Q42 · CSIR NET Chemistry, December 2019
Paper: CSIR NET December 2019 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Group Theory – General · Marks: 2 · Difficulty: Hard
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 $\mathrm{BCl_3}$ $\Gamma_{\text{vib}}=A_1^{\prime}+2E^{\prime}+A_2^{\prime\prime}$, the frequency of $A_1^{\prime}$ mode in $\mathrm{cm^{-1}}$ is
| $D_{3h}$ | E | $2C_3$ | $3C_2$ | $\sigma_h$ | $2S_3$ | $3\sigma_v$ | |
|---|---|---|---|---|---|---|---|
| $A_1^{\prime}$ | 1 | 1 | 1 | 1 | 1 | 1 | $x^{2}+y^{2}, z^{2}$ |
| $A_2^{\prime}$ | 1 | 1 | -1 | 1 | 1 | -1 | $R_z$ |
| $E^{\prime}$ | 2 | -1 | 0 | 2 | -1 | 0 | $(x, y)$ |
| $A_1^{\prime\prime}$ | 1 | 1 | 1 | -1 | -1 | -1 | |
| $A_2^{\prime\prime}$ | 1 | 1 | -1 | -1 | -1 | 1 | $z$ |
| $E^{\prime\prime}$ | 2 | -1 | 0 | -2 | 1 | 0 | $(R_x, R_y)$ |
(a)244
(b)471
(c)480
(d)995
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
In D₃h the A₁′ (symmetric stretch) mode is Raman-active but IR-inactive. The band present only in the Raman spectrum is 471 cm⁻¹, so that is A₁′; 995 and 244 (E′) appear in both, 480 (A₂″) only in IR.
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