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GATE 2025 CY – Question 18

Physical Chemistry · Group Theory: Symmetry elements and symmetry operations. Basic postulates of groups and group multiplication tables. Classes, reducible and irreducible representations of symmetry elements. Classification and labelling of molecular point groups. Symmetry based selection rules and their application to electronic and vibrational spectroscopy. Internal coordinates and symmetry labelling of vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using molecular point group symmetry. · 1 mark · Multiple choice

The symmetry element that does NOT belong to $C_{4v}$ point group is

  1. $C_4$
  2. $C_2$
  3. $i$
  4. $\sigma_v$

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Correct answer: (C) $i$

Explanation

The point group $C_{4v}$ is the symmetry group of a square pyramid (such as $\text{BrF}_5$ or a tetragonal pyramid).

Its symmetry operations are: $E$, $2C_4$, $C_2$, $2\sigma_v$, $2\sigma_d$.

Answer **$i$** (C).