 folha de a o inox 3 forno 4 controlador de temperatura e termopar Procedimento 1 Reduzir a velocidade do motor de modo a que as duas componentes centrais do espectro do Fe estejam separadas digamos de 400 canais i e 70 aumentar a dispers o do espectr metro para que o pequeno efeito de temperatura seja capaz de provocar um desvio de v rios canais nos centr ides das linhas Calibrar a escala de velocidades com a folha de ferro me
166. o endere o http jersey uoregon edu vlab prf PRF_plugin html Tamb m no endere o http infrared als Ibl gov calculators bb2001 html se pode calcular a emiss o do corpo negro em fun o do comprimento de onda a partir do tamanho e temperatura do corpo O applet http webphysics davidson edu alumni MiLee java ob_mjl htm visualiza os resultados previstos pela lei de Stefan Boltzmann Estabelece se a temperatura do corpo negro e pode se ver uma simula o do espectro a cores Ainda em http Awww mhhe com physsci astronomy applets Blackbody applet files BlackBody htm l temos a visualiza o do espectro do corpo negro em fun o da temperatura Pode tamb m visualizar se a luminosidade estelar e seu tamanho em fun o do raio estelar Uma simula o de batimentos de uma onda pode se encontrar em http Avww walter fendt de ph1 te beats htm podendo se variar as frequ ncias das ondas envolvidas Ainda sobre batimentos temos simula es com tambores simula o sonora e osciladores mostrando as equa es matem ticas das ondas em http faraday physics utoronto ca PVB Harrison Flash ClassMechanics Beats Beats html Em http theory uwinnipeg ca Its java_phys html podemos visualizar o modelo do tomo de Bohr com os niveis de energia e simular experi ncias sobre interfer ncias de ondas que demonstram o princ pio da dualidade onda part cula Pode se ainda simular as rbitas do tomo de hidrog nio segundo a teoria de Bohr usando
167. o modelo de part cula ou o de onda em http www walter fendt de ph11e bohrh htm 20 A explica o montagem da experi ncia e visualiza o do efeito fotoel ctrico com v rios elementos como c todo pode ser feita em http Avww walter fendt de phi te photoeffect htm Ainda sobre o efeito fotoel ctrico pode se encontrar um applet em http www ifae es xec phot2 html mostrando o efeito da luz em v rios metais Simula es sobre a intera o da radia o com a mat ria podendo escolher se o tipo de intera o efeito fotoel ctrico efeito de Compton ou produ o de pares podem ser encontradas em http faraday physics utoronto ca PVB Harrison Flash Nuclear XRaylnteract XRaylnteract html Ainda sobre o efeito fotoel ctrico pode se visualizar em http www sc ehu es sbweb fisica a experi ncia mostrando a depend ncia da energia cin tica dos electr es emitidos em rela o intensidade da luz incidente e depend ncia do material do emissor Este site bastante interactivo encontrando se a muitas outras simula es relativas a outros temas da Mec nica Qu ntica e ao Movimento Ondulat rio A visualiza o da lei do decaimento radioactivo pode ser feita em http www walter fendt de ph1 le lawdecay htm http www phy ntnu edu tw ntnujava viewtopic php t 291 e http faraday physics utoronto ca P VB Harrison Flash Nuclear Decay NuclearDecay html 6 Bibliografia Todos os livros aqui indica
168. odo que de c sio Quanto tempo demorar at se ter igual quantidade dos dois is topos Ao fim de quanto tempo ser o as duas actividades iguais 20 O carbono 14 decai por emiss o B emiss o de electr es sendo o seu per odo de meia vida t 5730 anos a Escrever a reac o que traduz o decaimento do E Cx b Uma amostra de carv o produzido por queima de madeira recente tem cerca de 1 tomo de C 10 tomos de TC Calcular a actividade em becquerel Bg e em desintegra es minuto de uma amostra de 1 grama de carbono natural recente Determinar a actividade desta amostra decorridos 200 anos 600 anos e 10000 anos 21 O is topo pot ssio 40 E K usado na data o geol gica tendo como base o seu decaimento para rgon 40 z Ar sendo de 1 25 x 109 anos o seu per odo meia vida A an lise feita a um fragmento de rocha mostrou que a raz o entre o n mero de tomos de rgon e o n mero de tomos de pot ssio era igual a 10 3 Supondo que todos os tomos de rgon presentes resultaram do decaimento de tomos de pot ssio determinar a idade prov vel desta rocha 22 Quando um n cleo no estado excitado emite fot es recua no sentido oposto ao da emiss o do fot o 59 a O n cleo Co decai por captura electr nica para o ZF e o qual emite depois um fot o de 14 4 keV ao atingir o estado fundamental A massa do tomo sa Fe 9 5x10 kg Qual a redu o da energia do fot o devido ao
169. of the filament Equipment Recommended AC DC LV Power Supply SF 9584 or equivalent capable of 13 V 3 A max R Ry T EE Elg a ref For small temperature changes the temperature of the tungsten filament can be calculated using a the temperature coefficient of resistivity for the filament T Temperature R Resistance at temperature T T Reference temperature usually room temp R Resistance at temperature T a Temperature coefficient of resistivity for the filament amp 4 5 x 10 K for tungsten For large temperature differences however a is not constant and the above equation is not accurate PASC O scientific 95 Banana Connectors Connect to Power Supply 13 V MAX 2 A min 3 A max TD 8555 STEFAN BOLTZMAN LAMP CAUTION AP Figure 3 Stefan Boltzmann Lamp REPLACEMENT BULB GE Lamp No 1196 available at most auto parts stores NOTE When replacing the bulb the leads should be soldered to minimize resistance For large temperature differences therefore deter mine the temperature of the tungsten filament as follows Accurately measure the resistance R p of the tung sten filament at room temperature about 300 K Accuracy is important here A small error in R will result in a large error in your result for the fila ment temperature When the filament is hot measure the voltage and current into the filament and di
170. ometer When using a bright spectral light source such as the PASCO Mercury Vapor Light Source or the Low Pressure Sodium Light Source cover the source with an opaque cloth hood to block out ambient light Cover the light source opening with a mask that has a 0 5 to 1 0 cm wide rectangular slot in it to reduce ghost Collimating Slits images Use clothespins or binder clips to attach the edge a of the cloth hood to the plate on the Collimating Slits is re Fig 20 4 bay Fig sunlight Figure 20 Mask the Light Source When measuring solar spectra put an opaque cloth hood over the entire Spectrophotometer so that the only open ing to the sunlight is the Collimating Slit Use clothespins or binder clips to attach the edge of the cloth hood to the plate on the Collimating Slits Use one hand to hold up Figure 21 Mask the Spectrophotometer the center of the cloth hood Fig 21 Using the ScienceWorkshop Program Note See the ScienceWorkshop User s Guide for detailed information about using the ScienceWorkshop program 1 Start ScienceWorkshop Select the Light Sensor to be connected to Analog Channel A and select the Rotary Motion Sensor to be connected to Digital Channels 1 and 2 2 In ScienceWorkshop set the Rotary Motion Sensor so it can record 1440 divisions per rotation 3 In the program select a Graph display and set it to show Light Intensity max on its vertical axis 4 Use the
171. ometer in Michelson or lowing technique canhelp Fabry Perot mode Turn the micrometer knob as you g count off at least 20 fringes Carefully note the change in Center the interference the micrometer reading and record this value as d The pattern on the viewing actual mirror movement d is equal to N2 2 where is screen using the thumb the known wavelength of the light 0 6328 um for a Screws On the back of the fo standard helium neon laser and N is the number of fringes fixed mirror Select a ref that were counted In future measurements multiply your erence line on the milli micrometer readings by d d for a more accurate measure meter scale and line it up ment with the boundary be faye eee and a Fi 9 NOTE You can also adjust the micrometer minima see Figure 9 igure 7 rir g f Counting Fringes calibration mechanically The process isnot difficult Move the micrometer dial but for most accurate results the above procedure is until the boundary between the next maximum and minimum reaches the same position as the original boundary The fringe pattern should look the same as in the original position One fringe has gone by still recommended See the Maintenance section at the end of the manual for the mechanical calibration procedure 3 When turning the micrometer dial to count fringes al Demonstrations ways turn it one complete revolution before you start counting
172. on along the axis of the Optics Bench Be sure that the Microscope stays flush against the fence of the Optics Bench If this doesn t work re check the alignment beginning with step 1 20 Bring the cross hairs of the microscope into focus by sliding the microscope eyepiece up and down 21 Focus the microscope by loosening the lock screw and sliding the scope up and down If the appara tus is properly aligned you will see the point im age through the microscope Focus until the image is as sharp as pos sible Tissue paper N Lock serew Micrometer knob Lever for adjusting Figure 13 Looking the for the Beam Image beamsplitter angle Speed of Light 012 07135B Lo Ns 1 or 2 Figure 12 Turning L Slightly Askew to Clean Up the Image Alignment Summary IMPORTANT In addition to the point image you may also see some extrancous beam images resulting for example from reflection of the laser This summary is for those who are familiar with the beam from L To be sure you are observing the equipment and the experiment and just need a quick right image point place a piece of paper between reminder of the steps in the alignment procedure If you M and M while you watch the image in the have not successfully aligned the apparatus before we microscope If the point does not disappear it is not recommend that you take the time to go through the the correct image detailed ali
173. ontrol This experiment investigates the energy acceleration voltage in the Franck Hertz experiment with mercury oss of free electrons due to inelastic scattering and thus due schematic representation to collision excitation of mercury atoms 1105 Sel 186 P6 2 4 1 LEYBOLD Physics Leaflets Apparatus 1 Franck Hertz tube Hg Socket for Franck Hertz tube Hg with multi pin plug 1 Electric oven 220 V Franck Hertz supply unit Temperature sensor NiCr Ni 555 861 555 81 555 88 666 193 Recommended for optimizing the Franck Hertz curve Two channel oscilloscope 303 575211 2 Screened cables BNC 4 mm Recommended for recording the Franck Hertz curve XY Yt recorder SR 720 Connecting leads 575 663 The glass tube contains a cylindrically symmetrical system of four electrodes see Fig 1 The cathode K is surrounded by a grid type control electrode G4 at a distance of a few tenths of a millimeter an acceleration grid Gz at a somewhat greater distance and finally the collector electrode A outermost The cathode is heated indirectly in order to prevent a potential differential along K Electrons are emitted by the hot electrode and form a charge cloud These electrons are attracted by the driving potential U between the cathode and grid G4 The emission current is practically independent of the acceleration voltage Us between grids G4 and Go if we ignore the inevitable punch through A braking voltage U3 is p
174. or and the beam splitter by looking at the virtual images of the beam path as shown in Figure 3 S Virtual Me kes image of s i M Beamsplitter F a Ma L A l A EAS AST downto ve VY Al Ss 5 s E be As D B A Figure 3 Analyzing the Virtual Images The critical geometry of the virtual images is the same as for the reflected images Looking at the virtual images the problem becomes a simple application of thin lens optics With M at angle point S is on the focal axis of lens L Point S is in the focal plane of lens L but it is a distance AS S S away from the focal axis From thin lens theory we know that an object of height AS in the focal plane of L will be focused in the plane of point s with a height of i o AS Here i and o are the distances of the lens from the image and object respectively and the minus sign corresponds to the inversion of the image As shown in Figure 3 reflection from the beam splitter forms a similar image of the same height IPAS CC 012 07135B Speed of Light Therefore ignoring the minus sign since we aren t concerned that the image is inverted we can write an expression for the displacement As of the image point ay ee oo oA As As i o AS D B AS EQ2 Combining equations 1 and 2 and noting that AS S S the displacement of the image point relates to the initial and secondary positions of M by the formula 2D
