How Thick Should the Wall Be to Scatter Half the Particle Beam?

[leviathanX777]

Homework Statement

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

Homework Equations

the mean free path (λ) = 1/nσ

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.

 

[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?

 

[leviathanX777]

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

 

[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.