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.