Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
The X -ray diffraction pattern of a mon atomic cubic crystal with rigid spherical
atoms of radius 1.56 Å shows several Bragg reflections of which the reflection
appearing at the lowest 2𝜃 value is from (111) plane. If the wavelength of X -ray
used is 0.78 Å, the Bragg angle (in 2𝜃, rounded off to one decimal place )
corresponding to this reflection and the crystal structure, respectively, are
Options:
(A) 21.6 and body centered cubic
(B) 17.6 and face centered cubic
(C) 10.8 and body centered cubic
(D) 8.8 and face centered cubic
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.39)**
**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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