化學(xué)原理Chemistry課件-post+4+Quantun+Chemistry

QuantumTheoryandtheElectronicStructureofAtomsChapters7&8QuantumTheoryandtheElectro17.1LightandClassicQuantumTheory1.ClassictheoryofLightDifferentwaveshavedifferentcolor,anddifferentwavelength.Particles(Newton,1680):anarrayofparticles,emittedfromlightsource,thatmoveinspaceinonedimensionaldirection.forcespeedAccelerationspeedExactpositionandspeedcanbedeterminedatthesametime.Wave(Huygens,1690):anelasticvibrator,emittedfromlightsource,thatmoveinspaceinthreedimensionaldirection.Kineticenergy7.1LightandClassicQuant2Wavelength(l)7.1LightandClassicQuantumTheoryMaxwell(1893)wroteanequationforlightasawaveLightisanelectromagneticwavethatspreadinspace.Foralightinvacuum,

u=c=3.00x108m/sFrequency

n

isthenumberofwavesthatpassin1s.u=l·nabout1.28sfrommoontoEarth

Wavelength

l

isthedistancebetweentwosuccessivewaves.

Speed

u

isthedistanceofwavesthatpassin1s.Wavelength(l)7.1Lightand3Electromagneticradiationistheemissionandtransmissionofenergyintheformofelectromagneticwaves.Wavelength(l)a0amplitudeAtacertainposition(x),thewavechangewitht.Atacertaintime(t),thewavechangewithx.TheenergyintensityEnergychangescontinuously!EnergypassedthroughaunitareaperunittimeElectromagneticradiationist4化學(xué)原理Chemistry課件-post+4+Quantun+Chemistry5Planck’sQuantumHypothesis(1901):

Forasinglequantum,thesmallestquantityofenergy:

E=h

vPlanckconstanth=6.63x10-34J?sEnergychangeisonlybyhv,2hv,3hv,4hv...butneverby1.5hvor3.06hv…Thenin1918,hewonNobelPrizeinphysics.2.ClassicquantumtheoryofLight(Plank,1900)Classicaltheoryexplainsitwellatlowv,butverybadathighv.

Energyisemittedorabsorbedindiscreteunits(quantum).Blackbodyradiation:curveE

vs

vExplainsallresultswell.Planck’sQuantumHypothesis(16TheParticleNatureofLight:

PhotoelectricEffect:

hnvoltagecurrentV0(1)minimumfrequencyoflight(v0)(2)

v0isdependentofmetal.(3)Thecurrentlightintensity.TheParticleNatureofLight:7hv=pcParticlenatureWavenatureEinsteinPhotonTheory(1905)hn=KE+BEKE=hn-BEExplanationofthePhotoelectricEffect:Lighthasboth:Wavenaturel,E=hvParticlenaturem,momentump=mcEnergyE=mc2hv=pcParticleWaveEinstein87.2DualNatureofElectron1.Hydrogen

Emissionlinespectrum:Bohr’sPlanetarymodelHgLiCdSrCaNa7.2DualNatureofElec9e-canonlyhavespecific(quantized)energyvalueslightisemittedase-movesfromoneenergyleveltoalowerenergylevelBohr’sModelofHAtom(1913)En=-RH()1n2n(principalquantumnumber)=1,2,3,…RH

(Rydbergconstant)

=2.18x10-18J=13.6eVEphoton=DE=Ef-Ei3.ifDE=RH()1n21n2nf=1ni=2nf=1ni=3nf=2ni=3e-canonlyhavespecific(qua10Ephoton=2.18x10-18Jx(1/25-1/9)Ephoton=DE=1.55x10-19Jl

=6.63x10-34(J?s)x3.00x108(m/s)/1.55x10-19Jl

=

1280nmCalculatethewavelength(innm)ofaphotonemittedbyahydrogenatomwhenitselectrondropsfromthen=5statetothen=3state.Ephoton=hc/ll=hc/EphotonifDE=RH()1n21n2Ephoton=Ephoton=2.18x10-18Jx(1/11DeBroglie(1924)reasonedthate-isbothparticleandwave.2pr=nl

l=h/muu=velocityofe-m=massofe-2.DualnatureoftheElectron:MatteraswavesWhatisthedeBrogliewavelength(innm)associatedwitha2.5gPing-Pongballtravelingat15.6m/s?l=6.63x10-34/(2.5x10-3x15.6)l=1.7x10-32m=1.7x10-23nmNobelPrizein1929DeBroglie(1924)reasonedtha12&7.3QuantumMechanicalDescriptionofElectronsinAtomsSchr?dingerWaveEquationBasis:Bohr’stheory,goodtoexplaintheemissionspectrumofH,butcannotaccountforthespectrumofotherelements.Dualnatureofelectron(mandl).In1926,Schrodingerwroteanequationforelectronintheatom.?=E

