GATE 2026 CY – Question 30

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 · Numerical answer

The order of the point group of $[\mathrm{PdCl_6}]^{2-}$ is x and that of trans-$[\mathrm{PdBr_2Cl_4}]^{2-}$ is y. The integer x − y is _____

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Correct answer: 32

Explanation

**Point group order** is the number of symmetry operations.

**$[\text{PdCl}_6]^{2-}$:** a regular octahedron, point group $O_h$. Its order is $x=48$.
**trans-$[\text{PdBr}_2\text{Cl}_4]^{2-}$:** replacing two opposite ligands by Br lowers the symmetry to $D_{4h}$ (a $C_4$ axis along the Br–Pd–Br line). Its order is $y=16$.

$$x-y=48-16=\mathbf{32}.$$