Probability of Helium Atom Speed >1000 m/s @ 300K

[leroyjenkens]

Homework Statement

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.

Homework 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

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.

 

[DrClaude]

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.

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

 

[leroyjenkens]

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

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.