Q68 · CSIR NET Chemistry, June 2019
Paper: CSIR NET June 2019 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Medium
The $\pi$-orbital $\mathrm{p}_{1}+\mathrm{p}_{2}-\mathrm{p}_{3}-\mathrm{p}_{4}$ of cis-butadiene belongs to the irreducible representation
| $\mathrm{C}_{\mathrm{2v}}$ | E | $\mathrm{C}_{\mathrm{2}}$ | $\sigma_{v}$ | $\sigma_{v}{ }^{\prime}$ |
|---|---|---|---|---|
| $\mathrm{A}_{\mathrm{1}}$ | 1 | 1 | 1 | 1 |
| $\mathrm{A}_{\mathrm{2}}$ | 1 | 1 | -1 | -1 |
| $\mathrm{B}_{\mathrm{1}}$ | 1 | -1 | 1 | -1 |
| $\mathrm{B}_{\mathrm{2}}$ | 1 | -1 | -1 | 1 |
(a)$\mathrm{A}_{1}$
(b)$\mathrm{A}_{2}$
(c)$\mathrm{B}_{1}$
(d)$\mathrm{B}_{2}$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
With σ_v as the molecular plane, p₁ + p₂ − p₃ − p₄ is unchanged by C₂ (which sends p₁ → −p₄, p₂ → −p₃), changes sign under σ_v and under σ_v′: characters (1, 1, −1, −1) = A₂.
Study loop for Group Theory