Q76 · CSIR NET Chemistry, June 2012
Paper: CSIR NET June 2012 · Subject: Physical Chemistry · Chapter: Molecular Spectroscopy · Topic: Vibrational · Marks: 2 · Difficulty: Medium
The following data were obtained from the vibrational fine structure in the vibronic spectrum of a diatomic molecule: $\omega_{\mathrm{e}}=512 \mathrm{cm}^{-1}, \omega_{\mathrm{e}} \mathrm{x}_{\mathrm{e}}=8 \mathrm{cm}^{-1}$ where $\omega_{\mathrm{e}}$ is the energy associated with the natural frequency of vibration and xe is the anharmonicity constant. The dissociation energy (De) of the molecule is:
(a)$4096 \mathrm{cm}^{-1}$
(b)$6144 \mathrm{cm}^{-1}$
(c)$8192 \mathrm{cm}^{-1}$
(d)$16384 \mathrm{cm}^{-1}$
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
D_e = ω_e²/(4ω_eχ_e) = 512²/(4 × 8) = 8192 cm⁻¹.
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