 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2025/paper-1/a3/d/ii/solution

Use the two-body reduced mass, rather than the chlorine mass or hydrogen mass alone:

μ = \frac{1.0078 \times 34.9688}{1.0078 + 34.9688} m_{u} = 1.62661 \times 1 0^{- 27} kg .

ν_{harm} = \frac{1}{2 π} \frac{481}{μ} = 8.65467 \times 1 0^{13} s^{- 1}, ν_{harm} = \frac{ν _{harm}}{2.99792458 \times 1 0 ^{10} cm s ^{- 1}} = 2886.89 c m^{- 1} .

The requested “frequency in cm−1” is a spectroscopic wavenumber; the ordinary frequency is the value in s−1 above. This calculation uses the question's force constant in the harmonic model, rather than replacing it with a tabulated spectroscopic constant.

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