 Solution

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

x

from the carbon nucleus toward the sulfur nucleus. The definition of the center of mass gives

x_{cm} = \frac{m _{C} 0 + m _{S} r}{m _{C} + m _{S}} .

Therefore the requested distance is

r_{1} = \frac{m _{S}}{m _{C} + m _{S}} r .

The other distance is

r_{2} = r - r_{1} = m_{C} r / (m_{C} + m_{S})

, consistent with

m_{C} r_{1} = m_{S} r_{2}

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