Subtopic: Bragg's Law & X-ray Diffraction (Laue and Powder)
Question Statement:
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:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.39)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 7: Solid State Physics* | **Topic**: *Crystal Structure & Lattice Dynamics* (`Bragg's Law & X-ray Diffraction (Laue and Powder)`)
- **Question Type**: **MCQ** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Crystal Structure & Lattice Dynamics** (`Bragg's Law & X-ray Diffraction (Laue and Powder)`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `(i) - P,T; (ii) - S; (iii) - R,S; (iv) - S,T`**.
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