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The Maxwell Speed Distribution in 2D

  • Thread starter fatherdaly
  • Start date
  • #1

Homework Statement


YfFkl.png


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" [Broken]<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.
 
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Answers and Replies

  • #2
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0
You need some substitution to make the integral doable.
 
  • #3
Ok so I have the integral of v*exp(-[tex]\alpha[/tex]v2) 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.
 
Last edited:

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