175. os da Universidade da Virg nia encontram se em http rockpile phys virginia edu 252 html Entre outros encontram se apontamentos sobre Relatividade Restrita Ondas e Part culas e Teoria Qu ntica da Radia o Electromagn tica Tem em particular uma discuss o muito boa sobre as Transforma es de Lorentz H tamb m muitos problemas n o resolvidos Ainda da Universidade da Virg nia encontra se no endere o http galileo phys virginia edu classes 252 home html um curso que engloba Relatividade Restrita Introdu o F sica Qu ntica Ondas e Part culas tomos e Introdu o F sica Nuclear Este endere o tem tamb m apontadores para muitos exerc cios n o resolvidos e pontos de exame Tutoriais na Web sobre Teoria da Relatividade encontram se em http math ucr edu home baez RelWWW tutorial html Este endere o indica tamb m outros portais populares Um endere o mais geral o Relativity on the World Wide Web http math ucr edu home baez relativity htm http www2 slac stanford edu vvc theory relativity html um site com os conceitos b sicos da Teoria da Relatividade Restrita Em Hyperphysics http hyperphysics phy astr gsu edu hbase hframe html encontra se uma esp cie de Enciclop dia da Fisica que cobre v rias reas de entre as quais as 17 escolhidas para esta disciplina Como exemplos encontram se os seguintes portais http hyperphysics phy astr gsu edu hbase rutsca html c1 que explica a
176. other functions well filtered DC voltages are always required The individual voltage ranges and values are also reproduced in Fig 3 All voltages apart from the anode voltage can be taken from a universal power supply 11725 93 The anode current should not far exceed 1 mA Therefore a limiter resistor of some 10 MQ e g 10 Mg resistor with plug and socket Order no 07160 00 should generally be wired in front of the anode If a HV unit with short circuit current lt 1 mA is used to provide the anode voltage e g HV power supply 25 kV Order no 11730 93 then a limiter resistor is not required The HV cable coupled firmly to the anode has dialectric strength so that no special conductor lead is required If HV power supply 11730 93 is used no separate earthing of the cathode is needed as the negative pole on the unit has a zero potential i For all the experiments described in Paras 4 and 5 the following initial setting based on the cathode should be selected for the grid voltages any further adjustment then depends on the aim of each experiment Wehnelt cylinder Grid Gj 25 V Grid Gj 250 V Anode Grid G3 10 kV Grid Gq approx 250 V 4 DIFFRACTION OF THE GRAPHITE ELECTRONS ON The graphite layer on the diffraction film is made up of many micro crystals which are spatially randomly oriented Each crystal shows the typical structure for graphite The two largest grid level distances
177. otion Sensor for high resolution 1440 Divisions per Rotation and set the sample rate to 20 Hz or 20 measurements per second PASCO scientific 160 012 06575A Educational Spectrophotometer 3 In the ScienceWorkshop program use the Expression for the Angular Position Divide by 60 if the small Calculator to create a calculation of Actual of the Rotary Motion Sensor post of the Pinion is used or Angular Position based on the Angular Posi poe moa eaae soie tion measurement made by the Rotary Motion l Sensor and the ratio of the radius of the 1 angPos 60 NOTE The Experiment Spectrophotometer s Degree Plate to the ra Galeiilator for your version dius of the small post on the Pinion Fig 1 3 ue emu no Jow IN oF science Workshop may Refer to the Set Up section for more informa ma Calculation Name differ in appearance Refer tion aA actual Angular Position JE to your User s Guide El Short Name Units Select the Display LJ rec Refer to the User s Guide for your version of Figure 1 3 Create a Calculation ScienceWorkshop for detailed information on displays 1 Select a Graph display 2 Set the axes of the Graph display so Light Intensity is on the vertical axis and Actual Angular Position is on the horizontal axis Prepare to Record Data Refer to the User s Guide for your version of ScienceWorkshop for detailed information on monitor
178. ount Once the light from the source is collimated attach the Grating to the Grating Mount so that the glass side of the Grating faces the light source Fig 18 Mounting and Positioning the Focusing Lens The Degree Plate has markings on either side of the Light Sensor Arm that indicate the appoximate position in which to place the Focusing Lens The Focusing Lens has two small magnets in its base that hold it in place on top of the Light Sensor Arm Place the Focus ing Lens on the Light Sensor Arm between the Grating Mount and Figure 18 Grating Onto Mount the High Sensitivity Light Sensor The Focusing Lens focal length is about 10 cm so the lens should be positioned on the Light Sensor Arm about 10 cm from the front of the Aperture Disk Fig 19 Set up the light source Collimating Slits and Collimating Tens so a beam of light shines through the Grating and Focusing Lens Darken the room so you can see the spectral lines more clearly Move the Light Sensor Arm so the central ray of light called the zeroth order is centered on the slit at the bottom of the Aperture Disk You should be able to see the first order spectral lines on the Aperture Screen on either side of the central ray of light Adjust the position of the Focusing Lens until the spectral lines are sharply focused Note Because the Grating is strongly blazed the spectral lines on one side of the central ray zeroth order will be less
179. ovimento relativista Equa o fundamental da din mica relativista Varia o da massa com a velocidade N o proporcionalidade entre for a e acelera o Rela o entre massa e energia de um corpo a obten o da equa o E mc Energia de repouso Energia cin tica relativista e sua validade no limite cl ssico Rela o entre energia e quantidade de movimento 12 7 li o Transforma es de Lorentz para a energia total de um corpo e para as componentes da sua quantidade de movimento Transforma es de Lorentz para as componentes de uma for a Conserva o da energia e da quantidade de movimento Aplica o ao estudo do choque de duas part culas de massas iguais em dois referenciais distintos Introdu o teoria da Relatividade Geral O Princ pio da Equival ncia de Einstein Massa de in rcia e massa grav tica O desvio gravitacional para o vermelho Resultados obtidos em laborat rio pela espectroscopia de M ssbauer A experi ncia de Pound e Rebka Previs es de Josephson Buracos negros e raio de Schwarzchild A curvatura do espa o em teoria da Relatividade Geral 8 li o Introdu o F sica Qu ntica Radia o e radiadores Espectros de emiss o e de absor o Espectros de radia o t rmica Absorvilidade e emissividade O corpo negro ideal e o espelho ideal A radia o t rmica A teoria de troca de Pr vost Radia o do corpo negro Radi ncia espectral Lei de Stefan Boltzmann e
180. p tese pequenas e que se traduzem numa incerteza de medida que habitualmente se designa por Sa Isto de facto ak E Gk Faz Gk Fa Se repetirmos a medi o por for a dessas flutua es n o obteremos sempre o mesmo valor para a mas quantidades que se situam em geral no intervalo de incerteza Sendo por hip tese a vari veis independentes haver sempre um conjunto de vari veis independentes e sendo as flutua es inerentemente furtuitas ent o estas n o v o certamente todas no mesmo sentido em cada momento sendo por isso zero em m dia cada um dos produtos cruzados da da com k js Por conseguinte n o estando as vari veis por nenhuma forma correlacionadas ent o a incerteza ou erro em f que designaremos por o deve ser dada por N 2 3 5 52 02 4 dar onde ca a incerteza na vari vel ap com k 1 N e N o n de vari veis Exemplo Para obter o volume de um cilindro mediu se o raio da base e a altura tendo se obtido r 50 1 em eh 200 1 em respectivamente Qual a incerteza na determina o do volume V Sendo V V r h mr2h da eq 4 vem oy avy o2 24 2 yy a Por conseguinte tem se V nr h y 2rrh o2 ar 2o2 o que neste caso d V 1571 63 1Pois umas vezes day e da t m sinais opostos em outras n o considerando a soma de todas as combina es de valores obtemos certamente zero Por m se as vari veis estiverem de algum
181. peed of light being what it is and human reaction times being what they are Galileo was able to determine only that the speed of light was far greater than could be measured using his procedure Although Galileo was unable to provide even an approximate value for the speed of light his experiment set the stage for later attempts It also introduced an important point to mea sure great velocities accurately the measurements must be made over a long distance R mer The first successful measurement of the velocity of light was provided by the Danish astronomer Olaf R mer in 1675 R mer based his measurement on observations of the eclipses of one of the moons of Jupiter As this moon orbits Jupiter there is a period of time when Jupiter lies between it and the Earth and blocks it from view R mer noticed that the duration of these eclipses was shorter when the Earth was moving toward Jupiter than when the Earth was moving away He correctly interpreted this phenomena as resulting from the finite speed of light Geometrically the moon is always behind Jupiter for the same period of time during each eclipse Suppose however that the Earth is moving away from Jupiter An astronomer on Earth catches his last glimpse of the moon not at the instant the moon moves behind Jupiter but only after the last bit of unblocked light from the moon reaches his eyes There is a similar delay as the moon moves out from behind Jupiter but since the E
182. pends only on the difference in the angular position of M in the time it takes for the light to travel between the mirrors The displacement does not depend on the specific mirror angles for any given pulse If we think of the continuous laser beam as a series of infinitely small pulses the image due to each pulse will be displaced by the same amount All these images displaced by the same amount will of course result in a single image By measuring the displacement of this image the rate of rotation of M and the relevant distances between components the speed of light can be measured Speed of Light 012 07135B The Equipment What You Need to Measure the Speed of Light In order to measure the speed of light as described in this SE 9367 0 5 mW He Ne Laser manual you will need all the items listed below see Tigure 4 If you have an OS 9261 Complete Speed of Light Apparatus everything is included If you have the e OS 9172 Laser Alignment Bench OS 9262 Basic Speed of Li ght Apparatus or the OS OS 9142 Optics Bench Couplers 9263A High Speed Rotating Mirror you will need e OS 9103 One Meter Optics Bench additional components as listed to make the measure O8S 9133 Lens 48 mm FL ment OS 9135 Lens 252 mm FI The OS 9261 Complete Speed of Light Apparatus e OS 9109 Calibrated Polarizers 2 includes k OS 9107 Component Holders 3 e OS 9262 Basic Speed of Light Apparatus which includes e O
183. per unit area radiated by an object to T the absolute temperature of the object The equation is R 06T e 5673 x10 m K In this experiment you will make relative measurements of the power per unit area emitted from a hot object namely the Stefan Boltzmann Lamp at various temperatures From your data you will be able to test whether the radiated power is really proportional to the fourth power of the temperature Most of the thermal energy emitted by the lamp comes from the filament of the lamp The filament temperature can be determined using the procedure given on pages 3 and 4 of this manual Ammeter Power Supply 13 V MAX Millivoltmeter Voltmeter Figure 3 1 Equipment Setup IZEN 13 scientific 103 Thermal Radiation System 012 04695D Procedure IMPORTANT The voltage into the lamp should NEVER exceed 13 V Iligher voltages will burn out the filament O BEFORE TURNING ON THE LAMP measure T p the room temperature in degrees Kelvin K C 273 and Rir the resistance of the filament of the Stefan Boltzmann Lamp at room temperature Enter your results in the spaces on the following page Set up the equipment as shown in Figure 3 1 The voltmeter should be connected directly to the binding posts of the Stefan Boltzmann Lamp The Sensor should be at the same height as the filament with the front face of the Sensor approximately 6 cm away from the filament The en
184. podem se fazer anima es sobre velocidades de grupo e de fase de uma onda Visualiza es de figuras de interfer ncia na difrac o de electr es por dupla fenda podem ser feitas em http www upscale utoronto ca PVB Harrison DoubleSlit Flash Histogram html e http Avww upscale utoronto ca PVB Harrison DoubleSlit Flash DoubleSlit html O applet http Avww walter fendt de ph1 1 e interference htm mostra a interfer ncia de 19 duas ondas circulares provenientes de fontes que oscilam com a mesma fase Ainda em _http Awww quantum physics polytechnique fr se encontram anima es sobre a dualidade onda particula em mec nica qu ntica simulando a experi ncia de Young com fot es ou part culas Em www manole com br fisicamoderna est dispon vel a simula o da experi ncia de difrac o de electr es de Thomson Uma simula o bastante interactiva da experi ncia de difrac o de raios X encontra se em http www eser stonybrook edu projectjava brage index html e onde se mostram os difractogramas obtidos numa experi ncia Para fazer uma simula o de espectros de emiss o fazendo incidir um feixe paralelo de radia o num prisma consultar http micro magnet fsu edu primer java scienceoptics newton Para ver os espectros de emiss o e de absor o dos diversos elementos do Quadro Peri dico consultar http jersey uoregon edu viab elements Elements html Pode se visualizar a distribui o espectral de um corpo negro n
