Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
The energy, 𝜀𝜀kk for band electrons as a function of the wave vector, kk in the first Brillouin zone
(- 𝜋𝜋 aa⁄ ≤ kk ≤ 𝜋𝜋 aa⁄ ) of a one dimensional monatomic lattice is shown as (aa is lattice constant)
The variation of the group velocity vvkk is most appropriately represented by
(A)
(B)
(C)
(D)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.22)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Solid State Physics** within *Section 7: Solid State Physics* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Solid State Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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