Paper: CSIR-NET June 2011 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Medium
The character table of the $\mathrm{C}_{2 \mathrm{v}}$ point group is given below:
$\mathrm{C}_{2 \mathrm{V}}$
E
$\mathrm{C}_{2}$
$\sigma_{\mathrm{v}}$
$\sigma^{\prime}{ }_{\mathrm{v}}$
$\mathrm{A}_{1}$
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
1 atom of cis-butadiene and $\sigma_{\mathrm{v}}$ is the molecular plane) belong to
(a)$\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ respectively
(b)Both $\mathrm{A}_{2}$
(c)Both $\mathrm{B}_{2}$
(d)$\mathrm{B}_{1}$ and $\mathrm{B}_{2}$ respectively.
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
For p orbitals perpendicular to the molecular plane (σv), C₂ and σv change their sign while σv′ only swaps symmetric pairs: characters (1, −1, −1, 1) = B₂ for both combinations (c).