GATE 2021 PH – Question 33
The transition shown is between $^2D_{3/2}$ and $^2P_{1/2}$ in zero external magnetic field. How many spectral lines appear in a weak magnetic field? Give an integer.
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Correct answer: 6 to 6
Explanation
The upper level splits into $m_J=-3/2,-1/2,1/2,3/2$ and the lower into $m_J=-1/2,1/2$. E1 transitions allow $\Delta m_J=0,\pm1$. From each lower sublevel there are three allowed upper sublevels, giving six transitions. The Landé factors are $g_D=4/5$ and $g_P=2/3$, so the shifts $\mu_BB(g_Dm_D-g_Pm_P)$ are all distinct. Hence there are six lines.