UPSC Combined Geo-Scientist, Mains · 2026 · Mains Paper II
Q1(n). Raman activity and polarisability ellipsoids of CO₂
Question
(i) What is the condition for a molecular vibration to be Raman active? (ii) Draw the polarizability ellipsoids for symmetric stretching mode of vibration of CO₂.
Answer in brief
(i) The polarisability must change during the vibration: (∂α/∂ Q)₀≠0. (ii) In the symmetric stretch of CO₂ the ellipsoid grows and shrinks, so the mode is Raman active (and IR inactive).
Key points
- The induced dipole μ=α E. Raman scattering at ν₀±ν_(vib) needs α to oscillate at ν_(vib).
- both C=O bonds lengthen together, the electron cloud is looser and the ellipsoid is larger; on shortening it is smaller. The change is symmetric about the equilibrium shape. α changes: Raman active.
- the ellipsoid is only tilted or deformed in a way that is equal in both directions about equilibrium, so ∂α/∂ Q=0 (Raman inactive); they change the dipole (IR active). This is the rule of mutual exclusion for centrosymmetric…
The full model answer
Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.
- The induced dipole μ=α E. Raman scattering at ν₀±ν_(vib) needs α to oscillate at ν_(vib).
- CO₂ symmetric stretch (Σ_g⁺, 1388 cm⁻¹): both C=O bonds lengthen together, the electron cloud is looser and the ellipsoid is larger; on shortening it is smaller. The change is symmetric about the equilibrium shape. α changes: Raman active.
- Asymmetric stretch and bend: the ellipsoid is only tilted or deformed in a way that is equal in both directions about equilibrium, so ∂α/∂ Q=0 (Raman inactive); they change the dipole (IR active). This is the rule of mutual exclusion for centrosymmetric molecules.
CoversRamanRaman activity and polarisability ellipsoids of CO₂
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- 1(n) Raman activity and polarisability ellipsoids of CO₂5 marks
- 1(o) The incorrect statement on electronic spectra5 marks
- 1(p) Non-radiative decay competing with fluorescence5 marks