Discussion
Assuming that the L-S coupling scheme is valid, the number of permitted transitions from \({}^{2}P_{3/2} \rightarrow {}^{2}S_{1/2}\) due to a weak magnetic field is :
Answer: C
There are 6 permitted transitions.
In a weak field, \({}^{2}P_{3/2}\) splits into four levels (\(M_{J} = \pm 3/2, \pm 1/2\), \(g = 4/3\)) and \({}^{2}S_{1/2}\) into two (\(M_{J} = \pm 1/2\), \(g = 2\)). The selection rule \(\Delta M_{J} = 0, \pm 1\) allows:
- from \(+3/2\): to \(+1/2\) only
- from \(+1/2\): to \(+1/2\) and \(-1/2\)
- from \(-1/2\): to \(+1/2\) and \(-1/2\)
- from \(-3/2\): to \(-1/2\) only
That is 6 transitions, the anomalous Zeeman pattern of the \(D_{2}\) line. 4 is the count for \({}^{2}P_{1/2} \to {}^{2}S_{1/2}\), and 2 or 10 do not fit the selection rule.
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