Problem 2.105

A tall vertical vessel contains a gas composed of two kinds of molecules of masses \(m_{1}\) and \(m_{2},\) with \(m_{2}>m_{1} .\) The concentrations of these molecules at the bottom of the vessel are equal to \(n_{1}\) and \(n_{2}\) respectively, with \(n_{2}>n_{1}\). Assuming the temperature \(T\) and the free-fall acceleration \(g\) to be independent of the height, find the height at which the concentrations of these kinds of molecules are equal.