Subtopic: Wave Mechanics, Operators & Perturbation Theory
Question Statement:
Match the order of š½ - decays given in the left column to appropriate clause in the
right column. Here X(Ią°) and Y(Ią°) are nuclei with intrinsic spin I and parity š.
1. X į
ą¬µ
ą¬¶
ą¬¾
į ā Y į
ą¬µ
ą¬¶
ą¬¾
į
i) First forbidden š½-decay
2. X į
ą¬µ
ą¬¶
ą¬æ
į ā Y į
ą¬¹
ą¬¶
ą¬¾
į
ii) Second forbidden š½-decay
3. X(3ą¬¾) ā Y(0ą¬¾)
iii) Third forbidden š½-decay
4. X(4ą¬æ) ā Y(0ą¬¾)
iv) Allowed š½-decay
Options:
(A) 1 - i, 2 - ii, 3 - iii, 4 - iv
(B) 1 - iv, 2 - i, 3 - ii, 4 - iii
(C) 1 - i, 2 - iii, 3 - ii, 4 - iv
(D) 1 - iv, 2 - ii, 3 - iii, 4 - i
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.12)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantum Mechanics** within *Section 4: Quantum Mechanics* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Quantum Mechanics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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