Chapter10BaseofQuantumtheory-----HuangQiongMichelson-Morleyexperiment

Blackbodyradiation

PhotoelectricEffectAtomicSpectrumofHydrogen

ComptonEffect

QuantummechanicSpecialRelativityDarkCloudsinStretchesofBlueSky(1899)§1BlackbodyRadiation

1.BlackbodyRadiationThebodythatonlyabsorbsincidentelectromagneticwaveanddoesn’treflectiscalledtheblackbody.Theblackbodyisanidealmodel.thesmallholeisjustapproximatelyablackbody.DevicetoMeasuretheDistributionofEnergyinBlackbodyRadiation:acavitywithsmallhole,thetemperatureinthecavityiscontrolled.lensethelightbeamradiatedfromtheholeaparallellighttubeadisperseprismathermocouplemonochromaticlightTwoFeaturesoftheDistributionIntensity:themonochromaticenergyradiatedfromunitareaonthesurfaceoftheblackbodyforunittime.IntensityTheamountofradiationemitted(theareaunderacurve)increases(Stefan’slaw)Thepeakinthedistributionshiftstowardshorterwavelengths.(Wien’slaw)IntensityTheenergyofdifferentwavelengthsradiatedfromunitareaonthesurfaceoftheblackbodyforunittimeconformstotheequationinthefollowing:Stefan-BoltzmannlawIfrepresentsthewavelengthcorrespondingtothegreatestmonochromaticenergyfluxdensityIntensityWienDisplacementLawWiththeincreaseoftemperaturethevalueofmovesleft.Whatistheexpressionequationconformingtothefollowfigure?Thisisahotspot.0123456(μm)1700K1500K1300K1100KAnyattemptstouseclassicalideastoexplaintheshapesofthecurveisfailed.ExperimentaldataWienformula

Rayleigh-Jeansformula

UltravioletcatastropheinfiniteenergyPlanckFormulaAfterrepeatedthoughtPlanckbelievesthat,thekeyofsolvingthatquestionistorecognizetheenergyis

quantized.Wherenisapositiveintegercalledaquantumnumber,hisPlanck’sconstant.ThekeypointofPlanck’stheoryistheradicalassumptionofquantizedenergystates.Energy01234n0PlanckFormulaofBlackbodyRadiation

ForlowerfrequencythereisRayleigh-JeansformulaForhigherfrequencythereisWienformulaExperimentdataRayleigh-JeansformulaWienformulaT=1646kPlanck’stheoreticaldataAtallwavelengthsPlanckequationforthewavelengthdistributionthatisincompleteagreementwiththeexperimentalresults.Planckintroducedtheconceptofa“quantumofaction”inanattempttoexplainthespectraldistributionofblackbodyradiation,whichlaidthefoundationsforquantumtheory.In1918,hewasawardedtheNobelPrizeinphysicsforthediscoveryofthequantizednatureofenergy.(1858-1947)

Theabsorbedorradiatesenergyis

quantized.Thisdevelopmentmarkedthebirthofthequantumtheory.WhenPlanckpresentedhistheory,mostscientist(includePlanck!)didnotconsiderthequantumconceptrealistic.Itwasfelttobeamathematictrickthathappentopredictthecorrectresults.

Subsequentdevelopments,however,showedthatatheorybasedonthequantumconcept(ratherthanonclassicalconcepts)wasrequiredanumberofotherphenomenaattheatomlevel.在十年之后，1915年，不相信光量子的米立肯(1868—1953年)宣布他的實驗無歧義地證實了愛因斯坦的光電效應(yīng)理論和1922年康普頓(1892—1962年)發(fā)現(xiàn)Ｘ射線散射效應(yīng)必須由光量子論解釋之后，人們才正確評價了光量子論，宣布愛因斯坦由于“在理論物理學(xué)方面的成就，特別是光電效應(yīng)定律的發(fā)現(xiàn)”而授予他1921年度的諾貝爾物理學(xué)獎。愛因斯坦和普朗克不同，當(dāng)時就堅信自己的光量子論是“非常革命的”。的確，光量子論并不是簡單地復(fù)活光微粒說，而是揭示了光的波粒二象性。對統(tǒng)計平均現(xiàn)象光表現(xiàn)為波動，對瞬時漲落現(xiàn)象光表現(xiàn)為粒子。光量子論第一次確認(rèn)了光的波粒二象性這個最基本的性質(zhì)。

1.PhotoelectricEffectmetalExperimentsshowthatlightincidentoncertainmetallicsurfacescauseselectronstobeemittedfromthesurfaces.Thisphenomenoniscalledthephotoelectriceffect,andtheelectroniscalledthephotoelectron.§2PhotoelectricEffectOOOOOOOOLightASchematicDiagramofaPhotoelectricEffectApparatus.Whentheevacuatedglasstubeiskeptindark,theammeterreadszero,indicatingthatnocurrentisflowinginthecircuit.WhenlightoftheappropriatewavelengthshinesonplateE,however,acurrentisdetectedbytheammeter,indicatingaflowofchargesacrossthegapbetweenAandK.HighintensityLowintensitycurrentStoppingpotentialAppliedpotentialdifferencePhotoelectriccurrentversusappliedpotentialdifferencefortwolightintensity.Thecurrentincreaseswithintensitybutreachesasaturationlevelforlargevalues.2.Experimentallawofphotoelectriceffectanddifficultyofclassicaltheory

Independenceofphotoelectronkineticenergyonlightintensity.HighintensityLowintensitycurrentStoppingpotentialThisisshowninfigurebythefactthatbothcurvesfalltozeroatthesamenegativevoltage.Accordingtoclassicalprediction,electronsshouldabsorbenergycontinuouslyfromtheelectromagneticwaves.Amoreintensitylightshouldtransfermorekineticenergytotheelectrons,sothestoppingpotentialshouldbelarger.HighintensityLowintensityCurrentStoppingpotentialSupposetheinitialkineticenergyofphotoelectronescapedfromtheplateKisThelowestvoltagetomakethecurrentdropsjusttozerobetweentwopolesisiscalledtherestrictedvoltage,whichmakesthephotoelectronescapedfromthepoleKcouldnotjustarriveatthepoleL.restrictedvoltage(Stoppingpotential)v0CSKCUv01v02v03frequencyStoppingpotential

Dependenceofphotoelectronkineticenergyonlightfrequency.

Theinitialkineticenergyofphotoelectronisrelatedwiththefrequencyofincidentlightinsteadoftheintensity.Accordingtotheclassicaltheory,thegreaterintensityofincidentlightis,thegreaterinitialkineticenergyofphotoelectron.Theinitialkineticenergyofphotoelectronshouldberelatedwiththeintensityofincidentlightinsteadofthefrequency.

DependenceofejectionofelectronsonlightfrequencyAccordingtotheclassicaltheory,nomatterhowmanythefrequencyofincidentlightis,ifonlytheintensityisgreatenough,theelectroncanobtainenoughenergytoescapefromthemetal,existingnothecutofffrequency.Foronekindofmetalthereexistslowestfrequency,whichiscalledthecutofffrequency.Ifthefrequencyofincidentlightissmallerthanthecutofffrequency,nomatterhowmanytheintensityofincidentlightis,thephotoelectriceffectdoesn’tappear.

>0

TimebetweenincidenceoflightandejectionofphotoelectronsIfonlythefrequencyofincidentlightisgreaterthanthecutofffrequency,photoelectronsescapedrapidly,thehysteretictimedoesn’texist.Accordingtotheclassicaltheory,fromthestartofshiningtopoleKtotheescapeofphotoelectronsthereshouldexistthelongerorshorterhysteretictimeinwhichtheelectronabsorbsenergyofincidentlight.t(s)0

10-9I3.EinsteinPhotoelectronTheory(in1905)EinsteinextendedPlanck’sconceptofquantizationtoelectromagneticwaves.Heassumedthatlightoffrequencycanbeconsideredtobeastreamofquantawhichiscalledphotons.EachofthephotonshasanenergyEgivenbythefollowingequations:E=hEachphotonmoveswithavelocityC.EinsteinPhotoelectricEquationtheinitialkineticenergytheescapeworkofthemeta

Dependenceofejectionofelectronsonlightfrequency

Thecutofffrequencyis

Dependenceofphotoelectronkineticenergyonlightfrequency.v0CSKCUEinsteinreceivedthe1921NobelPrizeinPhysics"forhisservicestoTheoreticalPhysics,andespeciallyforhisdiscoveryofthelawofthephotoelectriceffect.§3ComptonEffect

AmericanphysicistCompton(A.H.Compton,1892-1962)startedtoresearchXray(10-10m)athimselfyouth.1896,RoentgenHediscoveredinexperimentthat,afterthroughthegraphitethewavelengthofsomescatteredwavesdoesn’tchange,andthewavelengthofanotherscatteredwavesincreases,theincrementofwavelengthincreaseswiththeincreaseofscatteringangle.ThisiscalledComptoneffect.AfterexplorationformanyyearshepublishedthearticleinMay1923,whichclaimsthatexperimentalphenomenoncouldbeexplainedonlybyuseofthequantumtheory.X-raysourcediaphragmCarbontargetIonizationchamber........................................................................................(a)(b)(c)(d)0.7000.7501.Twopeaks:0X-rayYXYXIftheelectroncollidedwiththephotonisinexternallayerofatom,sincetheboundactiontotheelectroninexternallayerisweaker,theelectronmaybeconsideredasafreeelectron.Sothemomentumofthephotonischangedafterthecollision,namelythewavelengthoflightisincreased.Butiftheelectronisininternallayerofatom,sincetheboundactiontotheelectronininternallayerisstranger,thecollisionofthephotonwiththeelectronmatchesuptothecollisionwithwholeatom,andthemassofatomisgreaterfarthanthemassofphoton,sothemomentumofthephotondoesn’tchangeafterthecollision,namelythewavelengthoflightdoesn’tchange.Thus,byuseoftheenergyconservationlawandthemomentumconservationlawexplainedperfectlyComptonEffect.Namely,theenergyconservationlawandthemomentumconservationlawarebothstricttenableinmicroscopicworld.Comptonwavelengthofelectron:Comptonshiftequation:?Comptoneffectisonlydetectableforwavelengthsthatareveryshort.§4BohrTheoryofHydrogenAtom1.AtomicSpectrumofHydrogenTheatomicspectrumofhydrogenisnotcontinuous.Rydbergformulareflectsreallytheatomicspectrumlawofhydrogen.Rydbergformula:AtomicSpectrumofHydrogen6562.794861.334340.474101.741215.681025.83972.5418.7540.50Lymanseries

Balmerseries

Paschenseries

Brackettseries

continuousn=4n=3n=2n=1r=a1r=4a1r=9a1r=16a1Lymanseries

BalmerseriesPaschenseries

Theorbit,velocity,energyofelectronarequantized.Niels

HendrikDavidBohr(1885~1962)receivedthe1922NobelPrizeinPhysics.

2.BohrAtomicTheoryofHydrogenBohrguessesthatorbitofelectronoutofnucleusisnotarbitrary,andshouldsatisfycertaincondition.AccordingtothistrainofthoughtBohrputforwardtwosuppositionsin1913.Theorbitofelectronoutofnucleusisnotarbitrar