Q126 · CSIR NET Chemistry, December 2019
Paper: CSIR NET December 2019 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Group Theory – General · Marks: 2 · Difficulty: Medium
The observed IR spectrum of $\mathrm{BCl_3}$ exhibits three bands at 995, 480 and $244\,\mathrm{cm^{-1}}$, while the Raman bands are observed at 995, 471 and $244\,\mathrm{cm^{-1}}$. Given that for $\mathrm{BCl_3}$ $\Gamma_{vib} = \mathrm{A_1}'+2\mathrm{E}'+\mathrm{A_2}''$, the frequency of $\mathrm{A_1}'$ mode in $\mathrm{cm^{-1}}$ is
| $\mathrm{D_{3h}}$ | E | $2\mathrm{C_3}$ | $3\mathrm{C_2}$ | $\sigma_h$ | $2\mathrm{S_3}$ | $3\sigma_v$ | |
|---|---|---|---|---|---|---|---|
| $\mathrm{A_1}'$ | 1 | 1 | 1 | 1 | 1 | 1 | $x^2+y^2, z^2$ |
| $\mathrm{A_2}'$ | 1 | 1 | -1 | 1 | 1 | -1 | $R_z$ |
| E' | 2 | -1 | 0 | 2 | -1 | 0 | (x,y) |
| $\mathrm{A_1}''$ | 1 | 1 | 1 | -1 | -1 | -1 | |
| $\mathrm{A_2}''$ | 1 | 1 | -1 | -1 | -1 | 1 | z |
| E'' | 2 | -1 | 0 | -2 | 1 | 0 | $(R_x,R_y)$ |
Answer
Answer (as printed): B
The options are missing from the source scan for this question, so there is nothing here for this letter to point at. The letter is what the book printed.
Explanation
A₁′ in D₃h is Raman-active but IR-inactive; the only band seen in Raman and absent in IR is 471 cm⁻¹.
Study loop for Group Theory