185. r 137 50 l 116 012 04049J h e Apparatus and h e Apparatus Accessory Kit Introduction The emission and absorption of light was an early subject for investigation by German physicist Max Planck As Planck attempted to formulate a theory to explain the spectral distribution of emitted light based on a classical wave model he ran into considerable difficulty Classical theory Rayleigh Jeans Law predicted that the amount of light emitted from a black body would increase dramati cally as the wavelength decreased whereas experiment showed that it approached zero This discrepancy became known as the ultraviolet catastrophe Experimental data for the radiation of light by a hot glowing body showed that the maximum intensity of emitted light also departed dramatically from the clas sically predicted values Wien s Law In order to rec oncile theory with laboratory results Planck was forced to develop a new model for light called the quantum model In this model light is emitted in small discrete bundles or quanta The relationship between the classical and quantum theo ries for the emission of light can be investigated using the PASCO scientific h e Apparatus Using the Apparatus in combination with the PASCO Mercury Vapor Light Source Model OS 9286 allows an accurate determina tion of the h e ratio and thus a determination of h Planck s constant Figure 1 The h e Apparatus Shown With
186. r ncial preferencial A hip tese da contrac o dos espa os de Fitzgerald Lorentz A hip tese do arrastamento do ter 3 li o Contradi es hip tese do arrastamento do ter A aberra o das estrelas e a experi ncia de Fizeau 11 Os Postulados de Einstein invari ncia das leis da Fisica em todos os referenciais inerciais e a constancia da velocidade da luz no vacuo como principios da Teoria da Relatividade Restrita Sincroniza o de rel gios 4 li o Consequ ncias dos postulados de Einstein Deriva o das transforma es de Lorentz As transforma es inversas Algumas consequ ncia das transforma es de Lorentz Contrac o dos espa os e dilata o dos tempos A relatividade da simultaneidade Comprimento pr prio e tempo pr prio Invari ncia das equa es do Electromagnetismo 5 li o O paradoxo dos g meos O conceito espa o tempo A n o invari ncia do intervalo de tempo entre dois acontecimentos quando sujeitos a uma transforma o de Lorentz Diagramas espa o tempo O espa o de Minkowski Cones de luz de um acontecimento linhas do universo O diagrama espa o tempo para o paradoxo dos g meos A adi o de velocidades em teoria da Relatividade Restrita Dedu o das transforma es das velocidades Casos particulares 6 li o O efeito Doppler e Doppler Relativista Din mica Relativista A necessidade de redefinir quantidade de movimento Quantidade de m
187. r Base Degree Plate with Light Sensor Arm Grating Mount Grating 600 lines per mm Focusing Lens Collimating Lens Collimating Slits Cuvettes 2 Rod Stand Mounting Brackets 2 Grating Grating Mount A Rod Stand Mounting Clamps 2 Focusing Lens Collimating Slits Collimating Lens Cuvettes 2 9 Figure 1a Educational Spectrophotometer Accessory Kit The pinion shown in Figure la can be mounted on a post on the Spectrophotometer Base when not in use Recommended Equipment for use with the Spectrophotometer Accessory Kit Basic Optics System OS 8515 High Sensitivity Light Sensor CI 6604 Aperture Bracket OS 8534 Rotary Motion Sensor CI 6538 IZH 3 scientific 147 Educational Spectrophotometer 012 06575A Components of the System The OS 8539 Educational Spectrophotometer System includes the items in the Spectrophotometer Accessory Kit plus the following Optics Bench 60 cm Rotary Motion Sensor C1 6538 High Sensitivity Light Sensor CI 6604 Aperture Bracket OS 8534 Rotary Motion Sensor Aperture Bracket 4 Go DIN to DIN cable High Sensitivity Light Sensor Optics Bench 60 cm Aperture Bracket Holder Figure 1b Additional Components of the Spectrophotometer System Recommended Equipment for use with both the Kit and the System Light Source such as OS 9286 Mercury Light Large Rod Stand ME 8735 2 Rod 45 cm ME 8736 2 Description The Spectrophoto
188. r center of move ment movement through full distance of travel is linear to within 1 5 IMPORTANT Avoid touching all mirror surfaces Minute scratches and dirt can impair the clarity of interference images See the Maintenance section at the end of this manual for cleaning instructions Experi ncia de Franck Hertz Manuais da Leybold LEYBOLD Atomic and Nuclear Physics em Atomic shell Leaflets Franck Hertz experiment Franck Hertz experiment with mercury Recording with the oscilloscope the XY recorder and point by point Objects of the experiment H Jorecord a Franck Hertz curve for mercury E To measure the discontinuous energy emission of free electrons for inelastic collision HM To interpret the measurement results as representing discrete energy absorption by mercury atoms Principles n 1914 James Franck and Gustav Hertz reported an energy joss occurring in distinct steps for electrons passing through mercury vapor and a corresponding emission at the ultraviolet ine A 254 nm of mercury Just a few months later Niels Bohr recognized this as evidence confirming his model of the atom The Franck Hertz experiment is thus a classic experiment for confirming quantum theory na previously evacuated glass tube mercury atoms are held at a vapor pressure of about 15 hPa which is kept constant by The electron current flowing to the collector as a function of the temperature c
189. r knob pointing toward you 2 Position the laser alignment bench to the left of the base approximately perpendicular to the interferometer base and place the laser on the bench 181 3 Secure the movable mirror in the recessed hole in the interferometer base 4 Turn the laser on Using the leveling screws on the la ser bench adjust its height until the laser beam is ap proximately parallel with the top of the interferometer base and strikes the movable mirror in the center To check that the beam is parallel with the base place a piece of paper in the beam path with the edge of the paper flush against the base Mark the height of the beam on the paper Using the piece of paper check that the beam height is the same at both ends of the bench 5 Adjust the X Y position of the laser until the beam is reflected from the movable mirror right back into the laser aperture This is most easily done by gently slid ing the rear end of the laser transverse to the axis of the alignment bench as shown in Figure 5 You are now ready to set up the interferometer in any of its three modes of operation 012 07137A Laserbeam je Movable mirror Slide the rear of the laser laterally on the alignment bench until the beam is reflected straight back into the HL laser aperture qa Figure 5 Aligning the Laser gt NOTE For ease of installation the placement of the individual components in the vario
190. raction tube X rays are produced As defined by the regulations with regard to protection against damage by ionising rays 13th October 1976 Regulations on Radiation Protection and the regula tions with regard to protection against damage by X rays of lst March 1973 Regulations on X rays the electron diffraction tube emits hazardous rays Clause 5 2 of the regulations on X rays states how the instrument should be handled Since under operating conditions maximum operating voltage Ua 12 kV the localised emission of X rays at a distance of 5 cm from the surface of the instrument is less than 36 pA kg the electron diffraction tube can be used in the lecture room without hesitation and without any special measures to protect against radiation The legislation demands no design permit The instrument can be used without special permission from or noti fication to authorities It should however be pointed out in this connection that if the maximum operating voltage of 12 kV is exceeded not only could the instrument be Acceleration voltage damaged but the radiation emission filtered 250 V becomes unacceptably high Anode voltage filtered 2 to 12 kV 9 EXPERIMENT LITERATURE Anode current lt 1 mA Experiments in Physics Wave Particle Dualism Focussing voltage Order No 16052 41 filtered 0 to 250 V University Laboratory Experiments Physics 11 EQUIPMENT LIST Part 2 Order No 16500 41 The mo
191. rdo com a Fig 1 A resist ncia de 220 assegura que a corrente no LED n o excede os 50 mA respeitando os limites de seguran a 2 Encontre a curva caracter stica para o LED verde apresente uma tabela com os valores medidos de tens o V e corrente 7 com a indica o das respectivas unidades fa a um gr fico de In J em fun o de V n o se esque a de converter a corrente de mA para A 3 A express o te rica que relaciona a corrente com a tens o cue a ashlee atear 111 em que Ip e n s o constantes caracter sticas de cada LED e a carga do electr o kB a constante de Boltzmann e T a temperatura ambiente em kelvin A express o aproximada v lida para V gt 2V O gr fico que obteve est de acordo com o que espera da express o te rica Justifique Fa a um gr fico de In I em fun o de V s com os pontos para os quais a express o aproximada v lida Determine o valor das constantes Ip e para o LED verde considere T 293 K 4 Ligue os LEDs em s rie e tamb m em s rie com a resist ncia de 11 4 kQ e aplique ao circuito a tens o de 9 V pode usar os crocodilos para fazer as liga es entre os LEDs de acordo com a Fig2 Registe a corrente que percorre o circuito Registe numa tabela o valor da tens o V nos terminais de cada LED bem como o valor do comprimento de onda tabela 1 e frequ ncia da radia o que cada um emite o valor para o LED verde determinado na
192. recuo do n cleo b H certos cristais aos quais os tomos est o ligados de tal modo que o cristal como um todo recua quando um fot o y emitido em vez do tomo isolado Este fen meno conhecido como efeito de M ssbauer Qual a redu o da energia do fot o nesta situa o se o n cleo E Fe fizer parte de 1 0 g de um tal cristal c emiss o sem recuo considerada na al nea anterior significa que poss vel construir uma fonte monoenerg tica emitindo fot6es monocrom ticos Uma fonte como esta foi usada na experi ncia de Pound e Rebka Qual a frequ ncia original e a varia o de frequ ncia de um fot o de energia 14 4 keV depois de cair 20m 60 Anexo B Folhas de Trabalhos Pr ticos Apresentam se nas p ginas seguintes folhas de trabalhos pr ticos gui es e manual com instru es do equipamento a ser usado para os alunos lerem e se poderem preparar para a execu o dos mesmos ao longo do semestre A maioria dos gui es apresentados foram coligidos por colegas do Departamento de F sica 1 Espectroscopia de M ssbauer eiee ee eot ie eee EEEE 63 2 Determina o da velocidade da luz pelo m todo de Foucault 73 3 Radia o TELM Casas saves Sida rumo postava OU shades EaD e aA Prom oa RREO Hola a so ova e Taa Seaia RG 91 4 D odos emissores de luz LED e a constante de Planck se i 109 5 Efeito fotoel ctrico e determina
193. repeat the data collection procedure Analyze the Data Refer to the User s Guide for your version of ScienceWorkshop for detailed information on using ScienceWorkshop for data analysis 1 Use the Graph display to examine the plot of Light Intensity versus Actual Angular Position for the first run of data GAIN select switch 1 2 Use the built in analysis tools to determine the angle of the first line in the spectral pattern and the angle of the matching line in the first order spectral pattern on the other side of the central ray 3 Determine the difference in angle between the two lines and use one half of the difference as the angle 0 to determine the wavelength of that color If you did not calibrate the Diffraction Grating assume d 1666 nm 4 Repeat the process for the other colors in the first order spectral pattern 5 Examine the plot of Light Intensity versus Actual Angular Position for your other two runs of data Look for other lines in the spectral pattern that may be too dim to record when the sensor was set to GAIN 1 Data Table Record your data here Color 0 0 AO 9 49 2 A dsin6 1 2 Conclusion 1 Compare your values for the wavelengths of color in the mercury vapor light spectrum to the accepted values for wavelengths Extensions Repeat the process for a different gaseous element such as hydrogen or helium a PASCO scientific 162 012 06575A Educational Spectrophotome
