1Chapter8AtomicStructure

Threeobjectives:Todescribethemovementstatesofelectrons

TointroducetheelectronconfigurationsTorevealtherelationshipbetweentheelectronicstructureandperiodicity21MovementsofElectronsinAtoms

Solutions:Experiments

ConclusionsApplyingthequantumnumbersobtainingfromtheSchr?dingerequationtodescribe.Movementsofsubmicroscopicparticles(r<10-8m)aredifferentfrommacroscopicalobjects.3玻爾In1922OttoStern斯特恩(1888–1969)In1943E.Schr?dinger薛定諤(1887-1961）In1933Ernest

Rutherford盧瑟福（1871-1937)in1908FatheroftheAtomicandNuclearPhysics‘allscienceiseitherphysicsorstampt-collecting’JosephJohnThomson湯姆孫（1856～1940)Cavendish卡文迪什實驗室

451-1CharacteristicsofElectronMovements

1-1-1TheEnergyofElectronsinAtomsIsQuantized量子性Figure8-1Experimentaldevicegeneratingthehydrogenspectrumandthehydrogenlinespectrumcontainsonlyafewdiscretewavelengthsinvisiblelightrange(1885,SwissphysicistBalmer).6In1913,SwedenphysicistRydberg

v=c/

=R(1/n12-1/n22)=3.289

1015(1/n12-1/n22)RydbergconstantR=

3.289

1015s-1;

n1,n2arepositiveintegrals,andn2>n1.7Anunsatisfactoryatomicmodel根據經典物理學概念：

電子在運動過程中要發射電磁波，氫原子光譜應為連續光譜；帶電微粒在力場中運動時總要產生電磁輻射并逐漸失去能量,運動著的電子軌道會越來越小,最終將與原子核相撞并導致原子毀滅.由于原子毀滅的事實從未發生而且原子光譜是線狀,且有規律性。這些都是經典物理學概念無法解釋的。8量子論：物質吸收和發射能量是不連續的，即物質只能以一最小單位(hν)一份一份的方式吸收或發射能量，能量最小的單位是光量子。玻爾理論建立在普朗克的量子論和愛因斯坦的光子學說的基礎上：愛因斯坦的光子學說認為光既是一種波，又有粒子性。

E=hν

Ｅ－光量子的能量ν－光的頻率

p－光量子的動量λ－光的波長

h—普蘭克常數9TheBohrmodelincludestwopoints:

(1)Electroninahydrogenmovesaroundthenucleusonlyincertainallowedcircularorbitswhichmustmeetthefollowingrequirement,eachorbitwasassignedanumbercalledtheprincipalquantumnumbern(主量子數):

mrv=nh/2πn=1,2,3…mismassofanelectron;

risthedistancefromanelectrontothenucleus;

visspeedofelectron;

h=6.626

10-34J?s(Plankconstant).10(2)Whentheelectronisinthelowestenergyorbit,thehydrogenatomissaidtobeinitsgroundstate(基態).Asenergy(electromagnetic,thermal,orelectrical)isaddedtotheatom,theelectronisraisedtohigherandhigherenergylevels(能級)fartherandhigherfromthenucleus.Whentheelectronisinanyhigherenergylevel,thehydrogenatomissaidtobeinanexcitedstate(激發態).

v=(Efinal-Einitial)/h

11

r=0.529n2Ao

E=-2.178×10-18Z2/n2J

n=1，r

1=0.529Ao,E

1=-2.179×10-18Jn=2，r

2=22×0.529Ao,E

2=-2.179×10-18/4Jn=3，r

3=32×0.529Ao,E

3=-2.179×10-18/9J……n=∞

,r∞

=∞

(infinite：電離了),E=0J12r

1=0.529Ao

Bohrradius

ΔE=Einfinite-E1

=[0-(-2.179×10-18J)]×6.02×1023mol-1

=l3l2kJ?mol-1.

ionizationenergyofthehydrogenatom

13Figure8-2Theenergylevelsoftheorbitsforhydrogenatom.v=(Efinal-Einitial)/h

14ThephenomenacannotbeinterpretedbyBohr’stheory:eachspectrallineconsistsoftwocloselineseachspectrallinesplitintotwoormorelinesinmagneticfieldsthespectraofpolyelectronicatoms

