Consider a crystal that has a basis of one atom. Its primitive vectors are a1⃗⃗⃗⃗ = aî ,
a2⃗⃗⃗⃗ = aĵ , a3⃗⃗⃗⃗ =
a
2 (î + ĵ + k̂), where î, ĵ, k̂ are the unit vectors in the x, y and z
directions of the Cartesian coordinate system and a is a positive constant. Which
one of the following is the correct option regarding the type of the Bravais lattice?
Options:
(A) It is BCC and the volume of the primitive cell is
a3
2
(B) It is FCC and the volume of the primitive cell is
a3
4
(C) It is BCC and the volume of the primitive cell is
a3
8
(D) It is FCC and the volume of the primitive cell is a3
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.12)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (1 Mark, 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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