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Atomic Spectroscopy:
Emission, Absorption & Fluorescence
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Term Symbols
2 1SJL
L = 0, 1, 2, ...S, P, D
J = L + S
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L = | l1 + l2 |, | l1 + l2 - 1 |, ..., | l1 - l2 |
S = | s1 + s2 |, | s1 + s2 - 1 |, ..., | s1 - s2 |
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J = L + S
| L + S |, | L + S - 1 |, ..., | L - S |
Russell-Saunders Coupling
jj β Coupling
ji = li + si
| j1 + j2 |, | j1 + j2 - 1 |, ..., | j1 - j2 |
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Hundβs Rules The lowest energy term is that which has the
greatest spin multiplicity.
For terms that have the same spin multiplicity, the term with the highest orbital angular momentum lies lowest in energy.
spin-orbit coupling (more pronounced for heavier nuclei) splits terms into levels.{ If the unfilled subshell is exactly or more than half
full, the level with the highest J value has the lowest energy.
{ If the unfilled subshell is less than half full, the level with the lowest J value has the lowest energy.
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π΅= β π―π₯π¬π2
π΅= ππ₯ππππ2 |πΈ| = |πΈ|πππ2 π³
π= β2πππ΅ππ β πΊ
βπΈ= βπ.π©β π³.πΊ
π½2 = (πΏ+ π)2 = πΏ2 + π2 + 2πΏ.π
2πΏ.π= π½2 β πΏ2 β π2 = π½αΊπ½+ 1α»β πΏαΊπΏ+ 1α»β π(π+ 1)
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Selection Rules
Helicity of a photon Ο = Β± 1
(Physically analogous to the angular momentum along the axis of propagation)
Upon absorption or emission of a photon the atom must change the momentum along the zz axis (considered collinear with the axis of propagation) in Β± 1
ΞJ = 0; Β± 1 (but J β 0 if ΞJ = 0)ΞMJ = 0; Β± 1 (but ΞMJ β 0 if J = 0)
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ππ₯,π¦,π§ππ = ΰΆ±ππβππ₯,π¦,π§ππππ β 0
Spin wave functions are differentially zero (Ξ±Ξ²) or one (Ξ±Ξ±).
ΞS = 0 allowed
ΞS β 0 forbidden
Electric dipole Transition moment