 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2025/paper-1/a4/c/i/solution

The C=O length is invariant under every operation, so its stretch is

A_{1}

. If

s_{L}, s_{R}

are the two C–H bond-length changes, their sum and difference give

Q_{CO} \sim A_{1}, Q_{CH, s} = \frac{s _{L} + s _{R}}{2} \sim A_{1}, Q_{CH, a} = \frac{s _{L} - s _{R}}{2} \sim B_{1} .

Hence

Γ_{stretch} = 2 A_{1} + B_{1}

. These are stretching symmetry coordinates; the two

A_{1}

motions can mix in actual normal modes, and mass-weighted atomic motions need not have the schematic arrow lengths below.

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