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GATE 2026 CY – Question 19

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

Among the following, the one for which the infrared active vibrational modes are Raman inactive and vice versa is

  1. H2O
  2. trans-planar conformer of H2O2
  3. eclipsed conformer of ethane
  4. CH4

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Correct answer: (B) trans-planar conformer of H2O2

Explanation

**Mutual exclusion rule.** In a molecule with a **centre of inversion** (centrosymmetric), the vibrations that are IR active are Raman inactive, and the vibrations that are Raman active are IR inactive. Without an inversion centre, some modes can be active in both.

Check each molecule:
- **$\text{H}_2\text{O}$** ($C_{2v}$): no inversion centre, so some modes are both IR and Raman active. ✗
- **trans-planar $\text{H}_2\text{O}_2$** ($C_{2h}$): has an inversion centre. ✓
- **Eclipsed ethane** ($D_{3h}$): no inversion centre ($D_{3h}$ lacks $i$; the staggered form, $D_{3d}$, has one). ✗
- **$\text{CH}_4$** ($T_d$): no inversion centre. ✗

Answer **trans-planar $\text{H}_2\text{O}_2$** (B).