Calculating Atmospheric Pressure at High Altitudes Using Quantum Mechanics

[max1995]

Homework Statement

I was given this as a homework question for my quantum mechanics section
Find the pressure in the earth’s atmosphere at 20,000m assuming the temperature is 350K.

Homework Equations

The Attempt at a Solution

First I assumed it was isothermal (we covered it in lecture so can assume that I think)
said the standard pressure at sea level is 101325Pa

number density= N/V=pressure/(kT)

so 101325/(1.38x10^-23x350) = 2.1x^25 = n₀

then I was going to use n=n₀e^-(mgh)/(kT) but don't know how to calculate or estimate m

I did post this question before but have decided I have no real idea what to do so I am reposting it now (not sure if this is allowed so sorry if it isn't)

1. Homework Statement
Find the pressure in the earth’s atmosphere at 20,000m assuming the temperature is 350K

Homework Equations

The Attempt at a Solution

I use PV=NkT

P/kT=N/V but as N/V = number density at sea level (n0)

the number density (n₀) = 101365/(1.38x10^-23*350 = 2.1x10^²⁵

and then I would of used n=n₀*e^-mgh/kT but 1. don't think this is the right way to do it (if it is could someone please say) and also don't know the mass without having to use loads of numbers pulled from the internet, which isn't normally done in my physics worksheets

Thanks for any help

 

[Bystander]

Assuming this is Earth atmosphere, atmospheric composition at sea level is ~ 80% N₂ and 20% O₂.

 

[max1995]

I decided I have no idea what I need to do with the question at all, can anyone please help?