E=V+KETotalenergyofthesystemPotentialenergykineticenergy(psi):wavefunction,oratomicorbitalthatdescribesthemovementofelectronintheatominthreedimensionalspace.?:HamiltonianOperator?2:LaplacianOperator2Uncertaintyprinciple(1927,WKHeisenberg):DXDph/4pItisimpossibletodeterminepreciselyboththepositionandmomentumofaparticleatthesametime.&7.3QuantumMechanicalDe131.ApplicationofSchr?dingertoHydrogenAtom

zxy(x,y,z)r?=E

?(x,y,z)

=E(x,y,z)

hereAftertransferredintospherecoordinate1.ApplicationofSchr?dinger14GeneralsolutionforHydrogenAtomSameasBohr’sresult,ie.

Onlydependentofn;AngularpartSpacialpartn=1l=0ml=0E1s=-13.6eV(Zisatomicnumber,andforH,Z=1)n=2l=0ml=0n=2l=1ml=0n=2l=1ml=-1n=2l=1ml=+1E**=-3.4eVGeneralsolutionforHydrogen15

r

distancefromthenucleusY2ElectrondensityButtheprobabilitytofindeinspace(DV)isP=Y2?DV,highestatr=0.529?90%ofelectrondensityfoundl=0n=1n=2n=3rdistancefromthenucleusY216ml=-1ml=1ml=0ml=-2ml=-1ml=0ml=1ml=27.6ml=-1ml=1ml=0ml=-2ml=17n:Principalquantumnumbern=1,2,3,4,….distanceofe-fromthenucleus,anddeterminationofenergyHeren,l,marecalledasthequantumnumberl:angularmomentumquantumnumberl

=0,1,2,3,…n-1n=1,l=0n=2,l=0,1n=3,l=0,1,2Shapeofthe“volume”ofspacethatthee-occupiesl=0123Orbitalspdfml

:

magneticquantumnumberml=-l,….,0,….+lifl=1(porbital),ml=-1,0,1ifl=2(dorbital),ml=-2,-1,0,1,

2orientationoftheorbitalinspacen:Principalquantumnumbern=18EnergyoforbitalsinasingleelectronatomEnergyonlydependsonprincipalquantumnumbernEn=-RH()1n2n=1n=2n=3GroundstateexcitedstateEnergyoforbitalsinasingle192.ApplicationofSchr?dingertoMany-electronatomszxy(xi,yi,zi)ri?=E

rjrij(xj,yj,zj)?Fortheithelectron,theaveragenetpotentialissphericallyapproximatedas:shieldingconstanti

=Eii

EffectivechargeofthenucleusGeneralsolution2.ApplicationofSchr?dinger20Energyoforbitalsinamulti-electronatomEnergydependsonnandln=1l=0n=2l=0n=2l=1n=3l=0n=3l=1n=3l=2Energyoforbitalsinamulti-21Orderoforbitals(filling)inmulti-electronatom1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6sOrderoforbitals(filling)in223.TheBuilding-UpPrincipleofelectronsintheorbitals:1.Electronsoccupyfirstthelowestenergyorbitalsavailable.2.Eachorbitalaccommodatesonlytwoelectrons,andthesetwoelectronsmusthaveopposingspins.Pauliexclusionprinciplespinquantumnumberms=+?or-?Todescriptoneelectroncompletely,Fourquantumnumbersofn,l,mlandmsareneeded.3.Inthedegenerateorbitals(samenandl),theelectronsoccupytheorbitalsasmanyaspossiblewithsamespins.N(Z=7)1s2s2p(Z=7)N1s22s22p3ElectronconfigurationHund’srule3.TheBuilding-UpPrincipleo23WhatistheelectronconfigurationofMg?Mg12electrons1s<2s<2p<3s<3p<4s1s22s22p63s22+2+6+2=12electronsAbbreviatedas[Ne]3s2[Ne]1s22s22p6Whatarethepossiblequantumnumbersforthelast(outermost)electroninCl?Cl17electrons1s<2s<2p<3s<3p<4s1s22s22p63s23p52+2+6+2+5=17electronsLastelectronaddedto3porbitaln=3l=1ml

