Past exam of the chemistry A course of the University of Cambridge 2022 Paper 1 A3 a iv Solution 2026-10-20
For a linear polyatomic molecule, the first-order polyatomic vibration-rotation interaction iswhere is the degeneracy of normal mode . The bending mode has , so the two measured states implyThe two stretching zero-point contributions are not supplied. The true all-mode equilibrium constant is therefore not uniquely determined by this band alone. Neglecting those unknown stretching corrections gives the bend-only estimateUsing and converting inverse centimetres to inverse metres,If the intended course approximation instead treats the observed vibration as a single nondegenerate oscillator with , its extrapolation givesThat is a useful effective one-coordinate estimate, but it should not be identified with an exact equilibrium constant of the doubly degenerate polyatomic bend. Both estimates give at the accuracy warranted here.