Scale Height for Planets

Breedlove

1. The problem statement, all variables and given/known data

I want to try to find the scale height of a planet using H=kT/Mg, where H is the scale height, k is the Boltzman constant, T is the surface temperature, g is the acceleration of gravity, and M is the mean molecular mass.

I am having a great deal of trouble understanding M and how to calculate it. In my handout, it says that it should be in units of nitrogen masses. On wikipedia it says that it should be in kg. Wikipedia also refers to mean molecular mass as being defined in terms of the unified atomic mass unit. Augh...

I know that the composition of the atmosphere is similar to ours, 78% nitrogen and 21% oxygen, but I don't know the density which prevents me from just plugging it into the ideal gas law.

Do you think that when my handout says "in SI units of nitrogen masses" it means molar masses or just the mass of one atom?

I think in the end it is safe for me to assume that the density is the same, as the planet has similar characteristics to Earth in it's radius and mass. I would really like to figure this out independent of any unnecessary assumptions though. Thanks for any help you can provide!!

Redbelly98

It would be the mass of one molecule (not necessarily a single atom, but definitely not the molar mass.)

Just FYI, when a formula has k in it, they are referring to single atoms or molecules. When they want you to use molar quantities, the gas constant R=N_Ak is used instead.