The moment of inertia of a rigid diatomic molecule A is 6 times that of another rigid diatomic
molecule B. If the rotational energies of the two molecules are equal, then the corresponding values
of the rotational quantum numbers JA and JB are
(A) JA = 2, JB = 1 (B) JA = 3, JB = 1 (C) JA = 5, JB = 0 (D) JA = 6, JB = 1
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.34)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Atomic & Molecular Physics** within *Section 6: Atomic and Molecular Physics* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Atomic & Molecular Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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