For nonrelativistic electrons in a solid, different energy dispersion relations (with
effective masses ma∗ , mb
∗ , and mc∗) are schematically shown in the plots.
Which one of the following options is CORRECT?
Options:
(A) ma∗ = mb
∗ = mc∗
(B) mb
∗ > mc∗ > ma∗
(C) mc∗ > mb
∗ > ma∗
(D) ma∗ > mb
∗ > mc∗
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.20)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 3: Electromagnetic Theory* | **Topic**: *Electromagnetic Waves in Media* (`Wave Propagation in Dielectrics & Conductors`)
- **Question Type**: **MCQ** | **Marks**: **1 Mark**
- **Theoretical Framework**: Governed by foundational physical principles in **Electromagnetic Waves in Media** (`Wave Propagation in Dielectrics & Conductors`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `mb
∗ > mc∗ > ma∗`**.
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