solid state chemistry chapter 3 atomic structure and spectra
TRANSCRIPT
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Solid State Chemistry
Chapter 3Atomic Structure and Spectra
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AGENDA
The structure and spectra of Hydrogenic atoms
The structure of many-Electron atoms1. Pauli’s principle 2. Penetration and shielding3. Building up principle
The spectra of complex atoms1. Quantum defects2. Singlet and triplets3. Spin-orbit coupling4. The total angular momentum5. Term symbols and selection rules
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The Structure of Many-electron Atoms
)()(,, 2121 rrrr
21 :atom Helium
electronsother theall of presence by the modified chargesnuclear toingcorrespondbut
orbitals, hydrogenic theresembling as orbitals individual The
s
The Orbital ApproximationJustification 10.5
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The Pauli Principle
paired. bemust spinsr then theiorbital, oneoccupy do twoif
and, orbitalgiven any occupy may electrons than twomore No
:principleexclusion Pauli
Pauli principle:
When the labels of any two identical fermions are exchanged, the total wavefunction changes sign. When the labels of any two identical bosons are exchanged, the total wavefunction retains the same sign
(2,1) = -(1,2) for two electrons
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Penetration and Shielding
orbitals d lower than lie orbitals p and shell,
given a of orbitals pn energy thain lower liegenerally orbitals s
ZZeff
:constant shielding chargenuclear shielded a sexperienceelectron
:chargenuclear Effective
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Penetration and Shielding
electron p a than shielding less sexperienceelectron s
:electron p a than shellinner through
n penetratiogreater a haselectron sA
state ground itsin atoman of shell
outermost in the electrons the:electrons Valence
21 :atom Li 12 ss
fdps
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The Building-up (Aufbou) Principle
orbitals 3din repulsionselectron -electron Strong -
ncorrelatioSpin -
electrons unpaired ofnumber
greatest heion with tconfigurat a
adopts state ground itsin atomAn -
:rulety multiplici maximum sHund'
themof oneany occupyingdoubly
before subshellgiven a of
orbitalsdifferent occupy Electrons -
6s 5p 4d 5s 4p 3d 4s 3p 3s 2p 2s s1
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Ionization Energies and Electron Affinities
2
1
energy, ionization second The -
energy, ionizationfirst The -
I
I
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Ionization Energies and Electron Affinities
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attacheselectron an when
releasedenergy the:Eaffinity Electron -
2
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Self-consistent Field Orbitals
i
iji
i r
e
r
ZeV
0
2
0
2
42
1
4
)1()1()correction exchange()1(electrons)other ()1()1( 22222 ppppp EVVH
• The first term on the left is the contribution of the kinetic energy and the attraction of the electron to the nucleus, just as in a hydrogenic atom
• The second takes into account the potential energy of the electron of interest due to the electrons in the other occupied orbitals
• The third term takes into account the spin correlation effects.
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The Spectra of Complex Atoms
Quantum defects and ionization limits
2
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thatdiffuse so are that states excited some :state Rydberg
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quantity empiricalpurely a : defect, Quantum
pyspectrosco atomic :energies ionization ofion Determinat
n
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n
hcRE
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Singlet and Triplet States
singlet
rulety multiplici maxinum sHund'
)2()1()2()1()21()2 ,1_( 21
)2()1( ,)2()1()2()1()21()2 ,1( ),2()1( 21
ncorrelatioSpin :differenceenergy oforigin The
state.singlet t theenergy thain lower lies state triplet The
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The Spectrum of Atomic Helium
states triplet andsinglet between ns transitioradiative No -
1 :ionconfigurat excitedOnly - 11nls
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Spin-Orbit Coupling
momentumangular orbital thefrom arising field magnetic with the
moment magneticspin ofn interactio the:couplingorbit -Spin
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The Total Angular Momentum
low is momentumangular total theopposed, are momentaangular twowhen the
high; is momentumangular totaltheparallel,nealy are momentaangular orbital andspin When the
opposed) are (when they 2
1
direction) same in the are momentaangular two(when the 2
1
lj
lj
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Fine Structure
) Z(asnumber atomic with
sharply increases coupling the-
chargenuclear on the depends
couplingorbit -spin theofStrength
)1()1()1(2
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A constant, couplingorbit -Spin
4
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sslljjhcAE jsl
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Term Symbols and Selection Rules
J. number, quantum momentumangular totalthe
of value theis )Pin 2
3 theexample,(for
symbol termon thesubscript right The 3.
term. theofty multiplici the
gives )Pin 2 theexample,(for
symbol termin thet superscripleft The 2.
L. number, quantum
momentumangular orbital total theindicates
examples) in the Dor P example,(for letter The 1.
232
232
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Total Orbital Angular Momentum
Total angular momentum quantum number L
Angular momentum =
{L(L + 1)}1/2h
L = l1+l2, l1+l2-1….,|l1-l2|
Clebsch-Gordan series
L: 0,1,2,3,4,… (S,P,D,F,G…)
Example:
d2 electron
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Multiplicity
Total spin angular momentum quantum number S
Spin angular momentum =
{S(S + 1)}1/2h
S = s1+s2, s1+s2-1….,|s1-s2|
Multiplicity: 2S + 1
Example:
Two unpaired electrons
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Total Angular Momentum
Total angular momentum quantum number J
J = j where j = l + ½, |l – ½|
Example:
[Ne]3s1
[Ne]3p1
Russell-Saunders coupling:
If spin-orbit coupling is weak, then it is effective only when all the orbital momenta are operating cooperatively
J = L + S, L + S – 1,….., |L – S|
Example:
[Ne]2p13p1Selection rules
S = 0 L = 0,±1 l = ±1 J = 0,±1
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Short Summary
The Structures and spectra of many electron atoms
1. The Pauli principle
2. Penetration and shielding
3. Singlet and triplet states
4. Spin-orbit coupling
5. Term symbols and selection rules
HW#2: 10.3d, 10.7d, Exe: 10.4b, 10.6a, 10.8a, 10.12b, 10.18b, 10.19a