Q34 · CSIR-NET Chemistry, June 2015

Paper: CSIR-NET June 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:

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

(a)$E+A_{1}$

(b)$E+A_{2}$

(c)$T_{1}$

(d)$T_{2}$

Answer

Answer: D ✓ checked by 4AB · confidence high

Explanation

For CH₄ (T_d) Γ_vib = A₁ + E + 2T₂. Only T₂ transforms as (x, y, z), so the IR-active modes are the two T₂ sets.

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