UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper II
Q1(n). Microwave activity of SF₆, CO, H₂, H₂O and CO₂
Question
Which of the following molecules is microwave active and why? Give reasons: SF₆, CO, H₂, H₂O, CO₂.
Answer in brief
CO and H₂O are microwave active (permanent dipole moment). SF₆, H₂ and CO₂ (μ = 0) are inactive.
Key points
- Gross selection rule: a pure rotational spectrum needs a permanent dipole moment.
- Active: CO, heteronuclear diatomic, μ = 0.11 D; H₂O, bent (C₂v), bond dipoles add, μ = 1.85 D.
- Inactive: H₂, homonuclear, μ = 0; CO₂, linear (D∞h), C=O dipoles cancel; SF₆, octahedral (Oh), six S–F dipoles cancel.
- H₂ and CO₂ are studied by rotational Raman spectra; SF₆ shows no pure rotational spectrum in either.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coversmicrowave spectroscopyrotational spectrapermanent dipole momentgross selection rulemicrowave active molecules
All parts of Question 1
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- 1(b) Exceptional behaviour of hydrogen and helium5 marks
- 1(c) Unit cell of solid C₆₀ and its carbon atoms5 marks
- 1(d) Planes that diffract: simple cubic, a = 5 Å5 marks
- 1(e) Chemical potential and its link with Gibbs energy5 marks
- 1(f) Debye–Hückel limiting law for γ±5 marks
- 1(g) Activation energy of 2HI → H₂ + I₂5 marks
- 1(h) Best coagulant for the Sb₂S₃ sol5 marks
- 1(i) E° of Na⁺/Na from ΔrH° and ΔrS°5 marks
- 1(j) pH from a calomel–quinhydrone cell5 marks
- 1(k) Degeneracy of the level 6h²/8mL² in a cubic box5 marks
- 1(l) Is Peⁱᵏˣ + Qe⁻ⁱᵏˣ an eigenfunction?5 marks
- 1(m) Zero-point energy in joule and in cm⁻¹5 marks
- 1(n) Microwave activity of SF₆, CO, H₂, H₂O and CO₂5 marks
- 1(o) Stark–Einstein law and the quantum yield5 marks
- 1(p) Decay routes of a photoexcited molecule5 marks