151913年《論原子構造和分子構造》，首次打開了人類認識原子結構的大門，為近代物理研究開辟了道路。量子力學是以玻爾為領袖的一代杰出物理學家集體才華的結晶。161-1-2TheMovementofElectronsinAtomsIsStatistical

統計性（1）DeBroglie’sEquation德布羅意方程（1924）

dualnatureoflight

Einsteinmass-energyrelation

:E=mc2E=h

P=mc=E/c=h

/c=h/

=h/P=h/mv

deBroglieequationDeBroglie’swaveortheparticle’swave.17Figure8-3Davissson-Germer

Electrondiffractionstestin1927.18(2)TheHeisenbergUncertaintyPrinciple(in1927)

海森堡不準確關系

?x·?P≥h/2π?x·?v≥h/2πm

?P:theuncertaintyinmomentum?x:theuncertaintyinpositionoftheparticle?v:theuncertaintyinitsspeedm:themassoftheparticleinkg

h=6.626×10-34J?s

19Usuallyelectronsmoveataspeedneartolightspeed,itssizeislargelysmallerthan10-10m.Thustolocateitprecisely,?xshouldbelessthan10-11m,thentheuncertaintyinthespeedoftheelectron

?v≥h/2πm·?x=6.626

10-34/2

3.14

9.11

10-31

10-11=1.16

107(m?s-1)20Table8-1

ComparisonsonMovementsofSubmicroscopicParticlesandMacroscopicalObjects

MacroscopicalObjectsNewtonmechanicallaw

F=ma

Thestateofobjects(speedandposition)atanyinstantcanbepreciselydetermined.SubmicroscopicParticles/r<10-8mQuantummechanicalmodel?2Ψ/?x2+?2Ψ/?y2+?2Ψ/?z2

=-8π2m(E–V)Ψ/h2Thestateofsubmicroscopicparticles(energyandpossibility)atanyinstantcanbeexpressedbyΨ(x,y,z).

?x·?v≥h/2πm

21在L.V.德布羅意的微觀粒子具有波粒二象性的基礎上，1926年薛定諤提出用波動方程描述微觀粒子運動狀態的理論，后稱薛定諤方程，奠定了波動力學的基礎.1944年，薛定諤著《生命是什么》一書，試圖用熱力學、量子力學和化學理論來解釋生命的本性。這本書使許多青年物理學家開始注意生命科學中提出的問題，引導人們用物理學、化學方法去研究生命的本性，使薛定諤成為蓬勃發展的分子生物學的先驅。E.Schr?dinger薛定諤（1887～1961）Austrianphysicist1933年，與狄拉克共同獲得諾貝爾物理學獎221-2Descriptionsofelectronmovements1-2-1波函數Ψ量子力學用波函數Ψ來描述原子中電子的運動。23Ψ是如何得到的？——薛定諤方程波函數與薛定諤方程24★

方程中既包含體現微粒性的物理量m,也包含體現波動性的物理量ψ★

求解薛定鍔方程,就是求得波函數ψ和能量

E★

解得的ψ不是具體的數值,而是包括三個常數(n,l,m)和三個變量(r,θ,φ)的函數式Ψn,l,m(r,θ,φ)★

數學上可以解得許多個Ψn,l,m(r,θ,φ),但其物理意義并非都合理★有合理解的函數式叫做波函數,它們以n,l,m的合理取值為前提。每個合理的解Ψ就是表示電子運動的某一穩定狀態。波函數=薛定鍔方程的合理解=原子軌道

25在量子力學中，用波函數和與其對應的能量來描述電子的運動狀態。Ψ是描述電子運動狀態的數學表達式，Ψ的空間圖象叫原子軌道，原子軌道的數學表達式就是波函數。26波函數的物理意義電子云是電子出現概率密度的形象化描述。

