1、Quantum Theory and the Electronic Structure of AtomsChapters 7&87.1 Light and Classic Quantum Theory 1.Classic theory of Light Different waves have different color,and different wavelength.Particles(Newton,1680):an array of particles,emitted from light source,that move in space in one dimensional di
2、rection.dtdumf forcedtdxu speedAcceleration speed22dtxddtdugOne can determine the exact position and speed at the same time.Wave(Huygens,1690):an elastic vibrator,emitted from light source,that move in space in three dimensional direction.Kinetic energy221muKE Wavelength(l l)7.1 Light and Classic Qu
3、antum Theory Maxwell(1893)wrote an equation for light as a waveLight is an electromagnetic wave that spread in space.For a light in vacuum,u=c=3.00 x 108 m/sFrequency n is the number of waves that pass in 1 s.u l l n nabout 1.28 s from moon to Earth Wavelength l is the distance between two successiv
4、e waves.Speed u is the distance of waves that pass in 1 s.Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.Wavelength(l l)a0 amplitude)(2cos),(0utxatxal At a certain position(x),the wave change with t.At a certain time(t),the wave change with
5、x.820uaI The energy intensityEnergy changescontinuously!Energy passed through a unit area per unit timePlancks Quantum Hypothesis(1901):For a single quantum,the smallest quantity of energy:E=h vPlanck constant h=6.63 x 10-34 JsEnergy change is only by hv,2hv,3 hv,4 hv.but never by 1.5 hv or 3.06 hvT
6、hen in 1918,he won Nobel Prize in physics.2.Classic quantum theory of Light(Plank,1900)238()v kTE v dvdvCClassical theory explains it well at low v,but very bad at high v.Energy is emitted or absorbed in discrete units(quantum).Black body radiation:curve E vs v4(constant)ET23/8()e1hv kTv kTdvE v dvC
7、Explains all results well.3.The Particle Nature of Light:Photoelectric Effect:hnvoltage currentV0Experimental evidence:(1)minimum frequency of light(v0)(2)v0 is dependent of metal.(3)The current light intensity.h v =p clhp ParticlenatureWavenatureEinstein Photon Theory(1905)hn=KE+BEKE=hn-BELight are
8、 both wave and particle:1.Wave nature(l):E=hv2.Particle nature(m):momentum p=mc3.Energy E=mc2 It explains well the evidence:(1)minimum frequency of light(v0)(2)v0 is dependent of metal.(3)The current light intensity.Here BE is the binding energy of the metal lattice electron7.2 Dual Nature of Electr
9、on 1.Hydrogen Emission line spectrum:Bohrs Planetary model1.e-only has a specific energy values(quantized)2.light is emitted as e-moves from one energy level to a lower energy levelBohrs Model of H Atom(1913)En=-RH()1n2n(principal quantum number)=1,2,3,RH(Rydberg constant)=2.18 x 10-18J=13.6 eVEphot
10、on=DE=Ef-Ei3.ifDE=RH()1n21n2nf =1ni =2nf =1ni =3nf =2ni =3Ephoton=2.18 x 10-18 J x(1/25-1/9)Ephoton=DE=1.55 x 10-19 Jl=6.63 x 10-34(Js)x 3.00 x 108(m/s)/1.55 x 10-19Jl=1280 nmCalculate the wavelength(in nm)of a photon emitted by a hydrogen atom when its electron drops from the n=5 state to the n=3 s
11、tate.Ephoton=h c/ll=h c/EphotonifDE=RH()1n21n2Ephoton=De Broglie(1924)reasoned that e-is both particle and wave.2r=nl l=h/muu=velocity of e-m=mass of e-2.Dual nature of the Electron:Matter as wavesWhat is the de Broglie wavelength(in nm)associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s?l=
12、6.63 x 10-34/(2.5 x 10-3 x 15.6)l=1.7 x 10-32 m=1.7 x 10-23 nmNobel Prize in 1929&7.3 Quantum Mechanical Description of Electrons in Atoms Schrdinger Wave EquationBasis:1)Bohrs theory,good to explain the H emission spectrum,but failed for the spectrum of other elements.2)Dual nature of electron(m an
13、d l l).In 1926,Schrodinger wrote an equation for electron in the atom.=E E =V +KETotal energy of the systemPotential energykinetic energy(psi):wave function,or atomic orbital that describes the movement of electron in the atom in three dimensional space.:Hamiltonian OperatorVm2222:Laplacian Operator
14、2222222zyxUncertainty principle(1927,W K Heisenberg):DX Dp h/4 It is impossible to determine precisely both the position and momentum of a particle at the same time.1.Application of Schrdinger to Hydrogen Atom zxy(x,y,z)r=E rem2222(x,y,z)=E(x,y,z)rem2222222cossinsincossinzyxrrzryrx222222sin1sin11rrr
15、rrr08222reEhm),(rhereAfter transferred into sphere coordinateGeneral solution for Hydrogen Atom,(,)ln l mr)()()(,lmlmllnrR)(6.1322eVnZEnSame as Bohrs result,ie.Only dependent of n;Angular partSpacial partn=1 l=0 ml=0)exp(011razNsE1s=-13.6 eV(Z is atomic number,and for H,Z=1)n=2 l=0 ml=0)2exp()2(0022
