Q71 · CSIR NET Chemistry, June 2019
Paper: CSIR NET June 2019 · Subject: Physical Chemistry · Chapter: Molecular Spectroscopy · Topic: Vibrational · Marks: 2 · Difficulty: Medium
The Berge-Sponer plot between $\Delta \mathrm{G}_{\mathrm{v}+\frac{1}{2}}=\left(\varepsilon_{\mathrm{v}+1}-\varepsilon_{\mathrm{v}}\right)$ and $v+1$ for CO in a straight line with slope of $-14 \mathrm{cm}^{-1}$ and intercept of $2170 \mathrm{cm}^{-1}$. The approximate value of dissociation energy of CO (in $c m^{-1}$ ) is (Assume CO as an Anharmonic oscillator with energy expression.
\[ \varepsilon_{v}=\left(v+\frac{1}{2}\right) \omega-\left(v+\frac{1}{2}\right)^{2} x_{e} \omega ; D=\frac{\omega}{4 x_{e}} \]
(a)42044
(b)84088
(c)168175
(d)336350
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
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Explanation
Birge–Sponer: ΔG(v+½) = ω_e − 2ω_eχ_e(v+1). Slope −2ω_eχ_e = −14 cm⁻¹, so ω_eχ_e = 7 cm⁻¹; intercept ω_e = 2170 cm⁻¹. D_e ≈ ω_e²/(4ω_eχ_e) = 2170²/28 ≈ 168,175 cm⁻¹ (c).
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