The GATE Grind

GATE 2024 PH – Question 42

Atomic and Molecular Physics · Zeeman, Paschen-Back and Stark effects · 2 marks · Multiple choice

An atom is subjected to a weak uniform magnetic field B⃗ . The number of lines in its Zeeman spectrum for transition from n= 2, l= 1 to n= 1, l= 0 is

  1. 8
  2. 10
  3. 12
  4. 5

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Correct answer: (B) 10

Explanation

**Weak-field (anomalous) Zeeman effect.** The 2p → 1s transition has two fine-structure components:
- $2p_{3/2}\to1s_{1/2}$,
- $2p_{1/2}\to1s_{1/2}$.

In a weak magnetic field each level splits into $2j+1$ sublevels with $g_j$-dependent spacings. The selection rule is $\Delta m_j=0,\pm1$.

**$2p_{3/2}\to1s_{1/2}$:** $m_j=\pm\tfrac32,\pm\tfrac12$ in the upper level and $\pm\tfrac12$ in the lower. The allowed transitions: $\tfrac32\to\tfrac12$, $\tfrac12\to\tfrac12$, $\tfrac12\to-\tfrac12$, $-\tfrac12\to\tfrac12$, $-\tfrac12\to-\tfrac12$, $-\tfrac32\to-\tfrac12$. That is **6 lines**.

**$2p_{1/2}\to1s_{1/2}$:** $m_j=\pm\tfrac12$ in both levels, with $\Delta m_j=0,\pm1$: 4 transitions. That is **4 lines**.

**Total:** $6+4=\mathbf{10}$ lines (option B).