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.