Q124 · CSIR-NET Chemistry, December 2019

Paper: CSIR-NET December 2019 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Medium

The reducible representation $\Gamma$, in the table is equal to the following superposition of the irreducible representation of $\mathrm{C_{2v}}$ point group.
$\mathrm{C_{2v}}$E$\mathrm{C_2}$$\sigma_v$$\sigma_v'$
$\mathrm{A_1}$1111
$\mathrm{A_2}$11-1-1
$\mathrm{B_1}$1-11-1
$\mathrm{B_{2}}$1-1-11
$\Gamma$8-2-64
(a)$\mathrm{A}_{1}+2 \mathrm{A}_{2}+5 \mathrm{B}_{1}$
(b)$\mathrm{A}_{1}+2 \mathrm{A}_{2}+5 \mathrm{B}_{2}$
(c)$5 \mathrm{A}_{1}+\mathrm{A}_{2}+2 \mathrm{B}_{1}$
(d)$\mathrm{A}_{1}+5 \mathrm{A}_{2}+2 \mathrm{B}_{1}$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
Reduction formula on Γ = (8, −2, −6, 4): n(A₁) = 1, n(A₂) = 2, n(B₁) = 0, n(B₂) = 5 → A₁ + 2A₂ + 5B₂.

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