Atomic Structure and Atomic Spectra

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Atomic Structure and Atomic Spectra
Chapter 10
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Spectra of complex atoms

• Energy levels not solely given by energies of
  orbitals
• Electrons interact and make contributions to E
• Singlet and triplet states
• Spin-orbit coupling

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Fig 10.18 Vector model for paired-spin electrons
Multiplicity (2S 1) (20
1) 1 Singlet state Spins are
perfectly antiparallel
Ground state
Excited state
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Fig 10.24 Vector model for parallel-spin
electrons
Three ways to obtain nonzero spin
Multiplicity (2S 1) (21
1) 3 Triplet state Spins are
partially parallel
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Fig 10.25 Grotrian diagram for helium
Singlet triplet transitions are forbidden
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Fig 10.26 Orbital and spin angular momenta
Spin-orbit coupling
Magnetogyric ratio
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Fig 10.27(a) Parallel magnetic momenta
Total angular momentum (j) orbital (l) spin
(s)
e.g., for l 0 ? j ½
for l 1 ? j 3/2
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Fig 10.27(b) Opposed magnetic momenta
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Fig 10.27 Parallel and 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
Result For l gt 0, spin-orbit coupling splits a
configuration into levels
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Fig 10.28 Spin-orbit coupling of a d-electron (l
2)
j l 1/2
j l - 1/2
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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 number j
• Energy of level with QNs s, l, and j
• where A is the spin-orbit coupling constant

El,s,j ½ hcA j(j1) l (l1) s(s1)
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Fig 10.29 Levels of a 2P term arising
from spin-orbit coupling of a 2p electron
El,s,j 1/2hcA j(j1) l(l1) s(s1)
1/2hcA 3/2(5/2) 1(2) ½(3/2) 1/2hcA and
1/2hcA 1/2(3/2) 1(2) ½(3/2) -hcA
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Fig 10.30 Energy level diagram for sodium D lines
Fine structure of the spectrum
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Fig 10.31 Types of interaction for splitting
E-levels
In light atoms magnetic Interactions are small
In heavy atoms magnetic interactions may
dominate the electrostatic interactions
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Fig 10.32 Total orbital angular momentum (L)
of a p and a d electron (p1d1 configuration)
L l1 l2, l1 l2 1,..., l1 l2
3, 2, 1
F
D
P
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Fig 10.33 Multiplicity (2S1) of two electrons
each with spin angular momentum 1/2
S s1 s2, s1 s2 1,..., s1 - s2
1, 0
Triplet
Singlet
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• For several electrons outside the closed shell,
• must consider coupling of all spin and all
  orbital
• angular momenta
• In lights atoms, use Russell-Saunders coupling
• In heavy atoms, use jj-coupling

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Fig 10.34 Correlation diagram for some states of
a two electron system
Russell-Saunders coupling for atoms with low Z,
? spin-orbit coupling is weak
J LS, LS-1,..., L-S
jj-coupling for atoms with high Z, ? spin-orbit
coupling is strong
J j1 j2
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Selection rules for atomic (electronic)
transitions

• Transition can be specified using term symbols
• e.g., The 3p1 ? 3s1 transitions giving the
• Na doublet are
• 2P3/2 ? 2S1/2 and 2P1/2 ? 2S1/2
• In absorption 2P3/2 ? 2S1/2 and 2P1/2 ?
  2S1/2
• Selection rules arise from conservation of
  angular
• momentum and photon spin of 1 (boson)

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Selection rules for atomic (electronic)
transitions
?S 0 Light does not affect spin directly ?l
1 Orbital angular momentum must change ?L 0,
1 Overall change in orbital angular momentum
depends on coupling ?J 0, 1 Total angular
momentum may or may or may not change J L S