=-1,0,or+1ms=?or-?NoblegascoreWhatistheelectronconfigura24Fe26electrons1s<2s<2p<3s<3p<4s<3d

1s22s22p63s23p64s23d6Abbreviatedas[Ar]4s23d6[Ar]1s22s22p63s23p6WhatistheelectronconfigurationofFe?WhatistheelectronconfigurationofMo?Mo42electrons1s<2s<2p<3s<3p<4s<3d<4p<5s<4d

<5p1s22s22p63s23p64s23d104p65s24d4Abbreviatedas[Kr]5s24d4[Kr]5s14d5Half-filledandfully-filledsubshellaremorestable.(p3,d5,f7)(p6,d10,f14)Onee-choiceFe26electrons1s<2s<2p<25Outermostsubshellbeingfilledwithelectrons&7.4PeriodicRelationshipsAmongtheElementsOutermostsubshellbeingfille26Ionizationenergyistheminimumenergy(kJ/mol)requiredtoremoveanelectronfromagaseousatominitsgroundstate.I1+X(g)X+(g)+e-I2+X+

(g)X2+(g)+e-I3+X2+

(g)X3+(g)+e-I1firstionizationenergyI2secondionizationenergyI3thirdionizationenergyI1<I2<I3Ionizationenergyistheminim27GeneralTrendinFirstIonizationEnergies8.4IncreasingFirstIonizationEnergyIncreasingFirstIonizationEnergyGeneralTrendinFirstIonizat28ElectronConfigurationsofCationsandAnionsNa[Ne]3s1Na+[Ne]Ca[Ar]4s2Ca2+[Ar]Al[Ne]3s23p1Al3+[Ne]Atomsloseelectronssothatcationhasanoble-gasouterelectronconfiguration.H1s1H-1s2or[He]F1s22s22p5F-1s22s22p6or[Ne]O1s22s22p4O2-1s22s22p6or[Ne]N1s22s22p3N3-1s22s22p6or[Ne]Atomsgainelectronssothatanionhasanoble-gasouterelectronconfiguration.ElectronConfigurationsofCat29ElectronConfigurationsofCationsofTransitionMetalsWhenacationisformedfromanatomofatransitionmetal,electronsarealwaysremovedfirstfromthensorbitalandthenfromthe(n–1)dorbitals.Fe:[Ar]4s23d6Fe2+:[Ar]4s03d6or[Ar]3d6Fe3+:[Ar]4s03d5or[Ar]3d5Mn:[Ar]4s23d5Mn2+:[Ar]4s03d5or[Ar]3d5ElectronConfigurationsofCat30+1+2+3-1-2-3CationsandAnionsOfRepresentativeElements+1+2+3-1-2-3CationsandAnions31Atomicradius:one-halfthedistancebetweenthetwonucleiintwoadjacentmetalatoms.EffectivenuclearchargeZeff=Z-shieldingconstant(0<<Z)Withinagroup,Zeffdecreaseswithn,duetostrongshieldingeffectfrominnershellelectrons.2)Withinaperiod,

ZeffincreaseswithZ,duetoweakshieldingeffectinthesameshell.Atomicradius:one-halfthed32Cationisalwayssmallerthanatomfromwhichitisformed.Anionisalwayslargerthanatomfromwhichitisformed.Ionicradius:theradiusofacationorananion,determinedbyX-raydiffractionofanioniccompoundinsolidstate.Cationisalwayssmallerthan33化學(xué)原理Chemistry課件-post+4+Quantun+Chemistry34ExercisesforChapters7and8:

7.167.797.807.1047.1067.1148.114ExercisesforChapters7and835QuantumTheoryandtheElectronicStructureofAtomsChapters7&8QuantumTheoryandtheElectro367.1LightandClassicQuantumTheory1.ClassictheoryofLightDifferentwaveshavedifferentcolor,anddifferentwavelength.Particles(Newton,1680):anarrayofparticles,emittedfromlightsource,thatmoveinspaceinonedimensionaldirection.forcespeedAccelerationspeedExactpositionandspeedcanbedeterminedatthesametime.Wave(Huygens,1690):anelasticvibrator,emittedfromlightsource,thatmoveinspaceinthreedimensionaldirection.Kineticenergy7.1LightandClassicQuant37Wavelength(l)7.1LightandClassicQuantumTheoryMaxwell(1893)wroteanequationforlightasawaveLightisanelectromagneticwavethatspreadinspace.Foralightinvacuum,

u=c=3.00x108m/sFrequency

n

isthenumberofwavesthatpassin1s.u=l·nabout1.28sfrommoontoEarth

Wavelength

l

isthedistancebetweentwosuccessivewaves.

