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 | $\mathrm{C_2}$ | $\sigma_v$ | $\sigma_v'$ |
|---|---|---|---|---|
| $\mathrm{A_1}$ | 1 | 1 | 1 | 1 |
| $\mathrm{A_2}$ | 1 | 1 | -1 | -1 |
| $\mathrm{B_1}$ | 1 | -1 | 1 | -1 |
| $\mathrm{B_{2}}$ | 1 | -1 | -1 | 1 |
| $\Gamma$ | 8 | -2 | -6 | 4 |
(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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