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Homework Help: Critical radius for fission

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data
    See the image below:

    2. Relevant equations
    In the previous part, it was proved that a particle moves through a distance x in a material without interacting with probability P given by

    [itex]P=\exp(-\sigma n x)[/itex]

    Here σ represents the cross section of the reaction between the incoming particle and the material. n represents the target (material) particles per unit volume.

    3. The attempt at a solution
    The only thing I have figured out so far is that we need the probability of the neutron not escaping without a reaction, so there is a factor of

    [itex] 1- exp(- (\sigma_f + \sigma_c) nr ) [/itex]

    in the equation.

    I am not sure of where the fractional factor at the start of the equation comes from, or why the total cross section appears in the exponent.
  2. jcsd
  3. Mar 19, 2013 #2
    Bump! Does no one have any ideas, I haven't been able to solve this since the last post.
  4. Mar 19, 2013 #3
    The sum in the exponent is simple: it is because cross-sections of different reactions are additive.

    Thus (1 - exp) is the probability that the neutron will be captured or cause fission. You need to express from this the probability of fission.
  5. Mar 19, 2013 #4
    Simple explanation! Looks like I wasn't thinking the right way, thanks.
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