Subtopic: Bragg's Law & X-ray Diffraction (Laue and Powder)
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. 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): `30`**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.