《无机化学简明教程》课件-Chapter 8 Atomic Structure

1Chapter8AtomicStructure

Threeobjectives:Todescribethemovementstatesofelectrons

TointroducetheelectronconfigurationsTorevealtherelationshipbetweentheelectronicstructureandperiodicity21MovementsofElectronsinAtoms

Solutions:Experiments

ConclusionsApplyingthequantumnumbersobtainingfromtheSchrödingerequationtodescribe.Movementsofsubmicroscopicparticles(r<10-8m)aredifferentfrommacroscopicalobjects.3玻尔In1922OttoStern斯特恩(1888–1969)In1943E.Schrödinger薛定谔(1887-1961）In1933Ernest

Rutherford卢瑟福（1871-1937)in1908FatheroftheAtomicandNuclearPhysics‘allscienceiseitherphysicsorstampt-collecting’JosephJohnThomson汤姆孙（1856～1940)Cavendish卡文迪什实验室

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根据经典物理学概念：

电子在运动过程中要发射电磁波，氢原子光谱应为连续光谱；带电微粒在力场中运动时总要产生电磁辐射并逐渐失去能量,运动着的电子轨道会越来越小,最终将与原子核相撞并导致原子毁灭.由于原子毁灭的事实从未发生而且原子光谱是线状,且有规律性。这些都是经典物理学概念无法解释的。8量子论：物质吸收和发射能量是不连续的，即物质只能以一最小单位(hν)一份一份的方式吸收或发射能量，能量最小的单位是光量子。玻尔理论建立在普朗克的量子论和爱因斯坦的光子学说的基础上：爱因斯坦的光子学说认为光既是一种波，又有粒子性。

E=hν

Ｅ－光量子的能量ν－光的频率

p－光量子的动量λ－光的波长

h—普兰克常数9TheBohrmodelincludestwopoints:

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

mrv=nh/2πn=1,2,3…mismassofanelectron;

risthedistancefromanelectrontothenucleus;

visspeedofelectron;

h=6.626

10-34J∙s(Plankconstant).10(2)Whentheelectronisinthelowestenergyorbit,thehydrogenatomissaidtobeinitsgroundstate(基态).Asenergy(electromagnetic,thermal,orelectrical)isaddedtotheatom,theelectronisraisedtohigherandhigherenergylevels(能级)fartherandhigherfromthenucleus.Whentheelectronisinanyhigherenergylevel,thehydrogenatomissaidtobeinanexcitedstate(激发态).

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：电离了),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《论原子构造和分子构造》，首次打开了人类认识原子结构的大门，为近代物理研究开辟了道路。量子力学是以玻尔为领袖的一代杰出物理学家集体才华的结晶。161-1-2TheMovementofElectronsinAtomsIsStatistical

统计性（1）DeBroglie’sEquation德布罗意方程（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)

海森堡不准确关系

∆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.德布罗意的微观粒子具有波粒二象性的基础上，1926年薛定谔提出用波动方程描述微观粒子运动状态的理论，后称薛定谔方程，奠定了波动力学的基础.1944年，薛定谔著《生命是什么》一书，试图用热力学、量子力学和化学理论来解释生命的本性。这本书使许多青年物理学家开始注意生命科学中提出的问题，引导人们用物理学、化学方法去研究生命的本性，使薛定谔成为蓬勃发展的分子生物学的先驱。E.Schrödinger薛定谔（1887～1961）Austrianphysicist1933年，与狄拉克共同获得诺贝尔物理学奖221-2Descriptionsofelectronmovements1-2-1波函数Ψ量子力学用波函数Ψ来描述原子中电子的运动。23Ψ是如何得到的？——薛定谔方程波函数与薛定谔方程24★

方程中既包含体现微粒性的物理量m,也包含体现波动性的物理量ψ★

求解薛定锷方程,就是求得波函数ψ和能量

E★

解得的ψ不是具体的数值,而是包括三个常数(n,l,m)和三个变量(r,θ,φ)的函数式Ψn,l,m(r,θ,φ)★

数学上可以解得许多个Ψn,l,m(r,θ,φ),但其物理意义并非都合理★有合理解的函数式叫做波函数,它们以n,l,m的合理取值为前提。每个合理的解Ψ就是表示电子运动的某一稳定状态。波函数=薛定锷方程的合理解=原子轨道

25在量子力学中，用波函数和与其对应的能量来描述电子的运动状态。Ψ是描述电子运动状态的数学表达式，Ψ的空间图象叫原子轨道，原子轨道的数学表达式就是波函数。26波函数的物理意义电子云是电子出现概率密度的形象化描述。

：原子空间上某点附近单位微体积内电子出现的概率，即概率密度（几率密度）。小黑点较密的地方，概率密度较大，单位体积内电子出现的机会多。如1s的电子云Ψ是描述核外电子运动状态的数学表达式，它描述了电子运动的方式和规律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角量子数,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磁量子数

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小结电子具有波粒二象性，需按几率分布的统计规律来进行研究。波函数是描述核外电子运动状态的数学表达式，其空间图象为“原子轨道”。几率密度|Ψ|2

是电子在原子核外空间某处单位体积内出现的概率。用小黑点表示其分布所得的空间图象。描述原子中电子状态需用四个量子数：主量子数(n)、角量子数(l)、磁量子数(m)、自旋量子数(ms)。37nιm轨道/数电子数(2n2)K1s00１s122L2s0０2s428p10、

±12p6M3s003s9218p10、

±1３p6d20、±1、±23d10N4s004s16232p10、±14p6d20、±1、±24d10f30、±1、±2、±34f1438Exercises：描述原子中电子运动状态的四个量子数的物理意义各是什么？它们的可能取值是什么？下列各组量子数哪些是不合理的，为什么？

