# Homework Help: Beam of particles, scattering

1. Dec 3, 2009

### leviathanX777

1. The problem statement, all variables and given/known data

A beam of particles strike a wall containing 2 x 10^29 atoms per m^3. each atom behaves like a sphere of radius 3 x 10^-15 m. Find the thickness of the wall that exactly half the particles will penetrate without scattering. What thickness would be needed to stop all but one particle in 10^6

2. Relevant equations

the mean free path (λ) = 1/nσ

3. The attempt at a solution

I'm not sure how to start the solution. I can't find an equation that will bring the thickness of the wall into the problem

Cheers.

Last edited: Dec 3, 2009
2. Dec 3, 2009

### lanedance

hmmm... you could consider the surface area effectivley covered by the spheres... what is that relative to the wall area in terms of the thickness?

3. Dec 3, 2009

### leviathanX777

I do not know the wall area, it didn't say.

4. Dec 3, 2009

### Grogs

Cool problem. I would approach it this way: The microscopic cross-section is ~ the area presented by a single nucleus, so in this case $\sigma$ = $\pi$*(3x10-15 m)2 = 2.83 x 10-29 m2

Once you have that, you can calculate the macroscopic cross section using $\Sigma$=N$\sigma$ and then you can use the exponential attenuation formula I = I0exp(-$\Sigma$t) to solve for the penetration depth t.