What is the molecular mass of the unknown gas in the atmosphere?

[annalise17]

Homework Statement

I need to calculate the mas of a molecule of an unknown gas in the atmosphere from the values:

T = 500 K
mass of the planet = 1.5 × 1024 kg
radius is 3.0 × 106 m
universal constant of gravitation, G = 6.67 × 10^−11 N m^2 kg^−2
P at ground level = 2.0 × 10^7 Pa
P at 50km altitude = 2.0 × 10^5 Pa

Homework Equations

g=kT/mλ

but I can't find an equation involving G :(

The Attempt at a Solution

I am completely stuck, if I can get ahint where to start I'll have a go and see if I get anywhere.

 

[Spinnor]

On Earth

F = mg = GmM/R^2 so g = GM/R^2

 

[annalise17]

Right, I've got so far as calculating g now and have calculated a very low value for g compared to Earth which is consistent with having a smaller mass than earth. I've also worked out an equation for m by rearranging λ=kT/mg ut the value doesn't match that of the two gases it could be by a factor of 10^3.