Statistical Mechanics: particle density of an atmosphere

[bjb406]

Homework Statement

I am supposed use stat mech to find the particle density in Earth's atmosphere given only the particle mass, and temperature, and the planet's mass I guess. And I don't really know where to begin. Obviously I need to use the grand canonical ensemble but I don't know where to start without knowing the number of particles in the system.

Homework Equations

Boltzmann distribution I guess? n(r) = A*e^(-(βρ^2)/(2m))*e^(-βmgr)

The Attempt at a Solution

I don't know what to do without knowing N

 

[Oxvillian]

Well if you're given the pressure (1 atmosphere?) and the temperature, you can just go ahead and use the ideal gas equation. No fancy grand canonical stuff required!