 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2013/paper-2/section-a/a4/solution

m_{i}

U_{i} (r) = - m_{i} ω^{2} r^{2} /2

\frac{n _{i} ( r )}{n _{i} ( a )} = exp [\frac{m _{i} ω ^{2} ( r ^{2} - a ^{2} )}{2 k _{B} T}] .

c = n_{1} / n_{2}

. At the axis,

c_{axis} = c_{wall} exp [\frac{( m _{2} - m _{1} ) ω ^{2} a ^{2}}{2 k _{B} T}] .

Thus the axis favours the lighter species. The expression assumes a dilute classical mixture at one temperature, equilibrium in the rotating reference frame, and sampling sufficiently close to

r = 0

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