A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called law of atmospheres ` n^2` = `n^1` exp [ -mg (`h_2` – `h_1`)/ kB T] where` n-2`, `n-1` refer to number density at heights `h_2` and `h_1` respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: `n_2` = `n_1`exp [ -mg NA (ρ - ρ′ ) (`h_2`–`h_1`)/ (ρ RT)] where ρ is the density of the suspended particle, and ρ′ ,that of surrounding medium.[NA is Avogadro’s number, and R the universal gas constant.] [Hint : Use Archimedes principle to find the apparent weight of the suspended particle.]