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Homework Help: 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

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


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    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.
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