Chapter33To35QuantumPhysics Planck sQuantumHypothesisThePhotoelectricEffectComptonEffectWaveNatureofMatterHeisenbergUncertaintyPrincipleSchr dinger sEquationHydrogenAtom 33 1Planck sQuantumHypothesis P763 Black bodyRadiation Oneoftheobservationsthatwasunexplainedattheendofthe19thcenturywasthespectrumoflightemittedbyhotobjects AweknownthatallobjectsemitradiationwhosetotalintensityisproportionaltothefourthpoweroftheKelvintemperature Therateatwhichanobjectemitsenergyviaelectromagneticradiationdependsontheobject ssurfaceareaAandthetemperatureTofthatareainKelvinsandisgivenby ThisiscalledtheStefan Boltzmannequation and isauniversal Stefan Boltzmann constant Thefactore calledtheemissivity 发射率 oftheobject ssurface isavaluebetween0and1thatischaracteristicofthematerial Asurfacethemaximumemissivityof1 0issaidtobeablackbodyradiator Ablackbody 绝对黑体 isabodythatwouldabsorballtheradiationfallingonit 在任何温度下对任何入射辐射能都全部吸收而不反射的物体 TwoimportanttheoreticalcurvesonblackbodybasedonclassicalidearswerethoseproposedbyW Wien in1896 andbyRayleigh Jeans in1900 NeitherWien snorRayleigh Jeansformulationswereinaccordwithexperiment Wien swasaccurateatshortwavelenthsbutdeviatedfromexp Atlongerones whereasthereversewastruefortheRayleigh Jeanstheory Acloudcoveredinfairskiesofphysics 物理学晴朗天空中的一朵乌云 紫外灾难 Thebreakcameinlate1900whenMaxPlanck 1858 1947 proposedanempiricalformula 经验式 thatnicelyfitthedate Planckconstant Rubensprovedbyexperimentsthatitfitwithexperimentalcurveinwholewavelengthregion M PlanckGermany 1858 1947 Planckthensoughtatheoredicalbasisfortheformulabymakinganewandradicalassumption Theenergyofanymolecularvibrationcouldbeonlysomewholenumbermultipleofhf quantumofenergy能量子 Energywouldnotbeacontinuousquantityashadbeenbelievedforcenturies ratheritisquantized itexistsonlyindiscreteamount h 6 63 10 34Js Planck sQuantumHypothesis P765 E n n 1 2 3 hf Quantum means discreteamount asopposedto continuous Thisisthefirsttimethatthequantumconceptwasproposedinphysics history Later thedayofDecember14 1900wascalledthebirthdayofquantumtheory PlanckgotthefirstNobelPhysicsPrizein1918forhisradicalinnovation 根本的改革 创新 普朗克量子假设与经典理论不相容 是一个革命性的概念 打破几百年来人们奉行的自然界连续变化的看法 圆满地解释了热辐射现象 并成为现代量子理论的开端 带来物理学的一次巨大变革 33 2ThePhotoelectricEffect光电效应 P765 Thephotoelectriceffect 1 Experimentalapparatus HenrichHertzproposedin1887first thechargedparticleswasprovedaselectronslater Photoelectriceffectisthephenomenonthatwhenlightshinesonametalsurface electronsareemittedfromthesurface 光照射某些金属时能从表面释放出电子的效应 这时逸出的电子称为光电子 1 ThenumbersofelectronsinunittimeemitedfromCproportionaltotheintensityofincidentlight 饱和光电流与入射光强成正比 2 Experimentalresults 2 AdjustingtheV thereexistsastoppingpotentialVstop截止电压 atwhichthereadingofmeter A hasjustdroppedtozero noelectronshavesufficientkineticenergytoreachcollectorC ThenKmax themaximumkineticenergyoftheemittedelectrons 光电子的最大初动能 canbedeterminedusingconservationofenergy Measurementsshowthat themaximumkineticenergyoftheseelectronsKmaxislinearlyincreasedwiththefrequencyofincidentlight Forlightofagivenfrequency Kmaxdoesnotdependontheintensityofthelightsource 与入射光强无关 3 VaryingthefrequencyfoftheincidentlightandmeasuretheassociatedstoppingpotentialVstop Thecutoffwavelength Thereexistcutofffrequencyf0 红限频率 入射光频率大于f0 belowwhichnophotoelectriceffectoccurnomatterhowintensetheincidentlightis 4 Theelectronsareejectedinstantaneously 光子打出光电子是瞬时发生的 l0 c f0 TheEinstein sphotoelectricequation Iftheelectronistoescapefromthetarget itmustpickupenergyatleastequaltoW0 Anyadditionalenergy hf W0 thattheelectronacquiresfromthephotonappearsaskineticenergyKoftheelectron Einsteinsummeduptheexperimentalresultsas whereW0istheworkfunction 逸出功 电子吸收一个光子的能量 电子的最大初动能 逸出功 In1913 1914 carefullyexperimentswerecarriedoutbyR A Millikan TheresultswerefullyinagreementwithEinstein sparticletheory Ifthefrequencyfislessthanthecutofffrequencyf0 wherehf0 W0 noelectronswillbeejectedatall nomatterhowgreattheintensity Lookatexamples33 3to33 5fromP767to768 Oneotheraspectofthephotoelectricalsoconfirmedthephotontheory Example Solution Showthat forlightofwavelength innanometers thephotonenergyhfinelectron voltsis1240 Forbluelight 450nm astheexample33 3 theenergyofphotonis Example33 5ofP768 Solution WhatistheKmaxandspeedofanelectronejectedfromasodiumsurfacewhoseW0 2 28eVwhenilluminatedbylightofwavelength a 410nm b 550nm b Noelectronsareejected Applicationsofthephotoelectriceffect Besidesplayinganimportanthistoricalroleinconfirmingthephototheoryoflight italsohasmanypracticalapplications 光电控制的路灯系统 Opticalsoundtrackonmoviefilm automaticdooropenermakinguseofthephotocellcircuit 33 3PhotonsandComptonEffect P769 在散射X射线中除有与入射波长相同的射线外 还有波长比入射波长更长的射线 这种现象称为康普顿效应 Thescatteredlighthadaslightlylonger thandidtheincidentlightbyanamountDl whichisincreaseasthescatteringangleincrease Comptonshift Comptonscatteredshortwavelength light X rays fromvariousmaterials Thescatteredlighthadaslightlylonger thandidtheincidentlightbyanamountDl whichisincreaseasthescatteringangleincrease ItiscalledtheComptonshift Whenlightpassthroughmateri