GATE PH 2022 • Q52
MCQ • 2 Marks
Section 7: Solid State Physics
Solid State Physics
Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
In a Hall effect experiment on an intrinsic semiconductor, which of the following
statements are correct?
Options:
-
(A) Hall voltage is always zero
-
(B) Hall voltage is negative if the effective mass of holes is larger than those of
electrons
-
(C) Hall coefficient can be used to estimate the carrier concentration in the
semiconductor
-
(D) Hall voltage depends on the mobility of the carriers
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.52)**
**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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