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

• nitefalls
In summary, the problem asks for the mass of a gas particle that will typically escape from a planet's gravitational pull, given the planet's mass, radius, and gas temperature. By using the escape velocity equation and substituting it into the Maxwell-Boltzmann speed distribution, the mass of the particle can be calculated.
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

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

## What is the purpose of calculating particle mass to escape a planet's gravity?

The purpose of calculating particle mass to escape a planet's gravity is to determine if a gas particle has enough mass to overcome the planet's gravitational pull and escape into space.

## What factors affect the calculation of particle mass to escape a planet's gravity?

The factors that affect the calculation of particle mass to escape a planet's gravity include the mass of the planet, the radius of the planet, and the velocity of the particle.

## How do you calculate the mass of a gas particle?

The mass of a gas particle can be calculated using the ideal gas law, which states that the mass of a gas is directly proportional to its volume and pressure, and inversely proportional to its temperature.

## What is the formula for calculating the escape velocity of a planet?

The formula for calculating the escape velocity of a planet is ve = √(2GM/r), where G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet to the particle's starting point.

## Can gas particles of any mass escape a planet's gravity?

No, not all gas particles can escape a planet's gravity. The particle must have a high enough velocity and a low enough mass in order to overcome the gravitational force of the planet and escape into space.

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