植物大战僵尸游戏僵尸摇摆怎样过关

WavefunctionsandEnergyLevelsSinceparticleshavewavelikepropertiescannotexpectthemtobehavelikepoint-likeobjectsmovingalongprecisetrajectories.ErwinSchrödinger:Replacetheprecisetrajectoryofparticlesbyawavefunction(y),amathematicalfunctionthatvarieswithpositionMaxBorn:physicalinterpretationofwavefunctions.Probabilityoffindingaparticleinaregionisproportionaltoy2.巨人猎手=y2(x,y,z)dxdydzSchrödingerEquationTheSchrödingerequationdescribesthemotionofaparticleofmassmmovinginaregionwherethepotentialenergyisdescribedbyV(x).-h2md2ydx2+V(x)y=EyOnlycertainwavefunctionsareallowedfortheelectroninanatomThesolutionstotheequationdefinesthewavefunctionsandenergiesoftheallowedstatesAnoutcomeofSchrödinger’sequationisthattheparticlecanonlypossesscertainvaluesofenergy,i.e.energyofaparticleisquantized.(1-dimension)IntheHatomthepotentialthattheelectronfeelsistheelectrostaticinteractionbetweenitandthepositivenucleusV(r)=-e2/(4peor)r:distancebetweentheelectronandthenucleus.SolvetheSchrödingerequationtodetermunetheallowedenergylevelsofanelectronintheHatomSolutionforallowedenergylevelsis:En=-hRn2n=1,2,...R=(mee4)/(8h3eo2)=3.29x1015Hzn:principlequantumnumber.LabelstheenergylevelsWhenn=1=groundstateoftheHatom.Electroninitslowestenergyn1:excitedstates;energyincreasesasnincreasesE=0whenn=∞,electronhaslefttheatom-ionizationAtomicOrbitalsWavefunctionsofelectronsinatomsarecalledatomicorbitals,haveadependenceonpositionSquareofthewavefunction-probabilitydensityofelectronThewavefunctionofanelectroninahydrogenatomisspecifiedbythreequantumnumbers,specifyingenergyandprobabilityoffindinganelectron.1)Principlequantumnumber,n:specifiesenergyoftheorbitals.Inahydrogenatom,allatomicorbitalswiththesamevalueofnhavethesameenergyandaresaidtobelongtothesameSHELLoftheatom.2)Orbitalangularmomentumquantumnumber,ll=0,1,2,….,n-1EachvalueoflcorrespondstoadifferenttypeoforbitalwithadifferentshapeTheorbitalsofashellwithprincipalquantumnumbernfallintongroups,calledSUBSHELLS;eachsubshellisidentifiedbyadifferentlvalue.l=0s-orbitalsl=1p-orbitalsl=2d-orbitalsl=3f-orbitalsMagneticquantumnumber,ml:distinguishestheorbitalswithinasubshell.Determineshowtheatombehavesinamagneticfield.ml=l,l-1,…-l2l+1mlvaluesforeachll=1;ml=+1,0,-1nisrelatedtothesizeoftheorbital,lisrelatedtoitsshape,andmlisrelatedtoitsorientationinspace.sorbitals:correspondtol=0andml=0ForHydrogenatomthegroundstateisn=0,l=0andml=0;asorbitalDensityofshadingrepresentstheprobabilityoffindinganelectronatanypoint.ThegraphshowshowprobabilityvarieswithdistanceWavefunctionsofsorbitalsofhigherenergyhavemorecomplicatedradialvariationwithnodes(pointsofzeroprobability)Boundarysurfaceenclosessurfacewitha90%probabilityoffindingelectronelectrondensitywavefunctionradialprobabilitydistributionporbitals:Threeporbitalsl=1,ml=+1,0-1dorbitals:Fiveporbitalsl=2,ml=+2,+1,0-1,-2forbitals:Sevenforbitalsl=3,ml=+3,+2,+1,0-1,-2.-3ThethreequantumnumbersforanelectroninaHatominacertainstatearen=4,l=2,ml=-1.Inwhattypeoforbitalistheelectronlocated?ElectronSpinSpectrallinesobserveddidnothaveexactlythesamefrequenciesasthosecalculatedbySchrödinger.S.GoudsmitandG.Uhlenbeckproposedelectronshavespin.Electronsbehavelikeaspinningsphere,likeaplanetrotatingonitsaxis.Anelectronhastwospinstates,representedbyandoraandb.Canthinkofthesestatesasacounterclockwise()spinoraclockwise(),bothatthesamerate.Spinquantumnumber,ms,distinguishesthetwospinstatesms=1/2electronms=-1/2electronO.SternandW.GerlachThestateofanelectroninahydrogenatomisdefinedbythefourquantumnumbers,n,l,ml,ms.Asthevaluesofnincreases,thesizeoftheatomincreases.Many-ElectronAtomsElectronicStructureofHatom(Z=1)Electroninthelowestenergylevel-groundstateoftheatom,n=1=1sorbitalQuantumnumbersofthis1selectronn=1,l=0,ml=0,ms=+1/2or-1/2Iftheelectronacquiresenergy,theelectroncanundergoatransitiontothen=2shellandcanoccupythe2soroneofthethree2porbitals(forH-atomallhavethesameenergy)ThestateofanelectroninaHatomisdefinedbythefourquantumnumbersn,l,ml,ms.Asthevalueofnincreases,thesizeoftheatomincreases.-h2md2ydx2+V(x)y=EyForHatom:V(r)=-Ze2/(4peor)(Z=1forHatom)Many-electronatoms(Z1)ElectronsoccupyorbitalslikethoseofaHatom.EnergiesoforbitalsofmanyelectronatomsarenotthesameasthosefortheHatom.NuclearattractionforelectronsisgreaterasZincreasesloweringtheelectrons’energy;alsohavetoaccountforelectron-electronrepulsion.IntheSchrödingerequation,V(r)hastoaccountforboththenuclear-electronattractionandtheelectron-electronreplusionForexampleforHe(Z=2),V(r)containsthreetermsV(r)=-[(2e2)/(4peor1)]-[(2e2)/(4peor2)]+e2/(4peor12)attractionattractionrepulsionFormany-electronatomsTheelectrondensityofanisolatedmany-electronatomis~sumoftheelectrondensitiesofeachelectrontakenindividuallyEveryelectroninanatomhasasetoffourquantumnumbers,n,l,mlandmsTheelectron-electronrepulsionopposeselectron-nuclearattraction.Therepulsion“shields”theelectronfromthefullattractionofthenucleus.