：原子空間上某點附近單位微體積內電子出現的概率，即概率密度（幾率密度）。小黑點較密的地方，概率密度較大，單位體積內電子出現的機會多。如1s的電子云Ψ是描述核外電子運動狀態的數學表達式，它描述了電子運動的方式和規律271-2-2TheThreeQuantumNumbersprincipalquantumnumber,n:1,2,3,4,5,6,7,8,…,

withcorrespondingsymbols:K,L,M,N,O,P,Q,R…tellsthesizeofanorbitalandlargelydeterminesitsenergyhydrogenandHe+,Li2+,B3+theenergy

En=-2.179×10-18

Z2/n2(J)

28angularmomentumquantumnumber角量子數,l:0,1,2,3,4,5,…n-1,spdfgh…tellstheshapeoftheorbitalsForpolyelectronicatoms,Ens

Enp

End

Enf,theenergiesofdifferentsubshellaredifferent,hereEnliscalledenergylevel.En,l=-2.179×10-18

Z*2/n2(J)29Figure8-4Boundarysurfacediagramsfors,p,dorbitals.30magneticquantumnumber磁量子數

ml:-lto+l

311-2-3PicturesofOrbitals

chargeclouds,boundarysurfacediagramandplotsofradialprobability.

Figure8-5(a)Chargecloudofthe1sorbitalofahydrogenatom.(b)Boundarysurfacediagramfor1sorbital.32Figure8-7Planarschematicforboundarysurfacesofs,p,dorbitals.33Figure8-6Radialprobabilityplottedagainstdistancefromthenucleusforahydrogenelectronindifferentorbitals.341-2-4

ElectronSpin

andPauliExclusionPrincipleIn1925,HollandgraduatesputforwardahypothesisofElectronSpin,AustrianphysicistPaulisuggestedthefourthquantum.Figure8-8SchematicofStern–Gerlachexperimentin1922.OttoStern斯特恩(1888–1969)In194335PauliexclusionprinciplePauliproposedthatinagivenatomnotwoelectronscanhavethesamesetoffourquantumnumbers(n,l,m,

and

ms).

36小結電子具有波粒二象性，需按幾率分布的統計規律來進行研究。波函數是描述核外電子運動狀態的數學表達式，其空間圖象為“原子軌道”。幾率密度|Ψ|2

是電子在原子核外空間某處單位體積內出現的概率。用小黑點表示其分布所得的空間圖象。描述原子中電子狀態需用四個量子數：主量子數(n)、角量子數(l)、磁量子數(m)、自旋量子數(ms)。37nιm軌道/數電子數(2n2)K1s00１s122L2s0０2s428p10、

±12p6M3s003s9218p10、

±1３p6d20、±1、±23d10N4s004s16232p10、±14p6d20、±1、±24d10f30、±1、±2、±34f1438Exercises：描述原子中電子運動狀態的四個量子數的物理意義各是什么？它們的可能取值是什么？下列各組量子數哪些是不合理的，為什么？

(1)n=2,l=1,m=0(2)n=2,l=2,m=-1(3)n=3,l=0,m=0(4)n=3,l=1,m=1(5)n=2,l=0,m=-1(6)n=2,l=3,m=2下列說法是否正確？不正確的應該如何改正？s電子繞核運動，其軌道為一圓周，而p電子是走8字形的；主量子數n為1時，有自旋相反的兩條軌道；主量子數n為4時，其軌道總數為16，電子層電子最大容量為32；主量子數n為4時，有3s,3p,3d三條軌道。39核外電子運動的特征核外電子運動的描述Reviewsn-1≥l

≥

∣m

∣,

ms=+1/2?x·?P≥h/2π?x·?v≥h/2πm

40zx++++++++++++++-------------zzzzzxxxxxxxyyyyspypxpzdxydyzdxzdz2

dx2-y2ReviewsHydrogenandHe+,Li2+,B3+:En=-2.179×10-18

Z2/n2(J)41Polyelectronicatoms:En,l=-2.179×10-18

Z*2/n2(J)422ElectronArrangements多電子原子的能級,原子軌道能級圖核外電子排布的規則，核外電子排布432-1OrbitalEnergyLevelsinPolyelectronicAtoms

