Discussion
Which one of the following is an allowed electric dipole transition?
Answer: B
The allowed transition is \({}^{2}\mathrm{P}_{3/2} \rightarrow {}^{2}\mathrm{D}_{5/2}\).
Electric dipole (LS coupling) selection rules: \(\Delta S = 0\), \(\Delta L = 0, \pm 1\) (with a one-electron jump changing \(l\) by \(\pm 1\)), \(\Delta J = 0, \pm 1\), and \(J = 0 \to 0\) forbidden.
For \({}^{2}\mathrm{P}_{3/2} \to {}^{2}\mathrm{D}_{5/2}\): \(\Delta S = 0\), \(\Delta L = +1\), \(\Delta J = +1\). All satisfied.
The others each break a rule. \({}^{1}\mathrm{S}_{0} \to {}^{3}\mathrm{S}_{1}\) changes the spin multiplicity and has \(\Delta L = 0\) between S states. \({}^{2}\mathrm{D}_{5/2} \to {}^{2}\mathrm{P}_{1/2}\) has \(\Delta J = 2\). \({}^{3}\mathrm{P}_{0} \to {}^{5}\mathrm{D}_{0}\) changes the spin and is a \(J = 0 \to 0\) transition.
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