194. resent between grid Gz and the collector A Only electrons with sufficient kinetic energy can reach the collector electrode and contribute to the collector current In this experiment the acceleration voltage Uz is increased from 0 to 30 V while the driving potential U4 and the braking voltage Us are held constant and the corresponding collector current la is measured This current initially increases much as in a conventional tetrode but reaches a maximum when the kinetic energy of the electrons closely in front of grid Gg is just sufficient to transfer the energy required to excite the mercury atoms Ekg 4 9 eV through collisions The collector current drops off dramatically as after collision the electrons can no longer overcome the braking voltage Us As the acceleration voltage U2 increases the electrons attain the energy level required for exciting the mercury atoms at ever greater distances from grid Ga After collision they are accel crated once more and when the accclcration voltage is suffi cient again absorb so much energy from the electrical field that they can excite a mercury atom The result is a second maximum and at greater voltages U gt further maxima of the collector currents fp 187 0000000000 0 Fig 1 Schematic diagram of the mercury Franck Hertz tube Preliminary remark The complete Franck Hertz curve can be recorded manually For a quick overview e g for optimizing the experime
195. rid Gq is used to focus the electron beam providing with the anode an electron optic lens system The accelerated particles land on a film attached vertically to the optical axis This film consists of a copper mesh on which there is a layer of polycrystalline graphite As the particles penetrate this film they are deflected from their path to varying degrees and enter the spherical section of the electron tube see also Fig 5 Where the electrons reach the inner wall of the glass sphere they encounter a fluorescent layer In areas where individual electrons land in clusters on the fluorescent layer they produce a clearly visible luminescence due to the fluorescent rays 136 substance Fig 2 3 OPERATION The functional elements of the electron diffraction tube s beam emission system H K G to Gq connect with the correspondingly marked sockets on the mounting The tube and the mounting form one unit which should not be split If this does happen then care must be taken when the tube is re fitted that the small connecting pins are not bent It should also be noted that one of the sockets on the tube mounting is sealed so that the tube can only be plugged in in the correct way for the contact arrangement Fig 3 o Diffraction A Fig 3 shows the electrical wiring for the electron diffraction tube taking in a meter for the anode voltage An AC current is sufficient for the heating To power the
196. rodu o e aniquila o de pares 7 li o Absor o da radia o pela mat ria Produ o de raios X Ondas e part culas Resolu o de problemas Observa o da demonstra o da Experi ncia de Franck Hertz 8 li o Resolu o de problemas sobre o Princ pio de Incerteza e sobre o decaimento radioactivo Demonstra o da Experi ncia do Espalhamento de Rutherford 9 li o a 14 li o Realiza o de trabalhos pr ticos 15 li o Discuss o dos trabalhos pr ticos realizados pelos alunos nas aulas anteriores 16 5 Aplica es inform ticas dispon veis na Internet 5 1 Apontamentos e problemas de disciplinas afins de outras universidades Na Internet est o dispon veis in meros apontamentos e exerc cios muitos deles resolvidos sobre assuntos tratados nesta disciplina Escolheram se alguns endere os com essas aplica es com a finalidade de dar um panorama sobre o tratamento destas mat rias noutras universidades No endere o http student mit edu catalog m8a html 8 05 encontram se apontamentos do MIT sobre a Teoria da Relatividade Restrita nas li es de Relativity e de Introdu o F sica Qu ntica e de Ondas e Part culas nas li es de Quantum Physics T Tamb m do MIT se encontram apontamentos e muitos problemas resolvidos sobre Teoria da Relatividade Restrita no apontador sobre li es de Relatividade do endere o http Aveb mit edu 8 033 Apontament
197. rro Quais as coordenadas deste acontecimento determinadas pelo condutor e pelo maquinista Uma bola de massa 1kg move se na direc o Sul Norte com velocidade de 3 m s e colide elasticamente com uma bola igual que se encontra em repouso Ap s o choque o movimento ainda segundo a mesma direc o Calcular o momento linear e a energia do sistema antes e depois da colis o b Calcular o momento linear e a energia antes e depois do choque medidos por um c 8 9 observador que se desloca de Sul para Norte velocidade de 1 5 m s Efectuar o c lculo pedido na al nea b mas agora para um observador que se desloca para Este velocidade de 2 m s Uma massa m ligada a uma mola el stica de constante k move se sem atrito sobre uma superf cie horizontal Mostrar que a equa o do movimento para a massa m tem a mesma forma quer para um observador em repouso em rela o mesa quer para outro que se mova com velocidade constante na direc o paralela mola Considerar uma colis o el stica unidimensional que ocorre ao longo do eixo x x do referencial O Mostrar que pelas transforma es cl ssicas das equa es a energia cin tica tamb m se conserva quando determinada por um segundo observador O que se mova com velocidade constante u ao longo do eixo x x de O 10 Mostrar que a equa o de uma onda electromagn tica 40 2 2 2 2 0 06 P 196 4 de O az e at n o invariante sob as tra
198. rror The Fixed Mirror is a spherical mirror with a radius of curvature of 13 5 meters It is mounted to a stand and has separate x and y alignment screws 4 OS 9103 Optics Bench The 1 0 meter long Optics Bench provides a flat level surface for aligning the optical components The bench is equipped with a one meter scale four leveling screws and a magnetic top surface The fence a raised edge on the back of the bench provides a guide for aligning components along the optical axis 5 SE 9367 Laser with the OS 9172 Alignment Bench The 0 5 mW TEM mode random polarization laser has an output wavelength of 632 8 nm The Alignment Bench attaches to the Optics Bench for precise stable position ing of the laser 6 Alignment Jigs 2 These jigs mount magnetically to the Optics Bench Each has a 2 mm diameter hole that is used to align the laser beam 7 Optical Components The use of the lenses and polarizers is described in the Setup and Alignment section of the manual Speed of Light 012 07135B Setup and Alignment The following alignment procedure is tailored for those using the OS 9261 A Complete Speed of Light Apparatus For those using only some of the compo nents in the complete system the general procedure is the same though the details depend on the optical components used Figure 6 Placing Components gt IMPORTANT Proper alignment is critical Flush Against the Fence not o
199. ry Concepts and Basic Principles Amos Harpaz Author and Eric Sheldon Am J Phys 61 762 1993 56 Newton to Einstein Ralph Baierlein Author and N David Mermin Am J Phys 61 188 1993 57 An elementary derivation of E mc Fritz Rohrlich Am J Phys 58 348 1990 58 Michelson Morley analysis V S Soni Am J Phys 57 1149 1989 59 E mc Mitchell J Feigenbaum and N David Mermin Am J Phys 56 18 1988 Introdu o Fisica Qu ntica 1 Complementarity in the Einstein Bohr photon box Dennis Dieks and Sander Lam Am J Phys 76 838 2008 2 Planets on the table A laboratory experiment on radiation and planetary effective temperature concepts Oleksandr Karabanov James C St John and William Chameides Am J Phys 76 692 2008 3 Revisiting the radiation from a suddenly moving sheet of charge J M Chung Am J Phys 76 133 2008 4 The wave particle duality of light A demonstration experiment T L Dimitrova and A Weis Am J Phys 76 137 2008 5 A storm in a wineglass Stephan V Joubert Temple H Fay and Esme L Voges Am J Phys 75 647 2007 6 Experimental demonstration of Doppler spectral broadening using the PC sound card A Azooz Am J Phys 75 184 2007 7 Revisiting the 1888 Hertz experiment Daniele Faccio Matteo Clerici and Davide Tambuchi Am J Phys 74 992 2006 8 Connecting linear momentum and energy for electromagnetic systems Timothy H
200. s AP 9368 x h e Apparatus Accessory Kit AP 9369 ia Mercury Vapor Light Source OS 9286 Installing the Batteries The h e Apparatus requires two 9 volt batteries supplied h e Apparatus AP 9368 but not installed The battery compartment is accessed by loosening the thumbscrew on the rear end panel and re moving the cover plate NOTE The h e Apparatus can also be powered using a 9 V dual power supply Just remove the Mercury Vapor light batteries and connect 9 V to the 6 V MIN bat Source 05 9286 tery test terminal and 9 V to the 6 V MIN bat tery test terminal ESSES mas Battery Voltage Check Although the h e Apparatus draws only a small amount of Lens Grating Light Aperture current and batteries normally last a long time it s a good Assembly Assembly idea to check the output voltage before each use Battery test points are located on the side panel of the Apparatus near the ON OFF switch Batteries functioning below the recommended minimum operating level of 6 volts may cause erroneous results in your experiments To check the batteries use a voltmeter to measure be tween the OUTPUT ground terminal and each BATTERY TEST terminal 6V MIN and 6V MIN If either battery tests below its minimum rating it should be replaced before running experiments Support Base Assembly Battery Test Terminals a Light Block for Light Source Coupling Bar Assembly h e Apparat
201. s us the value AU 5 1 V This corresponds to an energy transfer of AE 5 1 eV LEYBOLD Physics Leaflets A U 27 0V nA a 10 U 21 8V Fig 4 a Franck Hertz curve of mercury recorded with XY recorder b Curve section with ordinate enlarged five times We can compare this value with the literature value Fug 4 9 eV for the transition energy of the mercury atoms from the ground state So to the first 2P state The kinetic energy of the electrons at grid Gz can be calculated as Ekin Uh Us On the basis of this we would expect the first maximum of the collector current at Uj U2 4 9 V In fact the first maximum is not registered until U4 Uz 8 1 V The difference between the two values is the effective contact potential between cathode K and grid Gp Supplementary information A number of factors influence the effective contact potential The most important of these deserve mention here The actual contact potential is caused by the different work of emission of the cathode and grid materials The emission properties of the mixed oxide cathode and the gas charge resp the mercury coating of the grid play an important role here The electrons emitted by the hot cathode have an initial veloc ity which depends on the temperature of the cathode LEYBOLD DIDACTIC GMBH Leyboldstrasse 1 D 50354 H rth Phone 02233 604 0 Telefax 02233 604 222 Telex 17 223 332 LHPCGN D
202. senvolvimento da F sica como o caso dos resultados negativos da experi ncia de Michelson Morley 1887 para detectar o hipot tico ter a experi ncia de Hertz sobre o efeito fotoel ctrico 1887 a descoberta dos raios X Roentgen 1895 a radioactividade Becquerel 1896 as leis experimentais da radia o t rmica emitida por um corpo negro Stefan 1879 Boltzmann 1884 e de Wien 1893 A designa o de f sica Moderna refere se geralmente F sica que desabrochou nos fins do s culo XIX e que amadureceu fundamentalmente na primeira metade do s culo XX Os fen menos f sicos n o explicados pela F sica Cl ssica deram origem quase em simult neo a novas teorias a teoria dos quanta Max Planck 1900 a teoria da relatividade Einstein 1905 a teoria do efeito fotoel ctrico Einstein 1905 Estas teorias associadas descoberta do n cleo at mico e formula o do modelo do tomo com um n cleo central rodeado por electr es Rutherford 1911 levaram ao desenvolvimento de novas reas da F sica Teoria da Relatividade Mec nica Qu ntica F sica Nuclear F sica At mica e Molecular F sica do Estado S lido F sica das Particulas Elementares ptica Qu ntica Astrof sica etc A disciplina proposta est concebida com a preocupa o n o s de informar os alunos sobre os factos acima expostos como de os preparar para as disciplinas que frequentar o nos anos posteriores O programa que ser discutido adiant
203. sert the screw through the hole in the Support Base plate and attach the rod to the Support Base plate by tightening the screw use Phillips drive screwdriver Place the h e Apparatus onto the Support Base Assembly Place the Support Base assembly over the pin on the end of the Coupling Bar assembly Connect a digital voltmeter DVM to the OUTPUT terminals of the h e Apparatus Select the 2V or 20V range on the meter 10 Set the h e Apparatus directly in front of the Mercury Vapor Light Source By sliding the Lens Grating as sembly back and forth on its support rods focus the light onto the white reflective mask of the h e Appara tus Figure 9 PAS CC scientific 121 White Reflective Mask Window to White Photodiode Mask Light Shield shown tilted to Base Support Rod the open position 11 12 Figure 9 h e Light Shield Roll the light shield of the Apparatus out of the way to reveal the white photodiode mask inside the Appara tus Rotate the h e Apparatus until the image of the aperture is centered on the window in the photodiode mask Then tighten the thumbscrew on the base support rod to hold the Apparatus in place As in step 9 slide the Lens Grating assembly back and forth on its support rods until you achieve the sharpest possible image of the aperture on the window in the photodiode mask Tighten the thumbscrew on the Lens Grating assembly and replace the light sh
