Paper: CSIR-NET June 2012 · Subject: Physical Chemistry · Chapter: Group Theory · Topic: Symmetry Elements Point Groups · Marks: 2 · Difficulty: Medium
A square pyramidal, $\mathrm{MX_4}$, molecule belongs to $\mathrm{C_{4v}}$ point group. The symmetry operations are: $\mathrm{E}, 2\mathrm{C_4}, \mathrm{C_2}, 2\sigma_v$ and $2\sigma_d$. The trace for the reducible representation, when symmetry operations of $\mathrm{C_{4v}}$ applied to $\mathrm{MX_4}$, is:
(c)51111
(a)51113
(b)11111
(d)41113
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
Counting unshifted atoms of square-pyramidal MX₄: E 5, C₄ 1 (M only), C₂ 1, σ_v (through two X and M) 3, σ_d (between the X) 1 — with σ_v and σ_d labelled as in the option: 5, 1, 1, 1, 3.