# Distribution of speeds in a molecular beam.

1. Aug 18, 2008

### Narcol2000

I'm struggling to understand the basis for the following formula.

The goal is to find the distribution of molecular speeds emerging from a smal hole in an oven where molecules are allowed to come to thermal equalibrium with the oven walls before exiting through the small whole.

The book states:

'Suppose we consider particles with speed in the range u to u+du which cross an area A at an angle $$\theta$$ to the normal to the area. In a time t they travel a distance ut and sweep out a volume $$Autcos(\theta)$$. The number of particles in this volume with speeds in the range u to u+du and whose direction of motion lies in the range $$\theta$$ to $$\theta + d\theta$$ and $$\phi$$ to $$\phi + d\phi$$ is:

$$Autcos(\theta)\frac{n(u)du}{V}\frac{d\theta sin(\theta)d\phi}{4\pi}$$

where n(u) is the Maxwell distribution and V i assume is the total volume of the oven (i think... its not actually stated what the volume V is.)

I don't see where this formula comes from since it is just stated with no derivation, and would like to have some idea of where it comes from so any help would be appreciated.