Electronic specific heat of a solid at temperature T is C = 𝛾T, where 𝛾 is a
constant related to the thermal effective mass ൫m൯ of the electrons. Then which
of the following statements are correct?
Options:
(A) 𝛾 ∝ m
(B) m is greater than free electron mass for all solids
(C) Temperature dependence of C depends on the dimensionality of the solid
(D) The linear temperature dependence of C is observed at T ≪ Debye temperature
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.51)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, 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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