 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2021/paper-1/a3/a/iii/solution

I = m_{C} r_{1}^{2} + m_{S} r_{2}^{2} = \frac{m _{C} m _{S}^{2} + m _{S} m _{C}^{2}}{( m _{C} + m _{S} ) ^{2}} r^{2} = \frac{m _{C} m _{S}}{m _{C} + m _{S}} r^{2} .

The prefactor is the reduced mass

μ

; this is the standard reduction of a two-body linear rigid rotor to

I = μ r^{2}

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