Gas Distribution Homework: Calculating Particle Mass to Escape Planet's Gravity

[nitefalls]

Homework Statement

A planet has mass, 2 x 1022 kg, and radius, 2 x 106 m. Initially, its
atmosphere contains gas particles of various masses. If the gas is at temperature, 400 K,
and has a Maxwell-Boltzmann velocity distribution, what mass of particle will typically
escape from the planet’s gravitational pull? (Hint: You can just use the average velocity,
you don’t need to consider the full Maxwell-Boltzmann distribution).

Homework Equations

vrms=sqrt(3kbT/m)
P(v)=v^2*e^(-0.5mv^2/kbT)

The Attempt at a Solution

I have no clue at all
Please help me

 

[nitefalls]

wait i got it.. thx
the vrms was the escape velocity
hahaha XD

 

[cramster]

Im having problems with this problem too can you tell me how you got it?

 

[esmeralda.ty]

escape velocity v=sqrt2GM/ R
you need to use this velocity for maxwell-boltzmann speed distribution:
2GM/r= 3kT/m
you can find m from here.
I hope that helps