Discussion
An atom is subjected to a weak uniform magnetic field \(\vec{B}\). The number of lines in its Zeeman spectrum for transition from \(n = 2, l = 1\) to \(n = 1, l = 0\) is
Answer: B
The Zeeman spectrum has 10 lines.
In a weak field, spin-orbit coupling splits the n = 2, l = 1 level into 2P3/2 and 2P1/2, and the anomalous Zeeman effect splits each level into 2j + 1 sublevels with different Landé g-factors (g = 4/3, 2/3 and 2 for 2P3/2, 2P1/2 and 2S1/2). With the selection rule Δmj = 0, ±1:
- 2P3/2 → 2S1/2: 6 lines (the mj = ±3/2 → ∓1/2 transitions are forbidden);
- 2P1/2 → 2S1/2: 4 lines.
Because the g-factors differ, all 6 + 4 = 10 lines have different energies. 5 or 8 undercount the allowed transitions, and 12 counts all 4 × 2 + 2 × 2 pairs without the selection rule.
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