Q41 · 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 $C_{2v}$ point group. | $C_{2v}$ | $E$ | $C_2$ | $\sigma_v$ | $\sigma_v'$ |
|---|
| $A_1$ | 1 | 1 | 1 | 1 |
| $A_2$ | 1 | 1 | -1 | -1 |
| $B_1$ | 1 | -1 | 1 | -1 |
| $B_2$ | 1 | -1 | -1 | 1 |
| $\Gamma$ | 8 | -2 | -6 | 4 |
(a)$A_1+2A_2+5B_1$
(b)$A_1+2A_2+5B_2$
(c)$5A_1+A_2+2B_1$
(d)$A_1+5A_2+2B_1$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
Reduction formula with Γ = (8, −2, −6, 4): n(A₁) = (8 − 2 − 6 + 4)/4 = 1; n(A₂) = (8 − 2 + 6 − 4)/4 = 2; n(B₁) = (8 + 2 − 6 − 4)/4 = 0; n(B₂) = (8 + 2 + 6 + 4)/4 = 5. Γ = A₁ + 2A₂ + 5B₂.
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