Consider a particle on a ring that is perturbed by interacting with an applied electric field (E) with the… · ABC26PH1163

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Exam: CSIR NET 2020-2021 · Marks: 2 · Difficulty: Medium

Consider a particle on a ring that is perturbed by interacting with an applied electric field (E) with the perturbation being $\mathrm{H}^{\prime}=\mu \mathrm{E} \cos \phi \mathrm{E}$, where $\mu$ is the dipole moment. The energy levels correct upto first order are
(a)$\frac{\mathrm{m}_{1}^{2} \mathrm{h}^{2}}{2}-\frac{\mu \mathrm{E}}{\pi}$
(b)$\frac{\mathrm{m}_{1}^{2} \mathrm{h}^{2}}{2 \mathrm{I}}-\frac{\mu \mathrm{E}}{2 \pi}$
(c)$\frac{\mathrm{m}_{1}^{2} \mathrm{h}^{2}}{2 \mathrm{I}}+\frac{\mu \mathrm{E}}{2 \pi}$
(d)$\frac{\mathrm{m}_{1}^{2} \mathrm{h}^{2}}{2 \mathrm{I}}$
Answer
Answer: D ✓ checked by 4AB · confidence high
Explanation
The first-order correction is ⟨m|μE cos φ|m⟩ = 0, because ∫cos φ dφ over 0–2π vanishes. The levels stay at m²ħ²/2I (d).

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