The variation of the atmospheric pressure p with altitude h is predicted by the barometric formula to be p = p0 e^(-h/H) where p0 is the pressure at sea level and H=RT/Mg with M the average molar mass of air and T the average temperature. Obtain the barometric formula from te Boltzmann distribution. Recall that the potential energy of a particle at height h above the surface of the Earth is mgh. Convert the barometric formula from pressure to number density, N. Compare the relative number densities, N(h)/N(0), for 02 and H20 at h= 8.0 km, a typical cruising alttude for commercial aircraft