204. sic Optics System or the 0 6 meter 60 cm Optics Bench that is included with the OS 8539 Spectrophotometer System The Spectrophotom eter Base mounts into the T slots on the sides of the Optics Bench and the Collimating Slits and Collimating Lens snap into the center of the Optics Bench To mount the Spectrophotometer Base on the Optics Bench loosen the thumbscrew on each side of the Base so the square nuts can slip into the T slots on the sides of the Optics Bench Insert the square nuts into the slots and slide the Base along the bench until it is about 20 cm from the end Fig 13 Tighten the thumbscrews to hold the Base firmly on the bench Rod Stand Mounting Clamps You can adjust the height or angle of the Optics Bench using the Rod Stand Mounting Clamps and two rods and bases not included Each clamp has a thumbscrew a spacer washer and a square nut at one end and a second thumbscrew at the other end The thumbscrew with the square nut holds the Spectrophotometer Base thumbscrew Optics Bench T slot p square nut Figure 13 Base Onto Optics Bench End View clamp onto the bench and the other thumbscrew 152 PASC scientific 012 06575A Educational Spectrophotometer holds the clamp onto a rod Fixed Angle To mount the clamp on the bench so it is parallel to the bench at a fixed angle put the clamp on the bench with the spacer on the opposi
205. sor de luz Para isso carregue no s mbolo de sensor de luz e mude a sensibilidade de low para medium 4 Ligue a l mpada de s dio Reduza as fendas ao m nimo e foque a imagem das fendas Abra uma janela gr fica que represente a intensidade em fun o do desvio angular corrigido pelo factor 59 8 Registe os dados que devem incluir a posi o angular da linha de 1 ordem esquerda e direita da linha central Uma vez obtido o espectro registe a posi o 0esq e Odir das linhas de primeira ordem com o aux lio do cursor em forma de cruz 5 Determine o desvio angular 0 l 0esq Odirl 2 correspondente difrac o de 1 ordem da linha amarela do s dio Use estes resultados e o conhecimento do comprimento de onda 589 3 nm da linha amarela do s dio para determinar o espa amento d das linhas de rede de difrac o tal como indicado na p gina 13 do manual 6 Substitua a l mpada de s dio por uma l mpada de merc rio e registe o espectro incluindo linhas de 1 ordem esquerda e direita da linha central Analise o espectro e verifique se poss vel melhor lo reduzindo a luz parasita ajustando as fendas a focagem ou a amplifica o do sinal Determine o valor de 0 I0esg Odirl 2 para cada linha Use o valor d obtido anteriormente e a rela o d sin O para determinar os comprimentos de onda das linhas de merc rio Registe os dados e os resultados numa tabela 7 Substitua a l mpada de merc rio
206. ss in radioactive decay Lawrence Ruby Am J Phys 49 141 1981 25 Instructional Use of the Computer Simulation of Successive Radioactive Decays E J Gucker Am J Phys 40 616 1972 26 A Student Experiment on Successive Radioactive Decay J Scobie and R D Scott Am J Phys 39 962 1971 27 Rutherford Scattering Apparatus for Laboratory and Lecture Demonstration Richard H Lindsay David H Ehlers and Raymond R McLeod Am J Phys 33 1055 1965 34 28 Rutherford and the Nature of the Atom E N da C Andrade Am J Phys 33 416 1965 29 Rutherford and his Alpha Particles Thomas H Osgood and H Sim Hirst Am J Phys 32 681 1964 30 Thomson Atom Henry Zatzkis Am J Phys 26 635 1958 31 Concerning the Rutherford Scattering Formula M M Gordon Am J Phys 23 247 1955 32 Radiations from Radioactive Substances Ernest Rutherford Author James Chadwick Author C D Ellis Am J Phys 20 459 1952 33 Statistical Fluctuation in Radioactive Phenomena J A Grundl F G Karioris and A G Barkow Am J Phys 20 35 1952 35 36 Anexo A Folhas de exercicios Apresentam se nas paginas seguintes exemplos de folhas de problemas a ser usadas nas aulas te rico pr ticas A maioria dos problemas apresentados foram coligidos nos anos em que foram dadas as aulas pr ticas da disciplina 1985 86 1986 87 e 1987 88 Folha 1 Transforma es de Galileu Experi ncia de Michelson Mor
207. st important instruments used in connection with the electron diffraction 10 TECHNICAL DATA tube are given below with their order nos The complete equipment lists Diffraction substance Graphite required for various experiments can be found in the experiment literature Carrier Mesh Copper quoted Nominal distance from Order No Equipment diffraction substance to inner wall of sphere 127 mm 3 mm 11151 00 Electrostatic voltmeter 26 kV i 11725 93 Power supply universal Diameter 11730 93 HV power supply 25 kV of fluorescentscreen 10 cm Heating voltage UAC 6 3 V 300 mA Wehnelt voltage filtered 0 to 50 V PHYWE AG P O Box 3044 D 3400 G ttingen F R G Phone 0551 604 493 Telex 96808 Telegrams PHYWE Goettingen Druck Nr P 0685024 140 Determina o dos espectros de emiss o de H e Hg Gui o 1 Inicie o programa Scienceworkshop seguindo as indica es na p gina 11 do manual da Pasco 2 O sensor de rota o determina a posi o angular a partir das rota es do pino do sensor O pino tem um raio cerca de 60 vezes inferior ao da placa girat ria e por isso os desvios angulares na placa s o cerca de 60 vezes inferiores aos medidos pelo sensor Para corrigir os valores medidos pelo sensor use o programa ScienceWorkshop tal como est indicado no topo da p gina 17 do manual Em vez de 60 use o valor 59 8 que foi determinado como sugerido na p gina 7 3 Use o programa Science workshop para amplificar o sinal do sen
208. t lica nesta velocidade Colocar a folha de a o inox dentro do forno Adquirir um espectro temperatura ambiente com estat stica suficiente para que as posi es dos picos sejam determinadas com incerteza inferior a 11 canais Ajustar a temperatura do controlador de temperatura para 120 C ligar o forno e deixar estabilizar Adquirir um espectro a esta temperatura com a mesma estat stica Repetir as aquisi es a baixa e alta temperatura v rias vezes para diminuir e determinar o erro Determinar o coeficiente de temperatura a partir dos dados i e a frac o variacional nas energias dos picos por grau cent grado e comparar os resultados com as previs es te ricas 71 72 Determina o da velocidade da luz pelo m todo de Foucault Manual de instru es da Pasco incluindo gui o 012 07135B Speed of Light Apparatus Instruction Manual and Experiment Guide for the PASCO scientific Model OS 9261A 62 and 63A SPEED OF LIGHT APPARATUS M Fixed Mirror Beam splitter 5 L 1 E dA NM Ma Measuring j Rotating Mirror Microscope 7 7 Is 10101 Foothills Blvd e Roseville CA 95747 7100 Phone 916 786 3800 FAX 916 786 8905 www pasco com 73 012 07135B Speed of Light Apparatus Table of Contents Section Page Copyright Warranty and Equipment Return ri il Foi re 6 UC HOR scien Sec te eae hae Saad aaa A Ae
209. t as shown in the diagram below Focus the light from the Mercury Vapor Light Source onto the slot in the white reflective mask on the h e Apparatus Tilt the Light Shield of the Apparatus out of the way to reveal the white photodiode mask inside the Apparatus Slide the Lens Grating assembly forward and back on its support rods until you achieve the sharpest im age of the aperture centered on the hole in the photodiode mask Secure the Lens Grating by tight ening the thumbscrew Align the system by rotating the h e Apparatus on its support base so that the same color light that falls on the opening of the light screen falls on the window in the photodiode mask with no overlap of color from other spectral bands Return the Light Shield to its closed position Check the polarity of the leads from your digital voltmeter DVM and connect them to the OUT PUT terminals of the same polarity on the h e Apparatus Experiment 2 Equipment Setup PAS C Ce 11 scientific 126 h e Apparatus and h e Apparatus Accessory Kit 012 04049J Procedure 1 You can see five colors in two orders of the mercury light spectrum Adjust the h e Apparatus carefully so that only one color from the first order the brightest order falls on the opening of the mask of the photodiode 2 For each color in the first order measure the stopping potential with the DVM and record that measurement in the table below Use the yellow and green colored filt
210. t of the recorder in the X and Y direction and mark this point by briefly lowering the recorder pen onto the paper Torecord the curve set operating mode switch to Ramp and lower the recorder pen When you have completed recording raise the pen and switch to RESET Setup Fig 2 shows the experiment setup First Make sure the Franck Hertz supply unit is switched off Connect the heating oven via the 4 mm safety sockets a on the rear of the supply unit Additionally connect the copper lead of the copper sleeve with 4 mm plug to the green yellow safety socket to screen the Franck Hertz tube from interference fields Insert the DIN plug of the temperature sensor in socket b of the supply unit and the DIN plug of the Franck Hertz tube in socket c Heating Note If the thermal contact of the temperature sensor is poor the measured oven temperature will be too low resulting in over heating of the tube Insert the temperature sensor in the corresponding blind hole of the heating oven as far as it will go and slide the Franck Hertz tube with copper sleeve into the oven Turn the operating mode switch d to RESET and switch on the supply unit after a few seconds the LED indicator for mercury Hg changes from green to red Check the default setting Os 180 C and wait until the operating temperature is reached LED indicator changes from red to green the temperature 9 firs
211. t point s In order that the reflected point image can be viewed through the microscope a beam splitter is placed in the optical path so a reflected image of the returning light is also formed at point s Now suppose M is rotated slightly so that the reflected beam strikes M at a different point Because of the spherical shape of M the beam will still be reflected directly back toward M The return image of the source point will still be formed at points s and s The only significant difference in rotating M by a slight amount is that the point of reflection on M changes IPAS C Ci 77 Now imagine that M is rotating continuously at a very high speed In this case the return image of the source point will no longer be formed at points s and s This is because with M rotating a light pulse that travels from M to M and back finds M at a different angle when it returns than when it was first reflected As will be shown in the following derivation by measuring the displace ment of the image point caused by the rotation of M the velocity of light can be determined A Quantitative Description In order to use the Foucault method to measure the speed of light it s necessary to determine a precise relationship between the speed of light and the displacement of the image point Of course other variables of the experimen tal setup also affect the displacement These include e the rate of rotation of Mk e the
212. t reaches a maxi mum and then declines to the final value 188 Fig 2 Experiment setup for the Franck Hertz experiment with mercury If the indicator in the display flashes There is a mistake in the setup for temperature measure ment see the Instruction Sheet Optimizing the Franck Hertz curve Set the driving potential U1 1 5 V and the braking voltage U3 1 5 V and record the Franck Hertz curve see prelimi nary remark a Optimizing 9 If the Franck Hertz curve rises abruptly see Fig 3 a and you can see a gas discharge in the Franck Hertz tube through the insertion opening of the oven blue glow Immediately turn the operating mode switch to RESET and wait until the setup reaches the operating temperature If necessary raise the set value ds using the screwdriver potentiometer e g by 5 C and wait a few minutes until the system settles into the new thermal equilibrium Fig 3 Overview for optimizing the Franck Hertz curves by select ing the correct parameters 3 U and U3 a d b e c f al P6 2 4 1 b Optimizing U A higher driving potential U results in a greater electron emission current f the Franck Hertz curve rises too steeply i e the overdrive imit of the current measuring amplifier is reached at values below U2 30 V and the top of the Franck Hertz curve is cut off Fig 3b Reduce U until
