The expression for the second overtone frequency in the vibrational absorption spectra of a
diatomic molecule in terms of the harmonic frequency 𝜔e and anharmonicity constant xe is
(A) 2𝜔e(1 - xe) (B) 2𝜔e(1 - 3xe) (C) 3𝜔e(1 - 2xe) (D) 3𝜔e(1 - 4xe)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2018 Q.9)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Quantitative & Analytical Aptitude.
- 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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