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Choose the allowed transition

  • A.\(^{1}\Sigma_{g}^{+} \rightarrow {}^{3}\Sigma_{u}^{+}\)
  • B.\(^{1}\Sigma_{g}^{+} \rightarrow {}^{3}\Sigma_{u}^{-}\)
  • C.\(^{1}\Sigma_{g}^{+} \rightarrow {}^{1}\Sigma_{u}^{+}\)
  • D.\(^{1}\Sigma_{g}^{+} \rightarrow {}^{1}\Sigma_{u}^{-}\)

Answer: C

The allowed transition is \(^{1}\Sigma_{g}^{+} \rightarrow {}^{1}\Sigma_{u}^{+}\).

Electric dipole transitions in a diatomic molecule obey three rules that matter here:

  1. ΔS = 0: the spin multiplicity must not change;
  2. g ↔ u: parity must change (Laporte rule);
  3. for Σ to Σ transitions, + ↔ + and - ↔ -, never + ↔ -.

\(^{1}\Sigma_{g}^{+} \rightarrow {}^{1}\Sigma_{u}^{+}\) satisfies all three. The two transitions to \(^{3}\Sigma_{u}\) states change the multiplicity from singlet to triplet, so they are spin-forbidden. \(^{1}\Sigma_{g}^{+} \rightarrow {}^{1}\Sigma_{u}^{-}\) keeps the spin and changes parity, but goes from + to -, which is forbidden.

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