213. t the left edge of the mounting stage is aligned with the 82 0 em mark on the bench see Figure 5 The lever that adjusts the tilt of the beam splitter should be on the same side as the metric scale of the Optics Bench Position this lever so it points directly down CAUTION Do not look through the micro scope until the polarizers have been placed between the laser and the beam splitter in step 19 The beamsplitter will slightly alter the position of the laser beam Readjust L on the Component Holder so the beam is again centered on M Place the Fixed Mirror Mp from 2 to 15 meters from Mp as shown in Figure 11 The angle between the axis of the Optics Bench and a line from M to M should be approximately 12 degrees If it is greater than 20 degrees the reflected beam will be blocked by the Rotating Mirror enclosure Also be sure that M is not on the same side of the optical bench as the micrometer knob so you will be able to make the measurements without blocking the beam gt NOTE Best results are obtained when M is 10 to 15 meters from Mp See Notes on Accuracy near the end of the manual PAS C OH 012 07135B Speed of Light Rotating Mirror E Fixed Mirror Measuring Microscope er Figure 11 Positioning the Fixed Mirror Mp 15 Position M so the laser beam is reflected toward Mp Place a piece of paper in the beam path and walk the beam toward M
214. te side of the clamp from the square nut Tighten the thumbscrew Fig 14 Adjustable Angle To mount the clamp on the bench so it can be adjusted to any angle move the spacer so it is next to the square nut Put the clamp on the bench with the square nut in the T slot and the spacer between the bench and the clamp Adjust the clamp to the angle you need and then tighten the thumbscrew Fig 15 Mounting and Adjusting the Collimating Slits and Lens The Collimating Slits consist of two parts the Collimating Slits Plate and the Collimating Slits Holder The slits are in a piece of metal that is attached to a moveable slide The slide is held on the Collimating Slits Plate with a small thumbscrew and two permanently attached socket screws The Collimating Slits Plate is attached to the Collimating Slits Holder with two brass thumbscrews Loosen the small thumbcrew in the Collimating Slits Plate in order to move the slits slide back and forth The narrow slot in the Collimating Slits Plate lets light through one slit at a time The top half of the Collimating Slits Plate helps to prevent extra light from being measured Snap the Collimating Slits Holder into the Optics Bench near the end of Optics Bench square nut Align the square nut W with the T slot spacer thumbscrew Figure 14 Mounting Clamp onto Optics Bench Fixed Angle EEE Optics Bench square nut Put the spacer between the SSS
215. ter Activity 2 Absorption Dark Line Spectrum EQUIPMENT NEEDED Spectrophotometer System OS 8539 or Spectrophotometer Kit OS 8537 High Sensitivity Light Sensor CI 6604 Rotary Motion Sensor CI 6538 Basic Optics Bench part of OS 8515 Aperture Bracket OS 8534 and Incandescent Light Source DC regulated Large Rod Stand ME 8735 2 Rod 45 cm ME 8736 2 Colored Liquid Sample 5 mL Introduction The purpose of this activity is to determine the wavelengths of colors absorbed by a liquid sample Theory One of the most important applications of spectrophotometers is to identify substances by their absorption spec tra For example it is possible to identify tiny amounts of sodium dissolved in a complicated liquid such as beer because sodium has a unique absorption spectrum An incandescent source such as a hot solid metal filament produces a continuous spectrum of wavelengths A sub stance placed in the path of light from a continuous spec trum source will absorb certain colors from the continuous specrum The individual colors that are absorbed appear as gaps or dark lines in the otherwise continuous spectrum Fig 2 1 light ray Grating continuous spectrum Cuvette Procedure light ray In this activity the High Sensitivity Light Sensor measures the relative intensity of colors of light in an continuous spectrum produced by an i
216. terial causing electrons to be emitted The classical wave model pre dicted that as the intensity of incident light was increased the amplitude and thus the energy of the wave would in crease This would then cause more energetic photoelec trons to be emitted The new quantum model however predicted that higher frequency light would produce higher energy photoelectrons independent of intensity while increased intensity would only increase the number of electrons emitted or photoelectric current In the early 1900s several investigators found that the kinetic energy of the photoelectrons was dependent on the wave length or frequency and independent of intensity while the magnitude of the photoelectric current or number of electrons was dependent on the intensity as predicted by the quantum model Einstein applied Planck s theory and explained the photoelectric effect in terms of the quantum model using his famous equation for which he received the Nobel prize in 1921 E hv KE W max o 118 Background Theory where KE is the maximum kinetic energy of the emit ted photoelectrons and W is the energy needed to re move them from the surface of the material the work function E is the energy supplied by the quantum of light known as a photon The h e Experiment A light photon with energy v is incident upon an elec tron in the cathode of a vacuum tube The electron uses a minimum W of its energy to escape the
217. th all the way to the distant vertical surface Hold a piece of paper in the light beam s path at various distances along Collimating Slits Figure 17 Collimation Setup light ray path Light Sensor Arm PASC 9 scientific 153 Educational Spectrophotometer 012 06575A the beam s path Check to see that the light beam s width is about the same at each point along its path Note that the light may not be in focus during this process If the light beam is not perfectly vertical loosen the small thumbscrew that holds the Collimating Slits slide and adjust the slide or loosen the brass thumbscrews that hold the Collimating Slits Plate onto the holder and adjust the plate until the collimated beam is vertical Remember to tighten the thumbscrews after you make the adjust ment The distances between the light source and the Collimating Slits and between the Collimating Slits and the rest of the Spectrophotometer are not critical However the closer the light source the brighter the spectrum Mounting the Grating Caution Handle the Grating carefully Avoid touching the Grating or the glass plate to which the Grating is attached except by the edges of the glass plate The Grating is mounted on one side of a rectangular glass plate There are two magnetic pads on the same side of the glass plate as the glass side faces light source Grating These pads hold the Grating in place on the Grating M
218. that carries the graphite layer necessary for diffraction can be shown on the screen The connected electrical power supply equipment is adjusted to the initial setting The voltage at the Wehnelt cylinder Grid 6 amp 1 is reduced until the diameter of the patch of light is large enough for the shadow of the carrier mesh to be seen The mesh structure seen on the screen shows that objects can be represented geometrically with the help of electrons in an optical context 6 FAULT LEVELS With an anode voltage of 12 kV the speed of the electrons in relation to the speed of light is some 22 It is therefore acceptable to regard the electrons as non relativistic 139 For the de Broglie wavelength this approximation relates to a fault level of max 1 2 Systematic or equipment related devia tions in the experiment results as compared with theoretical values arise from the inevitable inaccuracy of D distance from graphite layer to glass sphere In accordance with the tolerances set for D a fault level of up to 2 5 can be expected 7 ADDITIONAL INFORMATION As well as the two strong diffraction rings other less intense rings of larger diameter can be seen If the room is in complete darkness these rings can also be seen clearly To demonstrate the diffraction phenomenon in a large room or lecture theatre it is advisable to use TV transmission equipment 8 PROTECTION FROM RAYS When using the electron diff
219. the curve steepness corresponds to that shown in Fig 3d f the Franck Hertz curve is too flat i e the collector current I remains below 5 nA in all areas see Fig 3c Increase Uh max 4 8 V until the curve steepness corre sponds to that shown in Fig 3d f the Franck Hertz curve is flat even after increasing U Reduce the set value ds for the oven temperature using the screwdriver potentiometer c Optimizing U3 A greater braking voltage U3 causes better defined maxima and minima of the Franck Hertz curve at the same time however the total collector current is reduced If the maxima and minima of the Franck Hertz curve are insuffi ciently defined see Fig 3d Alternately increase first the braking voltage U3 maximum 4 5 V and then the driving potential U1 until you obtain the curve form shown in Fig 3f If the minima of the Franck Hertz curve are cut off at the bottom see Fig 3e Alternately reduce first the braking voltage U3 maximum 4 5 V and then the driving potential U until you obtain the curve form shown in Fig 3f Carrying out the experiment Record the Franck Hertz curve see preliminary remark To better demonstrate the first maxima you can increase the sensitivity of the Y input and repeat the recording process Measuring example and evaluation U 1 58 V Us 3 95 V s 180 C In Fig 4 the average of the intervals between the successive maxima give
220. thumbscrews and square nuts used for mounting the Spectrophotometer Base on the Optics Bench see Fig 4 The Rotary Motion Sensor has a three step pulley attached to its shaft with a small thumbscrew The sensor also has a rod clamp attached at end end First remove the small thumbscrew and three step pulley from the Rotary Motion Sensor shaft Then remove the rod clamp from the Rotary Motion Sensor see Fig 5 Figure 5 Prepare Rotary Motion Sensor three step pulley Rotary Motion Sensor rod clamp PASCO E scientific 149 Educational Spectrophotometer Remove the two small thumbscrews from the threaded storage holes on the side of the Spectrophotometer Base and set them aside for the moment Remove the Pinion from the storage post on the opposite side of the Spectro photometer Base and set the Pinion aside for a moment see Fig 6 Rotate the hinge away from the side of the base until the hinge is almost perpendicular to the base Use the two small thumbscrews to fasten the Rotary Motion Sensor to the lower set of holes on the inside of the hinge Place the Pinion all the way onto the Rotary Motion Sensor shaft and tighten the Pinion on the shaft by turning the small thumbscrew on the side of the Pinion see Fig 7 Connect the Rotary Motion Sensor plugs into the ScienceWorkshop interface Mounting the Degree Plate and Light Sensor Arm The Degree Plate and Light Sensor Arm are shipped as a u
221. ties Activity 1 Emission Spectrum cccscscsscsccsssssesssessessesssssscsesssscessesensseess 15 Activity 2 Absorption Spectrum ereta 19 Teachers Guide Technical Support 144 012 065754 Quick Start Educational Spectrophotometer Quick Start The following pages give an overview ofthe Spectrophotometer equipment setup Step One Prepare the Rotary Motion Sensor by removing the thumbscrew three step pulley and rod clamp three step pulley Rotary Motion Sensor rod clamp Quick Start 1 Prepare Rotary Motion Sensor Step Two Prepare the Spectrophotometer Base by removng the two small thumbscrews and Pinion and by rotating the hinge away from the Base Spectrophotometer Base Remove the Pinion Rotate the hinge Remove the Quick Start 2 Prepare the Hinge thumbscrews Step Three Attach the Rotary Motion Sensor to the Base hinge with the two small thumbscrews and attach the Pinion to the Rotary Motion Sensor shaft E Etolo scientific 145 Spectrophotometer Base Put the Pinion on the shaft Use the thumbscrews to attach the sensor Rotary Motion Sensor Quick Start 3 Attach the Sensor and Pinion Step Four Put the Degree Plate Light Sensor Arm on the Base Attach the Grating Mount Light Sensor Mount and Light Sensor Position the Focusing Lens Light Sensor Light Sensor Mount
222. tific 101 012 04695D Thermal Radiation System Calculations For each value of X calculate 1 X Enter your results in Table 2 2 Q Subtract the Average Ambient Radiation Level from each of your Rad measurements in Table 2 2 Enter your results in the table Ona separate sheet of paper make a graph of Radiation Level versus Distance from Source using columns one and four from Table 2 2 Let the radiation level be the dependent y axis If your graph from part 3 is not linear make a graph of Radiation Level versus 1 X using columns three and four from table 2 2 Questions OD Which of the two graphs is more linear Is it linear over the entire range of measurements Q The inverse square law states that the radiant energy per unit area emitted by a point source of radiation decreases as the square of the distance from the source to the point of detection Does your data support this assertion Is the Stefan Boltzmann Lamp truly a point source of radiation If not how might this affect your results Do you see such an effect in the data you have taken E Kleto u scientific 102 012 04695D Thermal Radiation System Experiment 3 Stefan Bolizmann Law high temperature EQUIPMENT NEEDED Radiation Sensor Stefan Boltzmann Lamp Ohmmeter Ammeter 0 3 A Voltmeter 0 12 V Millivoltmeter Ohmmeter Thermometer Introduction The Stefan Boltzmann Law relates R the power
