Which one of the following options is the most appropriate match between the
items given in Column 1 and Column 2?
Column 1 Column 2
(i) Visible light P. Transition between core energy
levels of atoms
(ii) X-rays Q. Transition between nuclear
energy levels
(iii) Gamma rays R. Pair production
(iv) Thermal neutrons S. Crystal structure determination
T. Photoelectric effect
Options:
(A) (i) - T; (ii) - P,S,T; (iii) - Q,R; (iv) - S
(B) (i) - P,T; (ii) - S; (iii) - R,S; (iv) - S,T
(C) (i) - T; (ii) - R,S; (iii) - Q,R; (iv) - S
(D) (i) - S,T; (ii) - P,S; (iii) - R,T; (iv) - S
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.39)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- 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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