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.