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Chemistry · Glossary

What is Russell–Saunders coupling?

Also known as: Russell--Saunders coupling · total orbital angular momentum quantum number · total spin quantum number · total angular momentum quantum number

Definition 2.10 University Chemistry — Year 3 · Chapter 2 — Many-Electron Atoms and Term Symbols

In Russell–Saunders coupling, the states of a configuration are labelled by the total orbital angular momentum quantum number LL (L^2=L(L+1)ℏ2\hat{\mathbf L}^2 = L(L+1)\hbar^2, with ML=∑mlM_L = \sum m_l), the total spin quantum number SS (MS=∑msM_S = \sum m_s), and the total angular momentum quantum number JJ, which takes the values ∣L−S∣,…,L+S|L - S|, \dots, L + S.

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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