Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
A neutron beam with a wave vector k⃗ and an energy 20.4 meV diffracts from a
crystal with an outgoing wave vector k⃗ ′. One of the diffraction peaks is observed
for the reciprocal lattice vector G of magnitude 3.14 Å
-1
. What is the diffraction
angle in degrees (rounded off to the nearest integer) that k⃗ makes with the plane?
(Use mass of neutron = 1.67 × 10-27 Kg)
Options:
(A) 15
(B) 30
(C) 45
(D) 60
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.45)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Solid State Physics** within *Section 7: Solid State Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Solid State 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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