1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Beam of particles, scattering

  1. Dec 3, 2009 #1
    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. jcsd
  3. Dec 3, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    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?
     
  4. Dec 3, 2009 #3
    I do not know the wall area, it didn't say.
     
  5. Dec 3, 2009 #4
    Cool problem. I would approach it this way: The microscopic cross-section is ~ the area presented by a single nucleus, so in this case [itex]\sigma[/itex] = [itex]\pi[/itex]*(3x10-15 m)2 = 2.83 x 10-29 m2

    Once you have that, you can calculate the macroscopic cross section using [itex]\Sigma[/itex]=N[itex]\sigma[/itex] and then you can use the exponential attenuation formula I = I0exp(-[itex]\Sigma[/itex]t) to solve for the penetration depth t.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook