Question

A tall vertical vessel contains a gas composed of two kinds of molecules of masses m₁ and m_2, with m₂ > m₁. The concentrations of these molecules at the bottom of the vessel are equal to n₁ and n₂ respectively, with n₂ > n₁. 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.

Answer 1

They are equal at a height h where n₁/n₂ = e^{gh(m₁-m₂)/kT}