The variation of the atmospheric pressure p with altitude h is predicted by the barometric formula to be p=p₀e^−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 the 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 O₂ and H₂O at h=8.0 km, a typical cruising altitude for commercial aircraft.