Speed

u

isthedistanceofwavesthatpassin1s.Wavelength(l)7.1Lightand38Electromagneticradiationistheemissionandtransmissionofenergyintheformofelectromagneticwaves.Wavelength(l)a0amplitudeAtacertainposition(x),thewavechangewitht.Atacertaintime(t),thewavechangewithx.TheenergyintensityEnergychangescontinuously!EnergypassedthroughaunitareaperunittimeElectromagneticradiationist39化學(xué)原理Chemistry課件-post+4+Quantun+Chemistry40Planck’sQuantumHypothesis(1901):

Forasinglequantum,thesmallestquantityofenergy:

E=h

vPlanckconstanth=6.63x10-34J?sEnergychangeisonlybyhv,2hv,3hv,4hv...butneverby1.5hvor3.06hv…Thenin1918,hewonNobelPrizeinphysics.2.ClassicquantumtheoryofLight(Plank,1900)Classicaltheoryexplainsitwellatlowv,butverybadathighv.

Energyisemittedorabsorbedindiscreteunits(quantum).Blackbodyradiation:curveE

vs

vExplainsallresultswell.Planck’sQuantumHypothesis(141TheParticleNatureofLight:

PhotoelectricEffect:

hnvoltagecurrentV0(1)minimumfrequencyoflight(v0)(2)

v0isdependentofmetal.(3)Thecurrentlightintensity.TheParticleNatureofLight:42hv=pcParticlenatureWavenatureEinsteinPhotonTheory(1905)hn=KE+BEKE=hn-BEExplanationofthePhotoelectricEffect:Lighthasboth:Wavenaturel,E=hvParticlenaturem,momentump=mcEnergyE=mc2hv=pcParticleWaveEinstein437.2DualNatureofElectron1.Hydrogen

Emissionlinespectrum:Bohr’sPlanetarymodelHgLiCdSrCaNa7.2DualNatureofElec44e-canonlyhavespecific(quantized)energyvalueslightisemittedase-movesfromoneenergyleveltoalowerenergylevelBohr’sModelofHAtom(1913)En=-RH()1n2n(principalquantumnumber)=1,2,3,…RH

(Rydbergconstant)

=2.18x10-18J=13.6eVEphoton=DE=Ef-Ei3.ifDE=RH()1n21n2nf=1ni=2nf=1ni=3nf=2ni=3e-canonlyhavespecific(qua45Ephoton=2.18x10-18Jx(1/25-1/9)Ephoton=DE=1.55x10-19Jl

=6.63x10-34(J?s)x3.00x108(m/s)/1.55x10-19Jl

=

1280nmCalculatethewavelength(innm)ofaphotonemittedbyahydrogenatomwhenitselectrondropsfromthen=5statetothen=3state.Ephoton=hc/ll=hc/EphotonifDE=RH()1n21n2Ephoton=Ephoton=2.18x10-18Jx(1/46DeBroglie(1924)reasonedthate-isbothparticleandwave.2pr=nl

l=h/muu=velocityofe-m=massofe-2.DualnatureoftheElectron:MatteraswavesWhatisthedeBrogliewavelength(innm)associatedwitha2.5gPing-Pongballtravelingat15.6m/s?l=6.63x10-34/(2.5x10-3x15.6)l=1.7x10-32m=1.7x10-23nmNobelPrizein1929DeBroglie(1924)reasonedtha47&7.3QuantumMechanicalDescriptionofElectronsinAtomsSchr?dingerWaveEquationBasis:Bohr’stheory,goodtoexplaintheemissionspectrumofH,butcannotaccountforthespectrumofotherelements.Dualnatureofelectron(mandl).In1926,Schrodingerwroteanequationforelectronintheatom.?=E

E=V+KETotalenergyofthesystemPotentialenergykineticenergy(psi):wavefunction,oratomicorbitalthatdescribesthemovementofelectronintheatominthreedimensionalspace.?:HamiltonianOperator?2:LaplacianOperator2Uncertaintyprinciple(1927,WKHeisenberg):DXDph/4pItisimpossibletodeterminepreciselyboththepositionandmomentumofaparticleatthesametime.&7.3QuantumMechanicalDe481.ApplicationofSchr?dingertoHydrogenAtom

zxy(x,y,z)r?=E

?(x,y,z)

=E(x,y,z)

hereAftertransferredintospherecoordinate1.ApplicationofSchr?dinger49GeneralsolutionforHydrogenAtomSameasBohr’sresult,ie.

