Discussion
The ground state of an alkali metal is a 2S1/2 state. The difference in energy levels arising in the presence of a weak magnetic field B, given in terms of Bohr magneton \(\mu_{B}\) is :
Answer: B
The splitting is \(2\mu_{B}B\).
For a \(^{2}S_{1/2}\) state, L = 0 and S = J = 1/2, so the Landé factor is \(g_{J} = 2\). In a weak field each level shifts by \(\Delta E = g_{J}m_{J}\mu_{B}B\), with \(m_{J} = \pm\frac{1}{2}\):
\[ \begin{aligned} E_{\pm} &= \pm\frac{1}{2} \times 2\mu_{B}B = \pm\mu_{B}B \\ E_{+} - E_{-} &= 2\mu_{B}B \end{aligned} \]
\(\mu_{B}B\) is the shift of each sublevel from the original level, not the difference between them. \(4\mu_{B}B\) and \(6\mu_{B}B\) would need larger g or J values.
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