1/4物理化学A(I)(教材第一至第九章)第一章：Problem1:a)Usethefactthattoshowthattheradiantenergyemittedpersecondbyunitareaofablackbodyis.b)Thesun’sdiameterismanditseffectivesurfacetemperatureis5800K.Assumethesunisablackbodyandestimatetherateofenergylossbyradiationfromthesun.c)Usetocalculatetherelativisticmassofthephotonslosebyradiationfromthesuninayear.Problem2:TheworkfunctionofKis2.2eVandthatofNiis5.0eV.a)Calculatethethresholdfrequenciesandwavelengthsforthesetwometals.b)Willvioletlightofwavelength4000AcausethephotoelectriceffectinK?InNi?c)Calculatethemaximumkineticenergyoftheelectronemittedinb).Problem3:OnthebasisoftheBohrtheory,calculatetheionizationenergyofthehydrogenatomandthelinearvelocityofanelectroninthegroundstateofthehydrogenatom.Problem4:WhatisthedeBrogliewavelengthofanoxygenmoleculeatroomemperature?Comparethistotheaveragedistancebetweenoxygenmoleculesinagasat1baratroomtemperature.WhatisthedeBrogliewavelengthofanelectronthathasbeenacceleratedthroughapotentialdifferenceof100V.2/4Whatisthewidthinenergydomainofa4fspulse?Problem5:a.Apossibleeigenfunctionforthesystemis:Showthat,theprobability,isindependentoftime.b.Provethatmmustbetheintegralinorderforthefunctiontobeanacceptablewavefunction.Problem6:ProvethatmomentumoperatorcorrespondingtoisaHermitianoperator.Problem7:Whatisthedegreeofthedegeneracyifthethreequantumnumbersofathree-dimensionalboxhavethevalues1,2and3?Calculatethelowestpossibleenergyforanelectronconfinedinacubeofsidesequaltoa)10pmandb)10-15m.Thelattercubeistheorderofthemagnitudeofanatomicnucleus;whatdoyouconcludefromtheenergyyoucalculateabouttheprobabilityofafreeelectronbeingpresentinanucleus?第二章：Problem1:Usehydrogenicorbitalstocalculatethemeanradiusofa1sorbital.AHydrogenatomisinits4dstate.Theatomdecaystoalowerstatebyemittingaphoton.Findthepossiblephotonenergiesthatmaybeobserved.GiveyouranswersineV)/2exp(),,(),,,(iEtzyxtzyxmsinxp?3/4Problem2:ThespinfunctionsandβcanbeexpressedasandThespinoperatorcanberepresentedbyShowthatProblem3:ShowthattheSlaterdeterminantsforHeliumatomandLithiumatom.Problem4:Estimatetheeffectivenuclearchargefora1selectroninHe,ifthefirstionizationenergyofheliumis24.6eV.Problem5:Estimatetheeffectivenuclearchargefeltbythe2selectroninthelithiumatom,iftheionizationenergyis5.83eVProblem6:ShowtheatomictermsymbolsforHeliumandNitrogenintheirgroundstates.Problem7:WhatisthespectroscopictermofthegroundstateoftheLiatom?Ifthe2selectronisexcitedtothe2pstate,whattermsarethenpossible?Problem8:0110100121?zS21?zS21?zS4/4for0xaUsingthetrialeigenfunctionandotherwise,computethevariationalenergyforaparticleofmassminaninfinitepotentialwellofwidtha.Nisthenormalizationconstant.第三章Problem1:Carryoutalinearvariationcalculationforaparticleofmassmine-dimensionalinfinitepotentialwellofwidthl.useandastrialeigenfunction.Comparetheresultwiththeexactground-stateenergy.3–2，4，6，12，13，24，27，30第四章:4-7,23,24,28第五章:5-18,24,29,39第七章7-5、13、16、26、29)(xaNx0321xxl7522xxl
