Q104 · CSIR-NET Chemistry, December 2015

Paper: CSIR-NET December 2015 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Medium

IR active normal modes of methane belong to the irreducible representation:

$T_{d}$	E	$8 C_{3}$	$3 C_{2}$	$6 S_{4}$	$6 \sigma_{a}$
$A_{1}$	1	1	1	1	1	$x^{2}+y^{2}+z^{2}$
$A_{2}$	1	1	1	-1	-1
E	2	-1	2	0	0	$2 x^{2}-x^{2}-y^{2}, x^{2}-y^{2}$
$T_{1}$	3	0	-1	1	-1	$R_{v}, R_{v}, R_{v}$
$T_{2}$	3	0	-1	-1	1	$x, y, z, x y, y z, z x$

(a)$\mathrm{E}+\mathrm{A}_{1}$

(b)$\mathrm{E}+\mathrm{A}_{2}$

(c)$\mathrm{T}_{1}$

(d)$\mathrm{T}_{2}$

Answer

Answer: D ✓ checked by 4AB · confidence high

Explanation

CH₄ (T_d): Γ_vib = A₁ + E + 2T₂; only T₂ transforms as (x, y, z), so the IR-active modes are T₂.

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