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GATE 2022 CY – Question 50

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. · 2 marks · Multiple choice

Which statement about the three illustrated normal modes of $SO_3$ is correct? + and − indicate out-of-plane motion.

Diagram for GATE 2022 CY question 50
  1. (I) and (II) are infrared active while (III) is infrared inactive
  2. (I) is infrared inactive while (II) and (III) are infrared active
  3. (I) and (III) are infrared inactive while (II) is infrared active
  4. None of the modes are infrared active since SO3 has zero dipole moment

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Correct answer: (B) (I) is infrared inactive while (II) and (III) are infrared active

Explanation

Symmetric stretching I preserves vector cancellation of the three bond dipoles and is IR inactive(A1′). Out-of-plane bending II changes dipole along z(A2″); asymmetric mode III changes in-plane dipole(E′), so both are IR active.

Therefore **B**. Zero equilibrium dipole does not prevent a vibration-induced dipole.