2-1-1OrbitalEnergiesinPolyelectronicAtomsSlater斯萊特中心勢場模型：Theelectronisscreenedorshieldedfromthenuclearchargebytherepulsionsoftheotherelectrons.Thedecreaseofthenuclearchargebytheother(Z-1)e-iscalledscreeneffect

or

shieldeffect屏蔽效應.Thedecreasedpartiscalledthescreenconstantorshieldconstant屏蔽常數

σ.TheeffectivenuclearchargeZ*=Z-σ

44Z－σ=Z*，Z*——有效核電荷數σ為屏蔽常數，可用斯萊特經驗規則算得。屏蔽效應：把多電子原子中其余電子對指定的某電子的作用近似地看作抵消一部分核電荷對該指定電子的吸引。En,l=-2.179×10-18

Z*2/n2(J)45(1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5p)…

(1)Theouterelectronsdon’tscreentheinnerelectrons,σ=0；(2)Whenthescreenedelectronisnsornpelectron,thescreenconstantforelectronsinthesamegroup:σ=0.35(forthetwoelectronsin1sorbital,σ=0.30);thescreenconstantforelectronsinthenext-to-the-outermostor(n-1)group:σ=0.85,thescreenconstantforelectronsinthenext-to-the-next-to-the-outermostor(n-2)shellandmoreinnershell:σ=1；(3)Whenthescreenedelectronisndornf,thescreenconstantamongthesamegroup:σ=0.35,thescreenconstantforelectronsintheleftside:σ=1.46Example8-1Calculatetheenergylevelsfor1sorbitaland2sorbitaloflithiumatom.

SOLUTIONLithiumatomhasthreeelectronswhichcanbedividedasbelow:(1s)2(2s)1

For1selectron,σ=0.3,Z*=3-0.3=2.7E1s=-2.179

10–18

2.72/12=-15.88

10–18(J)

For2selectron,σ=2

0.85=1.7,Z*=3-1.7=1.3E2s=-2.179

10–18

1.32/22=-0.92

10–18(J)

Therefore,E1s

<E2s47Example8-2Calculatetheenergylevelsfor3s、3p、3dand4sorbitalsofpotassiumatom.

SOLUTIONConsiderthepotassiumatom,whichhas19electrons:(1s)2(2s,2p)8(3s,3p)8(3d)1(4s,4p)For3selectron,σ=1×2+0.85×8+0.35×7=11.25，

Z*=19-11.25=7.75，

E3s=-2.179×10-18×7.752/32=-14.542×10-18(J)AccordingtoSlaterrule,E3s=E3p(Infact,E3s<E3passhowninFigure8-9,forSlaterruleisjustanapproximatecalculation.)For3delectron,σ=18，Z*=1,E3d=-2.179×10-18/32=-0.242×10-18(J)Supposethattheoutmostelectronisin4sorbital,thenfor4sorbital:σ=1×10+0.85×8=16.8，Z*=2.20,E4s

=-2.179×10-18

Z*2/n2=-2.179×10-18×2.202/42

=-0.66×10-18(J)Thatis,E3s=

E3p

<E4s<E3d.能級分裂;能級交錯.482-1-2Cotton’sOrbitalDiagram

Figure8-9PlotsoforbitalenergiessequencesuggestedbyCotton.49(1)Forhydrogenatom,Z=1,itsorbitalenergyisdeterminedbytheprinciplequantumnumber,n;

En=-2.179×10-18

Z2/n2J

,andEns=Enp

=End

=Enf.

(2)Forpolyelectronicatoms,theattractionofnucleuschargestotheelectronsincreasewiththeincreasingatomicnumber,theorbitalenergydecreaseswiththeincreasingatomicnumber.E1s(Cl)=-2.179×10-18(17-0.3)2/12J=-607.7×10-18(J)；

E1s(H)=-2.179×10-18JE1s(Cl)<E1s(H).50Figure8-9PlotsoforbitalenergiessequencesuggestedbyCotton.51(3)Forpolyelectronicatoms,theelectronsindifferentoutersubshellsarescreeneddifferently,whichcausesplitoforbitalenergies(能級分裂);thatis,Ens<Enp<E

nd<Enf.Thesephenomenacanbeexplainedbypenetrationeffect(鉆穿效應).

