MODREN PHYSICS Chapter 9 Complex Atoms and Molecules.docx

MODREN PHYSICS Chapter 9 Complex Atoms and Molecules.docx

《MODREN PHYSICS Chapter 9 Complex Atoms and Molecules.docx》由会员分享，可在线阅读，更多相关《MODREN PHYSICS Chapter 9 Complex Atoms and Molecules.docx（10页珍藏版）》请在冰豆网上搜索。

MODRENPHYSICSChapter9ComplexAtomsandMolecules

Chapter9ComplexAtomsandMolecules

Chapter9-1EnergyintheHeliumatom

PartoneThebasicideasforHeliumatom

A.Heliumatomhastwoelectronscirculatingoutsideanucleuswithtwopositivelychargedprotons

B.Thepotentialenergyforheliumconsistsofthreeterms：

TworepresenttheinteractionofthetwoelectronswiththenucleusofchargeZ=2oneforeachelectron

Threetermrepresentstheelectronrepulsion

C.ifweuseaverycrudeapproximationweignoretheelectron-electronrepulsion

ThisputseachelectroninahydrogenlikeatomwithZ=2

Becausethebindingenergyis13.6

eVforeachelectron

Sothetotalbindingenergyis

Eachofthetwoelectronsisinanorbitofradius

Where

istheBohrradius

D.Thewavefunctioninapproximationistheproductoftwohydrogenlikeground-statewavefunctiongroundstaten=1andl=0

Consider:

onethetotalwavefunctionmustbeantisymmeticunderelectronexchangetwowemusthaveforgottenthespins.Sototalwavefunctionis:

Since,tothelevelofapproximationofourwork,thespinsdonotenterintotheenergy,sothisstatehasenergy-108.8eV

ParttwoWeconsiderthefirstexcitedstateofhelium

A.Wecontinuetoignoretheelectron-electronrepulsionweplaceoneelectroninthen=1l=0state,theotherinann=2l=0state,sotheenergyisthen

B.ThetotalspinofthetwoelectronscanbeeitherS=1orS=0

IfS=1thespatialwavefunctiontobeantisymmetric

IfS=0thespatialwavefunctiontobesymmetric

c.Whentheelectron-electron-electronrepulsionistakenintoaccount,thesestatesarenolonger（不再）degenerate.

Thereasonisbasicallythatwhenthespatialwavefunctionisantisymmetric,theprobabilitythateachelectronisatthesameplaceiszero.Moregenerally,foranantisymmetricwavefunctionitismoreeachprobablethattheelectronsstayawayfromeachotherandtheeffectofrepulsionisdecreased--exchengeforce

Inchapter8,weshowedthattheexclusionprinciplealtered（改变）theprobabilityoffindingparticlesclosetogether.

PartthreeWhenthespinsofthetwoelectronsareparalled,theelectronsarekeptapartbyadistance

istheDeBrogliewavelength,

Thisexclusion-principleeffectisabsent（缺席，不在的）whenthetwoelectronsareinaspinsingletstate.

Sotheenergydifferencebetweenthesingletandtripletstatesduetocoulombrepulsionistheelectrostaticenergyofasphereofchargeeandradius

thecoulombpotential

PartfourConsidertheelectron-electronrepulsion

Ifweneglectrepulsion.Theground-stateenergyofheliumis-108.8eV

Ifweconsidertwoelectronsliesbetween

and

Sothiscorrespondstoarepulsionenergybetween27.2eVand54.4eV

Sothebindingenergyforthegroundstatethenliesbetween108.8eV-27.2eV=81.6eV

And108.8eV-54.4eV=54.4eV

Iffact,theexperimentvalueis79eVwhichotherwayuse

changeZ

Theaveragevalue

Wefindthat

whichisindeedlessthantheunscreenednuclearchargeofZ=2

PartfiveThesingle-electronionizationenergy

A.Whenoneoftheelectronisremovedtheremainingelectronisina1SstateofaZ=2hydrogenlikeatom

Thebindingenergyofthisremainingelectronis-54.4eVsothatthedifferenceof79eV-54.4eV=24.6eV

Thisisthesingle–electronionizationenergy----theenergyrequiredtoremoveasingleelectronfromhelium

Bthefirstexcitedstateofheliumwillbeeitheraspatiallystateofheliumwillbeeitheraspatiallysymmetric（spinantisymmetricS=01S2S）oraspatiallyantisymmtic（spinsymmetricS=11S1S）

Thesecondofthesehasthelowerenergysinceinaspatiallyantisymmtricstatetheelectronstendtobeawayfromeachother

Thefirstofthesetheenergyis

Soittakesapproximately79eV-68eV=11eVtoexciteanelectrontothefirstexcitedstate11eVbiggerenough

Chapter9-2BuildingupthePeriodictable

Chapter9-3BeyondZ=10andGeneralcomments

Chapter9-4Molecules

Amoleculeisastablearrangementofelectronsandmorethanonenucleus,welimitourselvestodiatomicmolecules.

ForexampleHClO2N2COH2

Twoapproximatething:

1weassumethatthenucleiarefixedinspace

2themovingelectronscreateasmeared–outchangedistribution

PartoneThe

molecule

The

moleculewasthesimplestmoleculeandsinglyionizedH2,consistingoftwoprotonsandoneelectron.

