Q67 · CSIR-NET Chemistry, June 2016

Paper: CSIR-NET June 2016 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Reducible Representations · Marks: 2 · Difficulty: Hard

The character table of $\mathrm{C}_{3 \mathrm{v}}$ point group is provided below, along with an additional reducible representation, $\Gamma$

$\Gamma$ is given by

(a)$\mathrm{A}_{1}+\mathrm{A}_{2}+\mathrm{E}$

(b)$2 \mathrm{A}_{1}+2 \mathrm{E}$

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

(d)$2 \mathrm{A}_{1}+2 \mathrm{A}_{2}+\mathrm{E}$

Answer

Answer: B ✓ checked by 4AB · confidence high

Explanation

Reduce Γ = (6, 0, 2): n(A₁) = (6 + 0 + 6)/6 = 2, n(A₂) = (6 + 0 − 6)/6 = 0, n(E) = (12 + 0 + 0)/6 = 2. So Γ = 2A₁ + 2E (b).

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