The GATE Grind

GATE 2023 PH – Question 25

Quantum Mechanics · orbital and spin angular momenta · 1 mark · Multiple choice

An atom with non-zero magnetic moment has an angular momentum of magnitude √12 ħ. When a beam of such atoms is passed through a Stern- Gerlach apparatus, how many beams does it split into?

  1. 3
  2. 7
  3. 9
  4. 25

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Show answer and explanation

Correct answer: (B) 7

Explanation

The magnitude of the angular momentum is $\sqrt{j(j+1)}\,\hbar$, so
$$j(j+1)=12\;\Rightarrow\;j=3 .$$

In a **Stern-Gerlach apparatus** the beam splits into one beam for each allowed value of the $z$-component $m_j\hbar$, with $m_j=-j,\dots,+j$. The number of beams is
$$2j+1=2(3)+1=\mathbf{7}\quad(\text{option B}).$$