223. ting Mirror M Two alignment jigs are provided for this purpose Place one jig at each end of the Optics Bench as shown in Figure 8 with the edges flush against the fence of the bench When properly placed the holes in the jigs define a straight line that is parallel to the axis of the Optics Bench Turn on the Laser CAUTION Do not look into the laser beam either directly or as it reflects from either mirror Also when arranging the equipment be sure the beam path does not traverse an area where someone might inadvertently look into the beam Adjust the position of the front of the laser so the beam passes directly through the hole in the first jig Use the two front leveling screws to adjust the height Adjust the position of the laser on the Laser Alignment Bench to adjust the lateral position Then adjust the height and position of the rear of the laser so the beam passes directly through the hole in the second jig Hol le in Alignment Jig Reflected laser beam Paper Figure 9 Aligning the Rotating Mirror M SC OH 83 Speed of Light 012 07135B Rotating Mirror M L Position L at 93 0 cm then adjust its position on the holder to center the beam on My 93 0 cm Figure 10 Positioning and Aligning L 8 To fix the laser in position with respect to the Optics Bench tighten the screws on the Bench Coup
224. tion Sensor and the ratio of the radius of the Degree Plate to the radius of the small post on the Pinion typically a 60 to 1 ratio 5 Select a Graph display Set the vertical axis to Light Intensity and the horizontal axis to your calculation of Actual Angular Position 6 Set the sampling rate to 20 Hz 20 measurements per second Step Nine Scan the Spectrum 1 Mask or hood the light source if necessary 2 Move the Light Sensor Arm so the Light Sensor is beyond the edge of the first order spectral pattern 3 Start recording data Slowly and continuously scan the spectrum Scan the first order spectrum on one side of the central ray through the central ray and through the first order spectrum on the other side Scan slowly and continuously in one direction first order spectral lines central ray zeroth order Ei Quick Start 9 Scan the Spectrum Step Ten Analyze Your Data IZUEN scientific 012 06575A Educational Spectrophotometer Introduction About This Manual This manual describes the PASCO OS 8537 Educational Spectrophotometer Accessory Kit and the PASCO OS 8539 Educational Spectrophotometer System The OS 8537 Accessory Kit is designed to be mounted on the Optics Bench of the OS 8515 Basic Optics System Components of the Kit The OS 8537 Educational Spectrophotometer Accessory Kit see Figure 1a includes the following items Spectrophotomete
225. toelectrons as well as the charging time after pressing the discharge button 2 Describe the effect that different colors of light had on the stopping potential and thus the maximum energy of the photoelectrons 3 Defend whether this experiment supports a wave or a quantum model of light based on your lab results Explain why there is a slight drop in the measured stopping potential as the light intensity is decreased gt NOTE While the impedance of the zero gain amplifier is very high 4 10 Q it is not infinite and some charge leaks off Thus charging the apparatus is analogous to filling a bath tub with different water flow rates while the drain is partly open Light Color Stopping Potential Yellow Green Blue Violet Ultraviolet IZEIA screntific 125 012 04049J h e Apparatus and h e Apparatus Accessory Kit Experiment 2 The Relationship between Energy Wavelength and Frequency According to the quantum model of light the energy of light is directly proportional to its frequency Thus the higher the frequency the more energy it has With careful experimentation the constant of proportionality Planck s constant can be determined In this lab you will select different spectral lines from mercury and investigate the maximum en ergy of the photoelectrons as a function of the wavelength and frequency of the light Setup Set up the equipmen
226. tomos de s dio 11 O comprimento de onda mais elevado ainda vis vel para um determinado observador em repouso na Terra 6500 A Determinar a velocidade a que dever mover se uma nave de modo que sinais de luz na regi o do verde 5000A emitidos a partir da nave j n o sejam captados por este observador 12 Observa se um desvio para o vermelho redshift de 100 A na risca D A 5890 A do s dio proveniente de uma estrela distante Determinar a velocidade a que se desloca a estrela 13 Um sat lite aproximando se velocidade de 10 000 km h e altitude de 200 km emite um sinal com a frequ ncia de 1 GHz quando se encontra a 500 km da vertical da esta o receptora a Admitindo que a superf cie da Terra plana calcular a frequ ncia com que o sinal recebido b Calcular o tempo que o sinal demora a ir do sat lite para a esta o receptora para um observador no sat lite e para um observador na esta o receptora 14 Mostrar usando o efeito de Doppler relativistico que um fot o quando cai de uma altura H a varia o da sua frequ ncia dada por v v gH c desde a velocidade com que cai seja pequena quando comparada com a da luz Nesta queda h um desvio gravitacional redshift ou blueshift 15 A Torre Eiffel tem uma altura de 300m Qual a frac o do desvio gravitacional devido a esta altura 49 50 Fundamentos de Fisica Moderna Folha 4 Varia o
227. tora necess rio realizar um certo trabalho W Este trabalho convertido em grande parte na energia dos fot es emitidos No entanto h pequenas perdas de energia devidas ao efeito de Joule e processos que ocorrem no interior da jun o que t m um valor praticamente constante para LEDs dum mesmo tipo quando atravessados por uma mesma corrente el ctrica Nestas condi es W E k 5 onde E a energia do fot o emitido e k uma constante que representa outras perdas de energia A luz emitida por um LED praticamente monocrom tica poss vel fabricar LEDs que emitem luz de diferentes cores alterando a composi o qu mica do material semicondutor Os LEDs mais comuns s o feitos de ligas de g lio ars nio e alum nio Alterando a propor o de g lio e alum nio poss vel fabricar LEDs que emitem v rias cores na gama do vis vel e do infravermelho Os LEDs comerciais s o fornecidos com o material semicondutor encapsulado pl stico e com dois terminais sendo o mais longo o positivo lado p C 109 Para determinar o comprimento de onda da luz emitida por um LED podemos usar uma rede de difrac o Os ngulos 0 para os quais ocorrem os m ximos de intensidade difractada por uma rede com espa amento entre linhas d s o dados pela equa o dsind n n um n mero inteiro MATERIAL e R gua graduada e Folhas de papel branco A3 e Conjunto de LEDs do mesmo tipo montados num suporte e Pilha
228. tos exerc cios com v rios graus de dificuldade Para os alunos do primeiro ano tem a vantagem de ser um livro em Portugu s 6 2 Livros de consulta Arthur Evett Understanding the space time concepts of Special Relativity John Wiley and Sons 1982 Livro que explica detalhadamente a parte da cinem tica relativista Tem muitos diagramas explicativos e aconselha v rios outros livros de leitura na mesma rea Serway Moses e Moyer Modern Physics 3 edition Thomson Brooks Cole 2005 Livro bastante completo com muitos exerc cios e exemplos de resolu o de exerc cios No que respeita F sica Qu ntica aborda os assuntos com pormenor mais extenso do que poss vel leccionar nesta disciplina Paul A Tipler Elementary Modern Physics Worth Publishers 1992 Excelente livro com uma extensiva abordagem de diversos temas de fisica moderna embora por vezes de modo pouco aprofundado Na parte da Teoria da Relatividade por este tema n o voltar a ser abordado por alunos de Engenharia Fisica e outros de 23 algumas especialidades de F sica o livro n o apresenta um n vel de aprofundamento suficiente Frank J Blatt Modern Physics Mc Graw Hill 1992 um bom livro de texto para estudo da disciplina sobretudo no que diz respeito parte da F sica Qu ntica John J Brehem e William J Mullin Introduction to the Structure of Matter A Course in Modern Physics
229. tos quando medida por O que mede a sua separa o espacial como sendo de 1200 km 14 Uma barra de 15 m est em repouso num sistema S e faz um ngulo de 60 com o eixo x x Um observador S move se em rela o a S com velocidade v 0 8c segundo o sentido positivo do eixo comum x x coincidindo as origens dos dois sistemas parat t 0 a Determinar o comprimento da barra medido por S b Determinar as coordenadas dos dois extremos da barra medidas pelo observador S quando um dos extremos tem as seguintes coordenadas no sistema S x 2m y Im z 0m t 4s e h 4s c Se uma l mpada de iodo for colocada num dos extremos da barra tem uma vida m dia de 60h qual a sua vida m dia medida pelo observador S d Se uma segunda l mpada for ligada em x 10m et 2x 107 s em O qual o intervalo de tempo entre os dois acontecimentos medido por O 15 Duas naves espaciais com 100m de comprimento pr prio cada passam uma pela outra mas em sentidos opostos Se um astronauta na frente de uma das naves mede um intervalo de tempo de 2 50 x 10 6 s para a segunda nave passar por ele ent o a Qual a velocidade relativa das duas naves b Qual o intervalo de tempo medido na primeira nave para a frente da segunda nave passar dum extremo ao outro da primeira nave 16 Um mes o desloca se em rela o Terra com a velocidade v 0 8c atravessando um tubo fixo na Terra com 100m de comprimento e se
230. tra and Moseley s law using a scanning electron microscope C W S Conover and John Dudek Am J Phys 64 335 1996 28 Photon counting statistics Undergraduate experiment P Koczyk P Wiewi r and C Radzewicz Am J Phys 64 240 1996 29 Photon states made easy A computational approach to quantum radiation theory I D Johnston Am J Phys 64 245 1996 30 Huygens principle and the modelling of propagation Peter Enders Eur J Phys 17 No 4 226 1996 31 The de Broglie hypothesis leading to path integrals Tomas Tycrska Eur J Phys 17 No 3 156 1996 32 Compton scattering the electron mass and relativity A laboratory experiment P L Jolivette and N Rouze Am J Phys 62 266 1994 33 Diffraction of atoms by light Phillip Gould Am J Phys 62 1046 1994 34 Two slit interference classical and quantum pictures D G C Jones Eur J Phys 15 No 4 170 1994 35 Experimental verification of the Heisenberg uncertainty principle An advanced undergraduate laboratory P A DeYoung P L Jolivette and N Rouze Am J Phys 61 560 1993 36 Study of radiation matter interaction processes below 1 MeV from simulated data Fernando Arqueros and Sergio Martinez Am J Phys 60 232 1992 37 Doppler shift and stellar aberration from conservation laws applied to Compton scattering Don S Lemons Am J Phys 59 1046 1991 38 Observations of the modern photon Michael G Raymer Am J Phys 58
231. trance angle of the thermopile should include no close objects other than the lamp 8 Tum on the power supply Set the voltage V to each of the settings listed in Table 3 1 on the following page At each voltage setting record I the ammeter reading and Rad the reading on the millivoltmeter IMPORTANT Make each Sensor reading quickly Between readings place both sheets of insulating foam between the lamp and the Sensor with the silvered surface facing the lamp so that the temperature of the Sensor stays relatively constant 14 PASC O scientific 104 012 04695D Thermal Radiation System Data and Calculations Calculate R the resistance of the filament at each of the voltage settings used R V 1 Enter your results in Table 3 1 Use the procedure on pages 3 and 4 of this manual to determine T the temperature of the lamp filament at each voltage setting Enter your results in the table Calculate T for each value of T and enter your results in the table On a separate sheet of paper construct a graph of Rad versus T Use Rad as your dependent variable y axis In place of calculations and some may prefer to perform a power regression on Rad versus T to determine their relationship or graph on log log paper and find the slope Questions O What is the relationship between Rad and T Does this relationship hold over the entire range of measurements Q The Stefan Boltzmann L
