Subtopic: Einstein A and B Coefficients & Population Inversion
Question Statement:
Atomic numbers of V, Cr, Fe and Zn are 23, 24, 26 and 30, respectively. Which one
of the following materials does NOT show an electron spin resonance (ESR)
spectra?
Options:
(A) V
(B) Cr
(C) Fe
(D) Zn
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.21)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 6: Atomic and Molecular Physics* | **Topic**: *Lasers and Quantum Optics* (`Einstein A and B Coefficients & Population Inversion`)
- **Question Type**: **MCQ** | **Marks**: **1 Mark**
- **Theoretical Framework**: Governed by foundational physical principles in **Lasers and Quantum Optics** (`Einstein A and B Coefficients & Population Inversion`).
**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): `Cr`**.
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