16、razraZNsn=2 l=1 ml=0n=2 l=1 ml=-1n=2 l=1 ml=+1cos)2exp()(0022razraZNzpcossin)2exp()(0022razraZNxpsinsin)2exp()(0022razraZNypE*=-3.4 eV)exp(011razNs r distance from the nucleus 2ElectrondensityBut the probability to find e in space(DV)is P=Y2 D DV,highest at r=0.529 90%of electron density foundl=0n=1
17、n=2n=3ml=-1ml=1ml=0ml=-2ml=-1ml=0ml=1ml=27.6n:Principal quantum numbern=1,2,3,4,.distance of e-from the nucleus,and determination of energy),(,rmln)()()(,mmllnrRHere n,l,m are called as the quantum numberl:angular momentum quantum numberl=0,1,2,3,n-1n=1,l=0n=2,l=0,1n=3,l=0,1,2Shape of the“volume”of
18、space that the e-occupies l =0 1 2 3Orbital s p d fml:magnetic quantum numberml=-l,.,0,.+lif l=1(p orbital),ml=-1,0,1if l=2(d orbital),ml=-2,-1,0,1,2orientation of the orbital in spaceEnergy of orbitals in a single electron atomEnergy only depends on principal quantum number nEn=-RH()1n2n=1n=2n=3Gro
19、und stateexcited state2.Application of Schrdinger to Many-electron atomszxy(xi,yi,zi)ri=E rjrij(xj,yj,zj)jiijNiiNiirerZem212122212For the ith electron,the average net potential is spherically approximated as:iiiireZrV2)()(shielding constantjjiii=Ei i iiireZm222)(2Effective charge of the nucleus),(,r
20、lmln)()()(,lmlmllnrR)()(6.1322,eVnZEilnGeneral solutionEnergy of orbitals in a multi-electron atomEnergy depends on n and ln=1 l=0n=2 l=0n=2 l=1n=3 l=0n=3 l=1n=3 l=2Order of orbitals(filling)in multi-electron atom1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s3.The Building-Up Principle of electrons in the orbi
21、tals:1.Electrons occupy first the lowest energy orbitals available.2.Each orbital accommodates only two electrons,and these two electrons must have opposing spins.Pauli exclusion principlespin quantum number ms=+or-To descript one electron completely,Four quantum numbers of n,l,ml and ms are needed.
22、3.In the degenerate orbitals(same n and l),the electrons occupy the orbitals as many as possible with same spins.N(Z=7)1s2s2p(Z=7)N 1s2 2s2 2p3Electron configurationHunds ruleWhat is the electron configuration of Mg?Mg 12 electrons1s 2s 2p 3s 3p 4s 1s2 2s22p6 3s22+2+6+2=12 electronsAbbreviated as Ne
23、3s2Ne 1s22s22p6What are the possible quantum numbers for the last(outermost)electron in Cl?Cl 17 electrons1s 2s 2p 3s 3p 4s 1s2 2s22p6 3s23p52+2+6+2+5=17 electronsLast electron added to 3p orbitaln=3l=1ml=-1,0,or+1ms=or-Noble gas coreFe 26 electrons1s 2s 2p 3s 3p 4s 3d 1s2 2s22p6 3s23p6 4s23d6Abbrev
24、iated as Ar4s23d6Ar 1s22s22p63s23p6What is the electron configuration of Fe?What is the electron configuration of Mo?Mo 42 electrons1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p1s2 2s22p6 3s23p6 4s23d104p6 5s24d4Abbreviated as Kr5s24d4Kr5s14d5Half-filled and fully-filled subshell are more stable.(p3,d5,f7)(p6,d1
25、0,f14)One e-choice7.8Outermost subshell being filled with electrons&7.4 Periodic Relationships Among the Elementsns1ns2ns2np1ns2np2ns2np3ns2np4ns2np5ns2np6d1d5d104f5fGround State Electron Configurations of the ElementsIonization energy is the minimum energy(kJ/mol)required to remove an electron from
26、 a gaseous atom in its ground state.I1+X(g)X+(g)+e-I2+X+(g)X2+(g)+e-I3+X2+(g)X3+(g)+e-I1 first ionization energyI2 second ionization energyI3 third ionization energyI1 I2 I3General Trend in First Ionization Energies8.4Increasing First Ionization EnergyIncreasing First Ionization EnergyElectron Confi
27、gurations of Cations and AnionsNa Ne3s1Na+NeCa Ar4s2Ca2+ArAl Ne3s23p1Al3+NeAtoms lose electrons so that cation has a noble-gas outer electron configuration.H 1s1H-1s2 or HeF 1s22s22p5F-1s22s22p6 or NeO 1s22s22p4O2-1s22s22p6 or NeN 1s22s22p3N3-1s22s22p6 or NeAtoms gain electrons so that anion has a n
28、oble-gas outer electron configuration.Electron Configurations of Cations of Transition MetalsWhen a cation is formed from an atom of a transition metal,electrons are always removed first from the ns orbital and then from the(n 1)d orbitals.Fe:Ar4s23d6Fe2+:Ar4s03d6 or Ar3d6Fe3+:Ar4s03d5 or Ar3d5Mn:Ar
29、4s23d5Mn2+:Ar4s03d5 or Ar3d5+1+2+3-1-2-3Cations and Anions Of Representative ElementsAtomic radius:one-half the distance between the two nuclei in two adjacent metal atoms.Effective nuclear chargeZeff=Z-shielding constantjjii(0 Z)1)Within a group,Zeff decreases with n,due to strong shielding effect
30、from inner shell electrons.2)Within a period,Zeff increases with Z,due to weak shielding effect in the same shell.Cation is always smaller than atom from which it is formed.Anion is always larger than atom from which it is formed.Ionic radius:the radius of a cation or an anion,determined by X-ray diffraction of an ionic compound in solid state.Exercises for Chapters 7 and 8:7.16 7.79 7.80 7.104 7.106 7.114 8.114
