GATE 2021 PH – Question 24

Atomic and Molecular Physics · Spin-orbit interaction: L-S and j-j coupling schemes · 1 mark · Multiple select

Which atomic spectroscopic terms are allowed? Select all that apply.

$^4S_1$
$^2D_{7/2}$
$^3S_1$
$^2D_{5/2}$

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Show answer and explanation

Correct answer: (C) $^3S_1$; (D) $^2D_{5/2}$

Explanation

In $^{2S+1}L_J$, allowed $J$ values range from $|L-S|$ to $L+S$. For $^4S$, $S=3/2,L=0$, so $J=3/2$, not 1. For $^2D$, $S=1/2,L=2$, so $J=3/2$ or $5/2$, excluding $7/2$. For $^3S$, $S=1,L=0$ gives $J=1$. Therefore C and D are allowed.

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