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.