(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下列说法是否正确？不正确的应该如何改正？s电子绕核运动，其轨道为一圆周，而p电子是走8字形的；主量子数n为1时，有自旋相反的两条轨道；主量子数n为4时，其轨道总数为16，电子层电子最大容量为32；主量子数n为4时，有3s,3p,3d三条轨道。39核外电子运动的特征核外电子运动的描述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多电子原子的能级,原子轨道能级图核外电子排布的规则，核外电子排布432-1OrbitalEnergyLevelsinPolyelectronicAtoms

2-1-1OrbitalEnergiesinPolyelectronicAtomsSlater斯莱特中心势场模型：Theelectronisscreenedorshieldedfromthenuclearchargebytherepulsionsoftheotherelectrons.Thedecreaseofthenuclearchargebytheother(Z-1)e-iscalledscreeneffect

or

shieldeffect屏蔽效应.Thedecreasedpartiscalledthescreenconstantorshieldconstant屏蔽常数

σ.TheeffectivenuclearchargeZ*=Z-σ

44Z－σ=Z*，Z*——有效核电荷数σ为屏蔽常数，可用斯莱特经验规则算得。屏蔽效应：把多电子原子中其余电子对指定的某电子的作用近似地看作抵消一部分核电荷对该指定电子的吸引。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.能级分裂;能级交错.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(能级分裂);thatis,Ens<Enp<E

nd<Enf.Thesephenomenacanbeexplainedbypenetrationeffect(钻穿效应).

(4)Forpolyelectronicatoms,thesequenceoforbitalsinenergyisdifferent.Forsomeatoms,orbitalenergiesinterlace(能级交错).Forexample,Z=15~20,

E3d>E4s,whileZ<15andZ>20,E3d<E4s.Thisisduetothepenetrationeffectaswell.52钻穿效应:外层电子向内层钻穿的效应，进入原子内部空间，受到核的较强的吸引作用，能量会降低。3d与

4s轨道的径向分布图532-1-3Pauling’sOrbitalDiagramLinusCarlPauling鲍林（1901-1994）In195454Table8-3GroupsofOrbitalEnergyLevelsSuggestedbyPauling

GroupsofOrbitalEnergyLevels

OrbitalsinEachGroupⅠ1sⅡ2s2pⅢ3s3pⅣ4s3d4pⅤ5s4d5pⅥ6s4f5d6pⅦ7s5f6d7pⅧ8s5g6f7d8pⅨ9s6g7f8d9p552-2ThreeRulesforElectronArrangements

Lowest-energyrule

最低能量原理:电子在核外排列应尽先分布在低能级轨道上,使整个原子系统能量最低。Pauliexclusionprinciple

保里不相容原理:在同一原子中,不可能存在所处状态完全相同的电子。Hund’srule

洪特规则:在能量相同（n和l相同）的轨道上分布的电子,将尽先占据不同的轨道,且自旋平行。56应用核外电子填入轨道顺序图，根据保里不相容原理、能量最低原理、洪特规则，可以写出元素原子的核外电子分布式。如19K1s22s22p63s23p64s1

26Fe1s22s22p63s23p63d64s2

核外电子填入轨道的顺序正确书写是从内层到外层书写，将同一层电子放在一起，（可与填充顺序不一致。）57Figure8-10Orbitaldiagramsfornitrogenatom.58Electronconfigurations

N:1s22s22p3,1s22s22px12py12pz159Abbreviatedelectronconfigurations

原子实+最高能级组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单质和化合物的性质，随着元素的原子序数(核电荷数)的依次递增，呈现周期性的变化。642-3ThePeriodicTableandtheElectronConfigurations

Period(周期),Group（族），

Block（区）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元素周期系与核外电子分布的关系ⅠA0一1ⅡAⅢAⅣAⅤAⅥAⅦA2二345678910三1112ⅢBⅣBⅤBⅥBⅦBⅧⅠBⅡB131415161718四192021222324252627282930313233343536五373839404142434445464748495051525354六555657*727374757677787980818283848586七878889*104105106107108109110111112元素周期系与核外电子分布的关系镧系575859606162636465666768697071锕系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共价半径=两个相同原子形成共价键时，其核间距离的一半。定义d=198pmr(Cl)=99pmd=154pmr(C)=77pm72金属半径=金属单质晶体中，两个相邻金属原子核间距离的一半。定义d=256pmr(Cu)=128pm73主族元素：从左到右r减小；从上到下r增大。过渡元素：从左到右r缓慢减小；

从上到下r

略有增大。He50Ne160Ar191Kr198Xe21774解释:

电子层数不变的情况下,有效核电荷的增大导致核对外层电子的引力增大.

主族元素:电子逐个填加在最外层,对原来最外层上的电子的屏蔽参数(σ)小,有效核电荷(Z*)迅速增大。

副族元素:电子逐个填加在次外层,增加的次外层电子对原来最外层上电子的屏蔽较强,有效核电荷增加较小。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电离能较大

——半满，全满。同周期总趋势：自左至右I1逐渐增大,与原子半径减小的趋势相对应.同族总趋势：自上至下I1减小,与原子半径增大的趋势是对应的.773-3ElectronAffinity

A(g)+e-→A-(g)E1A-(g)+e-=A2-(g)E2电子亲合能正负号的规定与焓的正负号规定相反，即放热为正，吸热为负。电子亲合能用来衡量气态原子得电子的难易:电子亲合能越大,原子越易得到电子;电子亲合能越小,原子越难得到电子.78Figure8-12Firstionizationenergyandelectronaffinityasafunctionofatomicnumber.793-4Electronegativity

Electronegativityrepresentstheabilityofanatomina