Q92 · CSIR-NET Chemistry, December 2014

Paper: CSIR-NET December 2014 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Character Tables · Marks: 2 · Difficulty: Medium

The character table of $\mathrm{C}_{2 \mathrm{v}}$ point group is given below. In cis-butadiene molecule the vibrational modes belonging to $\mathrm{A}_{2}$ irreducible representation are IR inactive. The remaining IR active modes are
(a)$7 \mathrm{A}_{1}+5 \mathrm{B}_{1}+8 \mathrm{B}_{2}$
(b)$9 A_{1}+4 B_{1}+7 B_{2}$
(c)$7 \mathrm{A}_{1}+3 \mathrm{B}_{1}+7 \mathrm{B}_{2}$
(d)$9 \mathrm{A}_{1}+3 \mathrm{B}_{1}+8 \mathrm{B}_{2}$
Answer
Answer: D ✓ checked by 4AB · confidence medium
Explanation
cis-Butadiene (C₂v) has 24 normal modes: 9A₁ + 4A₂ + 3B₁ + 8B₂. The A₂ modes are IR-inactive, leaving 9A₁ + 3B₁ + 8B₂ (d, chapter key).

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