In a diatomic molecule of mass M, electronic, rotational and vibrational energy
scales are of magnitude E, Eோ and E, respectively. The spring constant for the
vibrational energy is determined by E. If the electron mass is m then
Options:
(A) Eோ ~ m
M E
(B) Eோ ~ ටm
M E
(C) E ~ ටm
M E
(D) E ~ ቀm
Mቁ
ଵ ସ⁄
E
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.50)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Atomic & Molecular Physics** within *Section 6: Atomic and Molecular Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Atomic & Molecular 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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