Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
The dispersion (E(k)) of the conduction band (CB) and valence band (VB) for a
semiconductor are shown schematically in the figure. Considering the possibility of an
electron making a transition from the bottom of the CB to the top of the VB, which of the
following options is/are correct?
Options:
(A) The transition is forbidden.
(B) A photon can be emitted with an energy exactly equal to Eg.
(C) A photon can be emitted with an energy less than Eg .
(D) A phonon can be created with a crystal momentum ℏq.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.54)**
**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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