How to find out if a planet can have a atmostsphere

[leonne]

Homework Statement

Need to figure out if a planet can have a hydrogen atmosphere

Homework Equations

ves=(2GM/R)^.5

Vrms=(3kt/m)^.5

The Attempt at a Solution

Ok so I would first find the escape velocity of the planet, than find the velocity of the molecule. I am given the mas of planet radius and the temperature.
I would just use ves to find escape velocity, but not sure about the hydrogen particles.
Would i just use Vrms? what would m =? for nitrogen its 28mp mp= mass of proton, but no idea where the 28 comes from.
also in my notes says
Tesc=1/54 (GMm/kR) than they do it for nitrogen on Earth and get 3900k and than does it for the moon and gets 175 k and says this is why Earth has a atmosphere and moon doesn't, but does not really explain wht the numbers mean. I know its temperature but how would i know if there is a atmosphere or not.
thanks

 

[revnaknuma]

I think it does not have such a simple solution.

 

[Claude Bile]

In order for a planet to retain gases, the escape velocity of the planet must exceed the rms velocity of the gas.

Would i just use Vrms? what would m =? for nitrogen its 28mp mp= mass of proton, but no idea where the 28 comes from.

m would be the mass of the particle. The 28 comes from the number of nucleons present in the atom. Thus for a Hydrogen atom, m would be approximately equal to the mass of the proton, since there is only one nucleon present.

Tesc=1/54 (GMm/kR) than they do it for nitrogen on Earth and get 3900k and than does it for the moon and gets 175 k and says this is why Earth has a atmosphere and moon doesn't, but does not really explain wht the numbers mean. I know its temperature but how would i know if there is a atmosphere or not.

I think the point they are getting to is that Earth has an atmosphere, because its escape velocity is larger than that of Nitrogens rms velocity, while the moon does not because its escape velocity is less than Nitrogens rms velocity.

Claude.

 

[leonne]

yeah figured it out thxs