232. uada Uma vez que os an is s o vis veis num intervalo de V entre 2 kV e 8 kV pode estimar os valores m nimos e m ximos esperados para e escolher os valores de V adequados para obter cerca de 10 pontos a intervalos aproximadamente regulares de A Por ex V 8 6 5 4 5 3 9 3 3 2 9 2 6 2 3 2 0 1 8 em kV 4 Construa uma tabela com os valores medidos de V OV 2rl 21 2r2 e O 22 do tipo V KV oV KV 2rl mm O21 mm 2r2 mm S 22 mm An lise 1 A partir da tabela dos dados originais construa uma nova tabela com valores calculados para as grandezas Al d1 r1 D oA1 A2 d2 r2 D 0 2 0A 1 p 2 m e V 2 61 p do tipo n o se esque a de indicar as unidades V Al dirl D oM A2 d22 D 632 oA Ip 2meV olf Use os valores D 127 mm dl 0 213 nm e d2 0 123 nm referidos no texto Note que para cada valor de V obt m dois valores independentes para Al d1 rl DeA2 d2 r2 D com incertezas GAl e OA2 diferentes Assim os valores 11 e A2 devem ser ponderados com as respectivas incertezas no c lculo do valor m dio i e dd 2 2 7 o T 1 E 1 2 2 Ta Th 133 As incertezas GA OA2 GA e 61 p s o calculadas usando a f rmula de propaga o de erros ver notas sobre an lise de dados Assim por ex Oy dh Oz 2D 0 Verifique as express es anteriores e deduza a express
233. ument for measuring the wavelength of light for using the wavelength of a known light source to measure extremely small distances and for investigating optical media Figure shows a diagram ofa Michelson interferometer The beam of light from the laser strikes the beam splitter which reflects 50 of the incident light and transmits the other 50 The incident beam is therefore split into two beams one beam is transmitted toward the movable mirror M the other is reflected toward the fixed mirror M Both mirrors reflect the light directly back toward the beam splitter Half the light from M is reflected from the beam splitter to the viewing screen and half the light from M is transmitted through the beam splitter to the viewing screen Viewing Screen Beam Compensator Splitter Plate 2 Movable Mirror Adjustable Mirror M Figure 1 Michelson Interferometer 012 07137A Tn this way the original beam of light is split and portions ofthe resulting beams are brought back together Since the beams are from the same source their phases are highly correlated When alens is placed between the laser source and the beam splitter the lightray spreads out and an interference pattern of dark and bright rings or fringes is seen on the viewing screen Figure 2 Since the two interfering beams of light were split from the same initial beam they were initially in phase Their relative phase when they
234. us Tilt the Light Shield of the Apparatus out of the way to reveal the white photodiode mask inside the Appara tus Slide the Lens Grating assembly forward and back on its support rods until you achieve the sharpest image of the aperture centered on the hole in the photodiode mask Secure the Lens Grating by tightening the thumbscrew Align the system by rotating the h e Apparatus on its support base so that the same color light that falls on the opening of the light screen falls on the window in the photodiode mask with no overlap of color from other spectral lines Return the Light Shield to its closed position Check the polarity of the leads from your digital voltmeter DVM and connect them to the OUTPUT terminals of the same polarity on the h e Apparatus Experiment 1 Equipment Setup 123 h e Apparatus and h e Apparatus Accessory Kit 012 04049J Procedure Part A 1 Adjust the h e Apparatus so that only one of the spectral colors falls upon the opening of the mask of the photodiode If you select the green or yellow spectral line place the corresponding colored filter over the White Reflective Mask on the h e Apparatus 2 Place the Variable Transmission Filter in front of the White Reflective Mask and over the colored filter if one is used so that the light passes through the section marked 100 and reaches the pho todiode Record the DVM voltage reading in the table below Press the instrument discharge
235. us Accessory Kit AP 9369 Figure 3 h e Equipment Identification ON OFF These items may be purchased separately from PASCO E i i Mitch roun scientific or together as an AP 9370 h e System Terminal Figure 4 Battery Test Points PASC Ce 3 scientific 119 h e Apparatus and h e Apparatus Accessory Kit 012 04049J JL Press to discharge the Light Block te Apparatus Light Aperture Assembly Light Connect to a digital Source voltmeter the output is a direct measurement of the stopping potential THE CONTROLS Lens Grating Assembly Support Base Assembly Coupling Bar Assembly Figure 5 Equipment Setup Using a Mercury Vapor Light Source and the h e Apparatus Equipment Setup Light Block The standard setup for h e experiments is shown in Figure 5 Details for setting up the apparatus are described below gt 1 The Light Source design allows simultaneous connec tion of two Light Aperture assemblies one on the front and one on the back If you are using only one Light Aperture and h e Apparatus install the Light Block supplied with the Accessory Kit in the mount ing groove closest to the body of the housing on the back of the Light Source see Figure 6 2 Slide the Light Aperture Assembly into the center mounting groove on the front of the Light Source Secure it in place by finger tightening the two thumb screws
236. us modes is indicated on the label Michelson Mode 1 Align the laser and interferometer base as previously described The laser beam should be approximately parallel with the top of the base should strike the center of the movable mirror and should be reflected directly back into the laser aperture 2 Mount the adjustable mirror on the interferometer base Position one component holder in front of the laser Place the other component holder opposite the adjust able mirror and attach the viewing screen to its mag netic backing See Figure 6 3 Position the beam splitter at a 45 degree angle to the laser beam within the crop marks so that the beam is reflected to the fixed mirror Adjust the angle of the beam splitter as needed so that the reflected beam hits the fixed mirror near its center 4 There should now be two sets of bright dots on the viewing screen one set comes from the fixed mirror and the other comes from the movable mirror Each set of dots should include a bright dot with two or more dots of lesser brightness due to multiple reflections Adjust the angle of the beam splitter again until the two sets of dots are as close together as possible then tighten the thumbscrew to secure the beam splitter 182 Precision Interferometer Interferometer base PRECISION INTERFEROME Compensator Viewing screen i optional P EA A Y 7 Laser Z yi Component holder Movable
237. usceptible to backlash However the effects of backlash can be practically eliminated by using proper technique when counting fringes see item 3 under Accurate Fringe Counting on the previous page Mirror Travel The amount of mirror movement per dial turn of the micrometer is constant to within 1 5 Most of this error occurs at the extreme ends of the mirror s total possible movement For very accurate measurements see Calibrating the Micrometer above and remember that the mirrors are flat to within 1 4 wavelength across their surface Troubleshooting If you have trouble producing a clear set of interference fringes consider the following possible sources of diffi culty 1 Warm up your Laser Many lasers vary in intensity and or polarization as they warm up To eliminate any possible fringe or intensity variations allow the laser to warm up prior to setting up an experiment The PASCO laser should warm up in about 1 hour 2 Check your Mirrors The beam splitter and movable mirror are carefully mounted in their brackets to remain perpendicular to the interferometer base when set up If the brackets are bent slightly out of alignment the resulting fringe patterns will be distorted somewhat If they are significantly out of alignment it may be impossible to obtain fringes 3 Background Fringes Reflections from the front and back surfaces of the mirrors and beam splitter of ten cause minor interference patt
238. va Decaimentos alfa beta e gama O recuo do n cleo na transi o gama efeito de Mossbauer Radioactividade natural 4 3 Sum rios das aulas te rico pr ticas Resolu o de alguns problemas sobre as transforma es de Galileu Electromagnetismo e relatividade Newtoniana A n o invari ncia da equa o de propaga o de uma Onda Electromagn tica quando sujeita a uma transforma o de Galileu Observa o das franjas de interfer ncia com um interfer metro de Michelson 2 li o Resolu o de problemas sobre a experi ncia de Michelson Morley e sobre os postulados de Einstein Resolu o de problemas sobre coordenadas de um acontecimento em referenciais de in rcia distintos 15 3 li o Problemas sobre a contrac o dos espa os e dilata o do tempo Transforma es de velocidades em relatividade 4 li o O efeito de Doppler relativista Dedu o das equa es que relacionam os ngulos e as frequ ncias de emiss o e recep o O efeito Doppler longitudinal e transversal Resolu o de exerc cios de aplica o sobre o efeito de Doppler relativista e n o relativista Caso do som e da luz 5 li o Quantidade de movimento e rela o massa energia resolu o de problemas Radi ncia e leis do corpo negro Resolu o de exerc cios de aplica o 6 li o Resolu o de problemas sobre a interac o da radia o com a mat ria Efeito fotoel ctrico efeito de Compton p
239. vide the voltage by the current to measure the resistance R Divide R by R to obtain the relative resistance Ryo Using your measured value for the relative resistiv ity of the filament at temperature T use Table 2 on the following page or the associated graph to de termine the temperature of the filament Thermal Radiation System 012 04695D Table 2 Temperature and Resistivity for Tungsten J Temp Resistivity Temp Resistivit Temp Resistivit Temp Resistivit R R 300K SK uO em R Raook aK uQ cm Y RiRao0K Eus uQ cm Y B R300K RP uQ cm y 1 0 300 5 65 5 48 1200 30 98 10 63 2100 60 06 16 29 3000 92 04 1 43 400 8 06 8 03 1300 34 08 11 24 2200 63 48 16 95 3100 95 76 1 87 500 10 56 6 58 1400 37 19 11 84 2300 66 91 17 62 3200 99 54 2 34 600 13 23 7 14 1500 40 36 12 46 2400 70 39 18 28 3300 103 3 2 85 700 16 09 7 71 1600 43 55 13 08 2500 73 91 18 97 3400 107 2 3 36 800 19 00 8 28 1700 46 78 13 72 2600 77 49 19 66 3500 111 1 3 88 900 21 94 8 86 1800 50 05 14 34 2700 81 04 26 35 3600 115 0 4 41 1000 24 93 9 44 1900 53 35 14 99 2800 84 70 4 95 1100 27 94 10 03 2000 56 67 15 63 2900 88 33 Temperature versus Resistivity for Tungsten 20 19 18 17 16 15 14 13 Relative 1a Resistivity 11 Rr R 300K 10
240. xperiment Note Protect the detector from light while measuring especially from fluorescent light If necessary cover the chamber with a black cloth or similar Each time 5 10 count at least 20 particles n 220 Note the measuring time At needed and calculate the counting rate N n o x Wheno is 30 replace the 1 mm slit by a 5 mm slit and repeat the measurement for 30 40 50 and 60 Measurement example For the following series of measurements 100 to 200 a particles were counted per angle setting in order to keep the statistical error small Table 1 8 n at min N 9 min 1 70 5 34 15 13 15 9 07 20 140 33 4 24 gt Im slit 25 103 au 2 58 30 10 105 0 962 30 124 16 7 75 35 170 40 4 24 40 190 80 2 38 as 133 93 1 43 b Sm slit 50 96 100 0 96 55 84 120 0 70 60 78 200 0 39 e Scattering angle 5 n Counting rate in the time At for the scattering angle e wcap 218 200 100 10 T T E Imp min E 01 E 0 01 i Fig 4 Nas a function of Open circles Measured values Closed circles Measured values when e gt 30 converted to 1 mm slit Conversion factor The ratio of the counting rate at 30 with a 5 mm slit and alm slit Solid line Theoretical curve Evaluation and results When 30 an
241. y coherent light source is used The phase relationship between the transmitted rays depends on the angle at which each ray enters the cavity and on the distance between the two mirrors The result is acircular fringe pattern similar to the Michelson pattern but with fringes that are thinner brighter and more widely spaced The sharpness of the Fabry Perot fringes makes it avaluable tool in high resolution spectrometry As with the Michelson Interferometer as the movable mirror is moved toward or away from the fixed mirror the fringe pattern shifts When the mirror movement is equal to 1 2 of the wavelength of the light source the new fringe pattern is identical to the original Partial Mirrors Adjustable gt gt gt gt Viewing Screen Figure 4 Fabry Perot Interferometer Setup and Operation Laser Alignment If you are using a PASCO Laser and Laser Alignment Bench the setup and alignment procedure is as fol lows If you are using a different laser the alignment proce dure is similar Adjust your laser so that the beam is approximately 4 cm above the table top Then align the beam as in steps 4 and 5 below If you are using a spectral light source instead ofa laser see Suggestions for Additional Experiments near the end of the manual To set up and align your PASCO Laser 1 Set the interferometer base on a lab table with the mi cromete

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