The reducible representation of pyramidal $\mathrm{AB}_{3}$ is
$\mathrm{C}_{3 \mathrm{v}}$
E
$2 \mathrm{C}_{3}$
$3 \sigma_{\mathrm{v}}$
$\Gamma$
12
0
2
The CORRECT option representing all the normal Raman active modes of pyramidal $\mathrm{AB}_{3}$ is:
(a)$\mathrm{A}_{1}+\mathrm{A}_{2}+2 \mathrm{E}$
(b)$2 \mathrm{A}_{1}+2 \mathrm{E}$
(c)$3 \mathrm{A}_{1}+\mathrm{A}_{2}+\mathrm{E}$
(d)3E
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
Γ_vib of pyramidal AB₃ (C₃v) reduces to 2A₁ + 2E; in C₃v both A₁ (x²+y², z²) and E (x²−y², xy; xz, yz) are Raman active, so all modes 2A₁ + 2E are Raman active (b).