Q65 · CSIR NET Chemistry, December 2017
Paper: CSIR NET December 2017 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Hard
Given below is a specific vibrational mode of $\mathrm{BCl_3}$ with $\oplus$ and $\ominus$ denoting movements of the respective atoms above and below the plane of the molecule respectively. The irreducible representation of the vibrational mode and its IR / Raman activity are
| $D_{3h}$ | $E$ | $2C_{3}$ | $3C_{2}$ | $\sigma_{h}$ | $2S_{3}$ | $3\sigma_{v}$ | |
|---|---|---|---|---|---|---|---|
| $A_{1}$ | 1 | 1 | 1 | 1 | 1 | 1 | |
| $A_{2}$ | 1 | 1 | -1 | 1 | 1 | -1 | $R_{z}$ |
| $E^{\prime}$ | 2 | -1 | 0 | 2 | -1 | 0 | $(x,\ y)$ |
| $A_{1}^{\prime}$ | 1 | 1 | 1 | -1 | -1 | -1 | |
| $A_{2}^{\prime}$ | 1 | 1 | -1 | -1 | -1 | 1 | $z$ |
| $E^{\prime}$ | 2 | -1 | 0 | -2 | 1 | 0 | $(R_{x},\ R_{y})$ |
(a)$\mathrm{A}_{2}^{\prime}$; neither IR nor Raman active
(b)$\mathrm{E}^{\prime}$; both IR and Raman active
(c)$\mathrm{A}_{1}^{\prime}$; Raman active
(d)$\mathrm{A}_{2}^{\prime \prime}$; IR active
Answer
Answer: D ✓ checked by 4AB · confidence high
Explanation
All atoms moving perpendicular to the BCl₃ plane (B one way, Cl the other) is the out-of-plane bend A₂″ of D₃h, which transforms like z: IR active, Raman inactive — 'A₂; IR active' (d).
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