(4)Forpolyelectronicatoms,thesequenceoforbitalsinenergyisdifferent.Forsomeatoms,orbitalenergiesinterlace(能級交錯).Forexample,Z=15~20,

E3d>E4s,whileZ<15andZ>20,E3d<E4s.Thisisduetothepenetrationeffectaswell.52鉆穿效應:外層電子向內層鉆穿的效應，進入原子內部空間，受到核的較強的吸引作用，能量會降低。3d與

4s軌道的徑向分布圖532-1-3Pauling’sOrbitalDiagramLinusCarlPauling鮑林（1901-1994）In195454Table8-3GroupsofOrbitalEnergyLevelsSuggestedbyPauling

GroupsofOrbitalEnergyLevels

OrbitalsinEachGroupⅠ1sⅡ2s2pⅢ3s3pⅣ4s3d4pⅤ5s4d5pⅥ6s4f5d6pⅦ7s5f6d7pⅧ8s5g6f7d8pⅨ9s6g7f8d9p552-2ThreeRulesforElectronArrangements

Lowest-energyrule

最低能量原理:電子在核外排列應盡先分布在低能級軌道上,使整個原子系統能量最低。Pauliexclusionprinciple

保里不相容原理:在同一原子中,不可能存在所處狀態完全相同的電子。Hund’srule

洪特規則:在能量相同（n和l相同）的軌道上分布的電子,將盡先占據不同的軌道,且自旋平行。56應用核外電子填入軌道順序圖，根據保里不相容原理、能量最低原理、洪特規則，可以寫出元素原子的核外電子分布式。如19K1s22s22p63s23p64s1

26Fe1s22s22p63s23p63d64s2

核外電子填入軌道的順序正確書寫是從內層到外層書寫，將同一層電子放在一起，（可與填充順序不一致。）57Figure8-10Orbitaldiagramsfornitrogenatom.58Electronconfigurations

N:1s22s22p3,1s22s22px12py12pz159Abbreviatedelectronconfigurations

原子實+最高能級組26Fe:1s22s22p63s23p63d64s2

Fe:[Ar]3d64s229Cu:1s22s22p63s23p63d104s1

Cu:[Ar]3d104s1(not[Ar]3d94s2）33As:1s22s22p63s23p63d104s24p3

As:[Ar]3d104s24p360Valenceelectronconfigurations

Valenceelectronsrefertoelectronsthatinvolveinbondformation.Theorbitalsthatoccupiedbyvalenceelectronsarecalledvalenceorbitals.

Foratomsofthemain-groupelements,theirvalenceelectronsaretheelectronswiththeoutmostprincipalquantumnumber.Forthetransitionmetals,theirvalenceelectronsaretheelectronsinthehighestgroupoforbitalenergy,forexample,thevalenceelectronconfigurationforironatomis3d64s2.61valenceelectronconfigurationFe2+is3d6Fe3+is3d5Forthetransitionmetals,theirvalenceelectronsaretheelectronsinthehighestgroupoforbitalenergy,forexample,thevalenceelectronconfigurationforironatomis3d64s2.62Pd:4d10insteadof4d85s2;Pt:5d96s1not5d86s2.63元素周期律：元素以及由它形成的單質和化合物的性質，隨著元素的原子序數(核電荷數)的依次遞增，呈現周期性的變化。642-3ThePeriodicTableandtheElectronConfigurations

Period(周期),Group（族），

Block（區）65Table8-4TheCorrespondingRelationshipbetweenthePeriod

inPeriodicTableandtheAtomicEnergyLevelGroup

Periods

GroupsofOrbitalEnergyLevels

NumbersoforbitalsMaximumNumbersofElectronsAccommodated=Numbersofelements

Types1I(1s)12supershort2II(2s2p)48short3III(3s3p)48short4IV(4s3d4p)918long5V(5s4d5p)918long6VI(6s4f5d6p)1632superlong7VII(7s5f6d7p)1632(notfinished)

