刁勇强34-35-A17

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1、CHAPTER2TheoryofSolidsThisvalueofenergymaybegiveninthemorecommonunitofelectron-volts(seeAppendixD).Theelectron-volt(ev)istheunitofenergyequalto1.6×10-19J.WecanthenwritenCommentThereciprocalrelationbetweenphotonenergyandwavelengthisdemonstrated:alarge

2、energycorrespondstoashortwavelength.ExerciseProblemEX2.1Determinetheenergy(ineV)ofaphotonhavingwavelengthsof(a)and(b).2.1.2wave-particleDualityprincipleWehaveseeninthepreviousparagraphsthatlightwaves,inthephotoelectriceffect,behaveasiftheyareparticle

3、s.In1924,deBrogliepostulatedtheexistenceofmatterwaves.Hesuggestedthatsincewavesexhibitparticle-likebehavior,thenparticlesshouldbeexpectedtoshowwave-likeproperties.ThehypothesisofdeBroglieistheexistenceofawave-particledualityprinciple.Themomentumofaph

4、otonisgivenby(2.2)Whereisthewavelengthofthelightwave.Then,deBrogliehypothesizedthatthewavelengthofaparticlecanbeexpressedas(2.3)WherepisthemomentumoftheparticleandisknownasthedeBrogliewavelengthofthematterwave.EXAMPLE2.2OBJECTIVEDeterminethedeBroglie

5、wavelengthofaparticle.Consideranelectrontravelingatavelocityof107cm/s=105m/s.nSolutionThemomentumisgivenbyP=mv=(9.11×10-31)(105)=9.11×10-26Kg-m/sThenthedeBrigliewavelengthis2.1PrinciplesofQuantumMechanicsornCommentThiscalculationshowstheorderofmagnit

6、udeofthedeBrogliewavelengthfora“typical”electron.ExerciseProblemEX2.2(a)Findthemomentumandenergyofaparticlewithmass5×10-31KgandadeBrogliewavelengthof.(b)Anelectronhasakineticenergyof20meV.DererminethedeBrogliewavelength.Togainsomeappreciationofthefre

7、quenciesandwavelengthsinvolvedinthewave-particledualityprinciple,Figure2.2showstheelectromagneticfrequencyspectrum.WeseethatawavelengthofobtainedinExample2.2isintheultravioletrange.Typically,wewillbeconsideringwavelengthsintheultravioletandvisibleran

8、ge.Thesewavelengthsareveryshortcomparedwiththeusualradiospectrumrange.Insomecases,electromagneticwavesbehaveasifareparticles(photons)and,insomecases,particlesbehaveasiftheyarewaves,Thiswave-particledualityprincipleofquantummechanicsappliesprimarilyto