Discussion
The \(D_{1}\) and \(D_{2}\) lines of sodium (\({}^{2}P_{1/2} \rightarrow {}^{2}S_{1/2}\) and \({}^{2}P_{3/2} \rightarrow {}^{2}S_{1/2}\)) will split on application of a weak magnetic field into :
Answer: D
In a weak field the D1 line splits into 4 lines and the D2 line into 6.
This is the anomalous Zeeman effect. The Lande g factors are 2 for \({}^{2}S_{1/2}\), 2/3 for \({}^{2}P_{1/2}\) and 4/3 for \({}^{2}P_{3/2}\). Because upper and lower g factors differ, every allowed transition (\(\Delta m_{J} = 0, \pm 1\)) has its own frequency.
For D1 (\(m_{J} = \pm\frac{1}{2}\) to \(\pm\frac{1}{2}\)) there are 4 allowed transitions. For D2, the upper level has four sublevels (\(m_{J} = \pm\frac{3}{2}, \pm\frac{1}{2}\)), and the allowed transitions to the two lower sublevels number 6, since \(\pm\frac{3}{2} \rightarrow \mp\frac{1}{2}\) would need \(\Delta m_{J} = 2\).
Three lines each is the normal Zeeman pattern, which applies only to singlet transitions, not to these doublets.
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