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

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The discussion revolves around calculating the mass of gas particles that can escape a planet's gravity, given its mass and radius, along with the temperature of the atmosphere. Participants mention using the root mean square velocity (vrms) and the escape velocity formula to find the relevant mass. The connection between escape velocity and the Maxwell-Boltzmann speed distribution is highlighted, indicating that the escape velocity can be derived from gravitational parameters. The exchange of insights suggests a collaborative effort to solve the problem, with participants expressing initial confusion but gradually arriving at a solution. This illustrates the importance of understanding the relationship between temperature, particle mass, and gravitational forces in gas distribution scenarios.
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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
 
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wait i got it.. thx
the vrms was the escape velocity
hahaha XD
 
Im having problems with this problem too can you tell me how you got it?
 
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:))
 

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