# Atom speed probability

1. Nov 21, 2013

### leroyjenkens

1. The problem statement, all variables and given/known data
Using classical statistics, find the probability that an atom of helium in a helium gas at temperature T = 300k will have a speed greater than 1000 m/s.

2. Relevant equations
I think this calls for the Maxwell speed distribution.
$$F(v)dv=4πCe^{\frac{-mv^{2}}{2kt}}v^{2}dv$$

Where k = Boltzmann's constant
T = temperature.
m = mass
C = some constant
v = velocity

3. The attempt at a solution

I tried integrating this from 1000 to infinity, to find the probability that the particle would be in that range of velocities, but that integral is apparently not possible. Is there any other way to approach this problem? The teacher doesn't expect us to do ridiculous integrals, so I'm thinking I must be making this harder than it has to be.

Thanks.

2. Nov 22, 2013

### Staff: Mentor

It is not impossible. You can surely find a way to reduce it to a form where you will ultimately get the error function.

3. Nov 22, 2013

### leroyjenkens

Yeah I got the error function from putting it into Wolframalpha. I assumed that meant that wolfram couldn't do it, hence the "error" part.
I can get the error function, but I have no idea what to do with it. I mentioned the error function to the teacher and he made it sound like I could get something workable besides that.

Edit: Ok, I inputted actual values for all those constants, and Wolfram actually spit out a number. It gave me 4.05x10^8. Is that the probability? I thought my teacher told me in his office that the probability would be 1. That's far from 1. The number I got doesn't sound like a probability at all.

Last edited: Nov 22, 2013