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Chemistry · Glossary

What is Spin–orbit coupling, fine structure?

Also known as: spin--orbit coupling · fine structure

Definition 2.20 University Chemistry — Year 3 · Chapter 2 — Many-Electron Atoms and Term Symbols

Spin–orbit coupling is the interaction between the magnetic moments of an electron’s spin and of its orbital motion, written A L^⋅S^/ℏ2A\,\hat{\mathbf L}\cdot\hat{\mathbf S}/\hbar^2 for a term. It splits a term into its levels of different JJ: the fine structure of the term.

The sodium D lines. The 3p level is split by spin–orbit coupling into 2P_1/2 and 2P_3/2; emission to the ground 3s level gives two yellow lines, D_1 at 589.76\, nm and D_2 at 589.16\, nm (vacuum wavelengths).
The sodium D lines. The 3p3p level is split by spin–orbit coupling into 2{}^2P1/2_{1/2} and 2{}^2P3/2_{3/2}; emission to the ground 3s3s level gives two yellow lines, D1_1 at 589.76 nm589.76\,\mathrm{nm} and D2_2 at 589.16 nm589.16\,\mathrm{nm} (vacuum wavelengths).

Examples

Example 2.22 (Testing the interval rule)

For 3{}^3P the rule predicts intervals in the ratio J=2:1J = 2 : 1, that is 2. Carbon: (43.4−16.4)/16.4=1.65(43.4 - 16.4)/16.4 = 1.65. Oxygen (2p42p^4, inverted, 3P2{}^{3}\mathrm{P}_{2} lowest, then J=1J = 1 at 158.3 cm−1158.3\,\mathrm{cm}^{-1} and J=0J = 0 at 227.0 cm−1227.0\,\mathrm{cm}^{-1}): 158.3/68.7=2.30158.3/68.7 = 2.30. The rule holds within 20 %: Russell–Saunders coupling is a good description of light atoms, not an exact one.

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