Onlydependentofn;AngularpartSpacialpartn=1l=0ml=0E1s=-13.6eV(Zisatomicnumber,andforH,Z=1)n=2l=0ml=0n=2l=1ml=0n=2l=1ml=-1n=2l=1ml=+1E**=-3.4eVGeneralsolutionforHydrogen50

r

distancefromthenucleusY2ElectrondensityButtheprobabilitytofindeinspace(DV)isP=Y2?DV,highestatr=0.529?90%ofelectrondensityfoundl=0n=1n=2n=3rdistancefromthenucleusY251ml=-1ml=1ml=0ml=-2ml=-1ml=0ml=1ml=27.6ml=-1ml=1ml=0ml=-2ml=52n:Principalquantumnumbern=1,2,3,4,….distanceofe-fromthenucleus,anddeterminationofenergyHeren,l,marecalledasthequantumnumberl:angularmomentumquantumnumberl

=0,1,2,3,…n-1n=1,l=0n=2,l=0,1n=3,l=0,1,2Shapeofthe“volume”ofspacethatthee-occupiesl=0123Orbitalspdfml

:

magneticquantumnumberml=-l,….,0,….+lifl=1(porbital),ml=-1,0,1ifl=2(dorbital),ml=-2,-1,0,1,

2orientationoftheorbitalinspacen:Principalquantumnumbern=53EnergyoforbitalsinasingleelectronatomEnergyonlydependsonprincipalquantumnumbernEn=-RH()1n2n=1n=2n=3GroundstateexcitedstateEnergyoforbitalsinasingle542.ApplicationofSchr?dingertoMany-electronatomszxy(xi,yi,zi)ri?=E

rjrij(xj,yj,zj)?Fortheithelectron,theaveragenetpotentialissphericallyapproximatedas:shieldingconstanti

=Eii

EffectivechargeofthenucleusGeneralsolution2.ApplicationofSchr?dinger55Energyoforbitalsinamulti-electronatomEnergydependsonnandln=1l=0n=2l=0n=2l=1n=3l=0n=3l=1n=3l=2Energyoforbitalsinamulti-56Orderoforbitals(filling)inmulti-electronatom1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6sOrderoforbitals(filling)in573.TheBuilding-UpPrincipleofelectronsintheorbitals:1.Electronsoccupyfirstthelowestenergyorbitalsavailable.2.Eachorbitalaccommodatesonlytwoelectrons,andthesetwoelectronsmusthaveopposingspins.Pauliexclusionprinciplespinquantumnumberms=+?or-?Todescriptoneelectroncompletely,Fourquantumnumbersofn,l,mlandmsareneeded.3.Inthedegenerateorbitals(samenandl),theelectronsoccupytheorbitalsasmanyaspossiblewithsamespins.N(Z=7)1s2s2p(Z=7)N1s22s22p3ElectronconfigurationHund’srule3.TheBuilding-UpPrincipleo58WhatistheelectronconfigurationofMg?Mg12electrons1s<2s<2p<3s<3p<4s1s22s22p63s22+2+6+2=12electronsAbbreviatedas[Ne]3s2[Ne]1s22s22p6Whatarethepossiblequantumnumbersforthelast(outermost)electroninCl?Cl17electrons1s<2s<2p<3s<3p<4s1s22s22p63s23p52+2+6+2+5=17electronsLastelectronaddedto3porbitaln=3l=1ml

=-1,0,or+1ms=?or-?NoblegascoreWhatistheelectronconfigura59Fe26electrons1s<2s<2p<3s<3p<4s<3d

1s22s22p63s23p64s23d6Abbreviatedas[Ar]4s23d6[Ar]1s22s22p63s23p6WhatistheelectronconfigurationofFe?WhatistheelectronconfigurationofMo?Mo42electrons1s<2s<2p<3s<3p<4s<3d<4p<5s<4d

<5p1s22s22p63s23p64s23d104p65s24d4Abbreviatedas[Kr]5s24d4[Kr]5s14d5Half-filledandfully-filledsubshellaremorestable.(p3,d5,f7)(p6,d10,f14)Onee-choiceFe26electrons1s<2s<2p<60Outermostsubshellbeingfilledwithelectrons&7.4PeriodicRelationshipsAmongtheElementsOutermostsubshellbeingfille61Ionizationenergyistheminimumenergy(kJ/mol)requiredtoremoveanelectronfromagaseousatominitsgroundstate.I1+X(g