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## Homework Statement

Derive (from the equation of motion of a neutral gas and an assumption of constant gravitational field) an expression showing why the concentrations of neutral molecules decrease approximately exponentially with increasing altitude, and why the concentration of atomic oxygen (O) decreases slower with altitude than the N2 density, which in turn decreases slower than the concentration of molecular oxygen (O2). State explicitly all assumptions you make.

## The Attempt at a Solution

I used the hydrostatic balance

[tex]\frac{dp}{dh} = -\rho g[/tex]

to get

[tex]\rho = \rho_0 \exp{-\frac{gh}{RT}}[/tex]

but this is not the equation of motion stated to start with, right?

Should I somehow use

[tex]m\frac{d\vec{v}}{dt} = q(\vec{E} + \vec{v} \times \vec{B}) - \nabla p + F_g[/tex]

instead?