AIftheprotonsareveryclosetogether-inotherwordsR→0

Themoleculelooksexactlylikeasinglyionizedheliumatom，sotheelectronicenergyofthissystemis

BIfthetwoprotonsarefarapart,thentheelectronwillbeboundtooneprotonortheoneasinordinaryhydrogensothat

Cthefullelectronicexpression

willinterpolatebetweenthesetwovalues

D.contributionsofelectronicandcoulombenergiestotheinternuclearpotential

P271Figure9-6

Considertheproton-protonrepulsionthereis

E.Thereisaminimumat

Thisisastableequilibriumpoint,anditcharacterizesthesizeofthemolecule

To

theexperimentalvalueisR0=0.106nmandtheenergyat

is2.8eV

F.ThewavefunctionisthesolutionofaSchrodingerequationoftheform

ThefirsttermistheKineticenergyoftheelectron

ParttwoThe

moleculeandvalencebonds

AThe

moleculeinvolvestwoelectronssospinandtheexclusionprincipleenterthestructureofthismoleculeinanimportantwaythe

moleculeistypicalofdiatomicmoleculeswhoseatomseachhaveunfilledshells.

Btheoverallwavefunctionof

mustbeantisymmetric

Ifthespatialwavefunctionofthetwoelectronsissymmetricundertheirinterchangethenthespinwavefunctionmustbeantisymmetricthatis,itmustbeaspinsinglet.

Ifthespatialwavefunctionisantisymmetric,thespinwavefunctionwillbeasymmetric,

itmustbeaspintriplet.

Infact,theground-statewavefunctionisthespatiallysymmetricstate

Figure9-7

CValencebond

In1927FriteLondonandWalterHeitlerfirstappliedquantummechanicstomolecularbonding.

Whenanelectroninanatomisnotalreadypairedupwithanotherelectroninthesameatomtoformanantisymmetricspinstatethenthatelectroncanpairuptoformantisymmetriccanpairuptoformanantisymmetricspinstatewithanelectronfromasecondatom,whereuponthetwoatomsformabond.

PartthreeIonicBonding（covalentbond）

AAnothermechanismthatdeterminesmolecularstructureisapparent（显然）inthebindingofatomsoneofwhichhasasingleelectronoutsideashell（Asinalkalimetals（碱金属））andtheotherofwhichhasasinglehole,inaclosedshell（asinhalogens（卤素））

Btheelectronaffinity:

theenergywasreleasedwhenasingleelectronfallsintotheholeintheoutershellofthehalogen,,

Ingeneral,theelectronaffinityissimilarinmagnitudetotheionizationenergy.

Chaper9-5Nuclearmotionanditsconsequences

Considernuclearmotion

becausethenucleiaresomassive,theirmotionisveryslowcomparedwiththatoftheelectrons.duringthisslowmotion,theelectronshaveplentyoftimetoadapttotheslowlyvaryinginternuclearseparationsthusthenuclearmotionisdescribedintermsofapotential

PartoneVibrationsinmolecules

Thecorrectpotentialenergyue（R）forthenucleiconsistsoftwoparts

WeexpandthepotentialenergyaboutR=R0,usingtheTaylorexpansion

So

Thequantizedenergiesofour“spring”arethengivenbyeq（3-34）

Example9-4

Todiatomicmolecule:

thecurveofthepotentialenergyofmoleculevarieswiththeinternucleardistanceR

Intheneighborhoodofthecurve,whichcorrespondstothenormalconfigurationofthemolecule,theshapeofthecurveisverynearlyaparabolainthisregion,then

Where

istheequilibriumseparationoftheatomstheinteratomicforcethatgivensrisetothispotentialenergymaybefoundbydifferentiatingu

LooklikesimpleharmonicoscillationHarmonicoscillator

ParttwoRotationsofmolecules

Themoleculecanactasarigidextendedstructureandrotate

wecanapproximateadiatomicmoleculeasadumbbell-likeobjectwithamomentofinertiaI,aboutanaxistheenergy

so

Example9-59-6

##

Crystals

Mostsolidsarecrystalline,withtheatoms,ions,ormoleculesofwhichtheyarecomposed（构成）fallingintoregularrepeated（重复）three-dimensionalpatterns.

Ioniccrystal（Covalentcrystal）

Cohesiveenergy（晶体内聚能，原子性内聚能）

Thecohesiveenergyofanioniccrystalistheenergythatwouldbeliberatedbytheformationofthecrystalfromindividualneutralatoms.

Latticeenergy（晶体离子性内聚能）

Theenergyneededtoseparateanioniccrystalintoindividualions（notintoatoms）

istheMadelungconstant（结构常数）

原子性内聚能=离子性内聚能

+正离子电离能

+负离子的电子亲和势

Exp:

InanNaClcrystal,theequilibriumdistancer0betweenionsis0.281nm.FindthecohesiveenergyinNaCl.

Solution

Since

=1.748and

=-7.96eV

Becausewemaynotcounteachionmorethanonce,onlyhalfthispotentialenergy,or-3.98eV,representsthecontributionperiontothecohesiveenergyofthecrystal.

WemustalsotakeintoaccounttheenergyneededtotransferanelectronfromaNaatomtoaClatomtoyieldaNa+-Cl-ionpair.Thiselectrontransferenergyisthedifferencebetweenthe+5.14eVionizationenergyofNaandthe-3.61eVelectronaffinityofCl,or+1.53eV.Eachatomthereforecontributes+0.77eVtothecohesiveenergyfromthis,

Thetotalcohesiveenergyperatomis

-3.98+0.77=-3.21eV

Rotationenergy

Wehavebeenconsideringonlyrotationaboutanaxisperpendiculartotheaxisofsymmetryofadiatomicmolecule,

end-over-endrotations.

Whataboutrotationsabouttheaxisofsymmetryitself?

Dissociate（分解）