The Maxwell Speed Distribution in 2D

[fatherdaly]

Homework Statement

It seemed much easier to screencap than to write out.

Homework Equations

It helps to know that the number of states with speed between u and u+du is 2pi*u du

The Attempt at a Solution

I've tried quite a few things but every time I get to trying to normalise I either get stuck integrating by parts over and over, or using http://en.wikipedia.org/wiki/Gaussian_integral" <that, which doesn't arrive at the answer wanted.

If someone could give me a push in the right direction it would be much appreciated.

 

[weejee]

You need some substitution to make the integral doable.

 

[fatherdaly]

Ok so I have the integral of v*exp(-\alphav²) dv between 0 and infinity to normalise. I don't know how a substitution would help because you would still have two functions multiplied by one another.

Edit: I think I'm being stupid. I've substituted for alpha*v^2. Hopefully it will work.