The solutions were used as a learningtool for students in the introductory undergraduate course Physics 200 Relativity and Quanta given by Malcolm McMillan at UBC during the 1998 and 1999 Winter Sessions The solutions were prepared in collaboration ID: 81888
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PhotonsfromaRadioTransmitter Problem2.9,page93AnFMradiotransmitterhasapoweroutputof100kWandoperatesatafrequencyof94MHz.Howmanyphotonsperseconddoesthetransmitteremit?Solution Aphotonoffrequency94MHzhasenergyE=hf=6:2310�26J(6)Theradiotransmitteremitsenergyatarateof100kJ/sso#photons unittime=energy/unittime energy/photon=1:611030s�1:(7)PhotoelectricE ect Problem2.19,page93Alightsourceofwavelengthilluminatesametalandejectsphotoelectronswithamaximumkineticenergyof1.00eV.Asecondlightsourcewithhalfthewavelengthoftherstejectsphotoelectronswithamaximumkineticenergyof4.00eV.Determinetheworkfunctionofthemetal.Solution TextEq.(2.24):Kmax=hc � (8)relatesthemaximumkineticenergyKmaxofaphotoelectronwiththewavelengthofthelightproducingthephotoelectronandtheworkfunction ofthemetal.ItwaswiththisequationthatEinsteinintroducedthenotionoflightquantain1905andforwhichhereceivedtheNobelPrizeforPhysicsin1922.Let1and2bethewavelengthsofthelightemittedbytherstandsecondsources,respectively,andletK1andK2bethemaximumkineticenergiesofthecorrespondingphotoelectrons.ItfollowsfromEq.(8)thatK1=hc 1� (9)K2=hc 2� (10)where2=0:51,soK2�2K1= (11)andtherefore =2eVwhenK1=1eVandK2=4eV.ComptonE ect Problem2.24,page942 sin 0=sin e(21)wherewehavewrittenpe=h=e.Weeliminate andefromtheseequations.Eliminating fromlasttwoequationsyields1 2e=1 2+1 02�2cos 0(22)which,withEq.(19),yieldsEq.(12).CommentsontheComptonFormula. ThederivationoftheComptonformulain1922wastherstapplicationoftheideathatthemomentumpofaphotonisrelatedtoitswavelengthbyp=h=.Thereconciliationofthis\wave-particleduality"wasresolvedwiththesubsequentinventionofQuantumMechanicsandthedevelopmentQuantumElectrodynamics.QuantumElectrodynamics(QED)istherelativisticquantumtheoryofMaxwell'sEquationsofElectro-dynamicsandsystemsofelectrons,positronsandphotons.QEDisthemostsuccessfulrelativisticquantumtheoryeverdeveloped.TherearenoknowndiscrepanciesbetweenQEDandexperiment.ComparingtheComptonE ectandthePhotoelectricE ect Problem2.37,page95InaComptoncollisionwithanelectron,aphotonofvioletlight(=400nm)isbackwardscatteredthroughanangle180.Howmuchenergyistransferredtotheelectroninthiscollision?Comparetheresultwiththeenergytheelectronwouldacquireinaphotoelectricprocesswiththesamephoton.CouldvioletlightejectelectronsfromametalbyComptoncollision?Explain.Solution Eq.(12)withEq.(13)givestheshiftinthewavelengthofaphotonwhenitisscatteredthroughananglebyanelectron.Thewavelengthshift(theComptonshift)is4.86pmwhen=180.Theenergylostbythephotonduringthecollisionishc �hc 0=hc0� 0'hc0� 2=37:7eV:(23)Byconservationofenergy,thisenergyisconvertedintokineticenergyKcoftherecoilingelectronsoKc=37:7eV.Inaphotoelectricprocess,theentireenergyoftheincidentphotonisconvertedintokineticenergyKpoftheelectron:Kp=hc =3:10eV:(24)TheworkfunctionforametalistypicallyontheorderofafeweV.AComptoncollisioninvolvingvioletlightcouldnotejectanelectronfromametalsurfacesincethekineticenergyKctransferredtotheelectronismuchtoosmall.BraggEquation Problem2.38,page954