notfinished

8VIII(8s5g6f7d8p)2550(119~168)-9IX(9s6g7f8d9p)2550(169~218)-66ThegroupslabeledIA,IIA,IIIA,IVA,VA,VIA,VIIA,VIIIA(somePeriodicTableuse0insteadofVIIIA,Seeappendix6.)arecalledmain-group,orrepresentative,elements.Everymemberofthesegroupshasthesamevalenceelectronconfiguration,andvalenceelectronsaretheelectronsintheoutmostshell.ThegroupslabeledIIIB,IVB,VB,VIB,VIIB,VIII(VIIIgroupoccupyingthreeverticallines),IB,IIB,arecalledtransition-metalgroups.Themain-groupscontainbothshortperiodsandlongperiods;thetransition-metalgroupscontainonlylongperiods.675-3-5元素周期系與核外電子分布的關系ⅠA0一1ⅡAⅢAⅣAⅤAⅥAⅦA2二345678910三1112ⅢBⅣBⅤBⅥBⅦBⅧⅠBⅡB131415161718四192021222324252627282930313233343536五373839404142434445464748495051525354六555657*727374757677787980818283848586七878889*104105106107108109110111112元素周期系與核外電子分布的關系鑭系575859606162636465666768697071錒系8990919293949596979899100101102103Sddspfns1~2

(n-1)d1~9ns1~2(n-1)d10ns1~2ns2np1~6(n-2)f0~14(n-1)d0~2ns268Example8-3Writetheelectronconfiguration,name,symbolandatomicnumberforanelementinthefifthperiodandGroupVA.SOLUTIONElectronconfiguration:36[Kr]4d105s25p3

Z=51,Sb,Antimony(Stibium).69Example8-4Theatomicnumberis23.Writeitselectronconfiguration,valenceelectronconfiguration,andpointoutitsposition.SOLUTION23Zelectronconfiguration:1s22s22p63s23p63d34s2,valenceelectronconfiguration:3d34s2,Thereforethiselementisatthefourthperiod,GroupVB.ItisV.703PeriodicTrendinAtomicProperties

3-1AtomicRadius

CovalentatomicradiiMetallicradiiVanderWaalsradii

71共價半徑=兩個相同原子形成共價鍵時，其核間距離的一半。定義d=198pmr(Cl)=99pmd=154pmr(C)=77pm72金屬半徑=金屬單質晶體中，兩個相鄰金屬原子核間距離的一半。定義d=256pmr(Cu)=128pm73主族元素：從左到右r減小；從上到下r增大。過渡元素：從左到右r緩慢減小；

從上到下r

略有增大。He50Ne160Ar191Kr198Xe21774解釋:

電子層數不變的情況下,有效核電荷的增大導致核對外層電子的引力增大.

主族元素:電子逐個填加在最外層,對原來最外層上的電子的屏蔽參數(σ)小,有效核電荷(Z*)迅速增大。

副族元素:電子逐個填加在次外層,增加的次外層電子對原來最外層上電子的屏蔽較強,有效核電荷增加較小。753-2IonizationEnergyMg(g)=Mg+(g)+e-

I1=738kJ?mol-1Mg+(g)=Mg2+(g)+e-

I2=1445kJ?mol-1

Mg2+(g)=Mg3+(g)+e-

I3=7730kJ?mol-1firstionizationenergy,I1secondionizationenergy,I2thirdionizationenergy,I

3.I

1<I

2<I3

76N、P、As、Sb、Be、Mg電離能較大

——半滿，全滿。同周期總趨勢：自左至右I1逐漸增大,與原子半徑減小的趨勢相對應.同族總趨勢：自上至下I1減小,與原子半徑增大的趨勢是對應的.773-3ElectronAffinity

A(g)+e-→A-(g)E1A-(g)+e-=A2-(g)E2電子親合能正負號的規定與焓的正負號規定相反，即放熱為正，吸熱為負。電子親合能用來衡量氣態原子得電子的難易:電子親合能越大,原子越易得到電子;電子親合能越小,原子越難得到電子.78Figure8-12Firstionizationenergyandelectronaffinityasafunctionofatomicnumber.793-4Electronegativity

Electronegativityrepresentstheabilityofanatomina