Q12 · CSIR-NET Chemistry, June 2019

Paper: CSIR-NET June 2019 · Subject: Physical Chemistry · Chapter: Molecular Spectroscopy · Topic: Rotational · Marks: 2 · Difficulty: Medium

The Berge-Sponer plot between $\Delta G_{v+\frac{1}{2}}=(\varepsilon_{v+1}-\varepsilon_{v})$ and $(v+1)$ for CO ia 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 $\mathrm{cm^{-1}}$) is (Assume CO as an Anharmonic oscillator with energy expression.
\[ \varepsilon_v=\left(v+\frac{1}{2}\right)\omega-\left(v+\frac{1}{2}\right)^{2}x_e\omega; \quad D=\frac{\omega}{4x_e} \]
(a)42044
(b)84088
(c)168175
(d)336350
Answer
Answer: C ✓ checked by 4AB · confidence medium
Explanation
Birge–Sponer: ΔG(v+½) = ε(v+1) − ε(v) = ω − 2(v+1)xₑω. A plot against (v+1) therefore has slope −2xₑω = −14 cm⁻¹ ⇒ xₑω = 7 cm⁻¹, and intercept ω = 2170 cm⁻¹. D = ω/(4xₑ) = ω²/(4xₑω) = 2170²/(4 × 7) = 4708900/28 = 168175 cm⁻¹ — option (c).

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