1. Atomic Structure and Atomic Spectra
Chapter 10

2. Structures of many-electron atoms
Because of electron correlation, no simple analytical
expression for orbitals is possible
Therefore ψ(r1, r2, ….) can be expressed as ψ(r1)ψ(r2)…
Called the orbital approximation
Individual hydrogenic orbitals modified by presence of
other electrons

3. Structures of many-electron atoms
Pauli exclusion principle – no more than two electrons
may occupy an atomic orbital, and if so, must be of opposite
spin

4. Structures of many-electron atoms
In many-electron atoms, subshells are not
degenerate. Why?
Shielding and penetration

5. Fig 10.19 Shielding and effective nuclear charge, Zeff
Shielding from core electrons
reduces Z to Zeff
Zeff = Z – σ
where σ ≡ shielding constant

6. Fig 10.20 Penetration of 3s and 3p electrons
Shielding constant different for s and p electrons
s-electron has greater
penetration and is bound more
tightly bound
Result: s < p < d < f

8. Structure of many-electron atoms
In many-electron atoms, subshells are not
degenerate. Why?
Shielding and penetration
The building-up principle (Aufbau)
Mnemonic:

9. Order of orbitals (filling) in a many-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

10. “Fill up” electrons in lowest energy orbitals (Aufbau principle)? ?
Be 4 electrons
Li 3 electrons
C 6 electrons
B 5 electrons
B 1s22s22p1
Be 1s22s2
Li 1s22s1
H 1 electron
He 2 electrons
He 1s2
H 1s1

11. Structure of many-electron atoms
In many-electron atoms, subshells are not
degenerate. Why?
Shielding and penetration
The building-up principle (Aufbau)
Mnemonic:
Hund’s rule of maximum multiplicity
Results from spin correlation

12. The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).
C 6 electrons
O 8 electrons
N 7 electrons
F 9 electrons
Ne 10 electrons
Ne 1s22s22p6
O 1s22s22p4
C 1s22s22p2
N 1s22s22p3
F 1s22s22p5

13. Fig 10.21 Electron-electron repulsions in Sc atom
Reduced repulsions
with configuration
[Ar] 3d1 4s2
If configuration was
[Ar] 3d2 4s1

14. Ionization energy (I) - minimum energy (kJ/mol) required to remove an electron from a gaseous atom in its ground state
I1 + X(g) X+(g) + e-
I1 first ionization energy
I2 + X+(g) X2+(g) + e-
I2 second ionization energy
I3 + X2+(g) X3+(g) + e-
I3 third ionization energy
I1 < I2 < I3

15. Mg → Mg+ + e− I1 = 738 kJ/mol
For Mg2+
1s22s22p6
Mg+ → Mg e− I2 = kJ/mol
Mg2+ → Mg e− I3 = kJ/mol

16. Fig 10.22 First ionization energies
N [He] 2s2 2p3 I1 = 1400 kJ/mol
O [He] 2s2 2p4 I1 = 1314 kJ/mol

17. Spectra of complex atoms
Energy levels not solely given by energies
of orbitals
Electrons interact and make contributions to E

18. Fig 10.18 Vector model for paired-spin electrons
Multiplicity = (2S + 1)
= (2·0 + 1)
= 1
Singlet state
Spins are perfectly
antiparallel

19. Fig 10.24 Vector model for parallel-spin electrons
Three ways to obtain nonzero spin
Multiplicity = (2S + 1)
= (2·1 + 1)
= 3
Triplet state
Spins are partially
parallel

20. Singlet – triplet transitions
Fig Grotrian diagram for helium
Singlet – triplet transitions
are forbidden

21. Fig 10.26 Orbital and spin angular momenta
Spin-orbit
coupling
Magnetogyric ratio

22. Fig 10.27(a) Parallel magnetic momenta
Total angular momentum (j) = orbital (l) + spin (s)
e.g., for l = 0 → j = ½

23. Fig 10.27(b) Opposed magnetic momenta
Total angular momentum (j) = orbital (l) + spin (s)
e.g., for l = 0 → j = ½
for l = 1 → j = 3/2, ½

24. Fig 10.27 Parallel and opposed magnetic momenta
Result: For l > 0, spin-orbit
coupling splits a configuration
into levels

25. Fig 13.30 Spin-orbit coupling of a d-electron (l = 1)
j = l + 1/2
j = l - 1/2

26. Energy levels due to spin-orbit coupling
Strength of spin-orbit coupling depends on
relative orientations of spin and orbital
angular momenta (= total angular momentum)
Total angular momentum described in terms of
quantum numbers: j and mj
Energy of level with QNs: s, l, and j
where A is the spin-orbit coupling constant
El,s,j = 1/2hcA{ j(j+1) – l(l+1) – s(s+1) }