The transition moment integral for a rotational transition between J=1; MJ=0 and J=2; MJ=0 states for a… · ABC26PH1302

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Exam: CSIR NET JUNE 2016 · Marks: 2 · Difficulty: Medium

The transition moment integral for a rotational transition between $J=1;\ M_J=0$ and $J=2;\ M_J=0$ states for a diatomic molecule along the $z$-axis is proportional to
(a)$\int_{0}^{\pi}\cos^{2}\theta(3\cos^{2}\theta-1)\,\mathrm{d}\theta$
(b)$\int_{0}^{\pi}\cos^{2}\theta(3\cos^{2}\theta-1)\sin\theta\,\mathrm{d}\theta$
(c)$\int_{0}^{\pi}\cos\theta(3\cos^{2}\theta-1)\sin\theta\,\mathrm{d}\theta$
(d)$\int_{0}^{\pi}\cos^{2}\theta(3\cos^{2}\theta-1)\sin^{2}\theta\,\mathrm{d}\theta$
Answer
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Explanation
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