Question Bank MCQ • 2 Marks Section 4: Quantum Mechanics Angular momentum

QB_PH_100: Angular momentum

Question Statement

Two angular momenta $j_1 = 1$ and $j_2 = 1/2$ are coupled. The possible total angular momentum quantum numbers $j$ are:
(A) 3/2 \text{ and } 1/2
(B) 3/2, 1, 1/2
(C) 1/2 \text{ only}
(D) 3/2 \text{ only}
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $|j_1 - j_2| \le j \le j_1 + j_2 \implies |1 - 1/2| \le j \le 1 + 1/2 \implies j \in \{1/2, 3/2\}$.
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