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Electromagnetic cascade in a calorimeter

  1. Dec 6, 2016 #1
    1. The problem statement, all variables and given/known data
    A calorimeter is made from layers of lead (1.75mm thick) alternated with layers of scintillator. The radiation length ##X_0## of lead is ##0.64cm##.

    In an EM shower the number of particles doubles and the energy of each particle halves per radiation length travelled. The shower stops when critical energy ##E_c## is reached. For lead ##E_c## is 9.6MeV. Estimate the calorimeter thickness required to completely contain a shower caused by a 10GeV electron. Neglect interactions in the scintillator.

    2. Relevant equations


    3. The attempt at a solution
    I know a calorimeter has to have scintillator as the first and last layers. So if there are n layers of scintillator, there will be n-1 layers of lead.

    Based on the information given. I'm thinking the equation should be something like
    ##E = \frac{E_0}{2^{t/X_0}}##
    Where t is the thickness of lead the shower travels through. Then thickness would be ##(0.175t) \times 0.4(t+1)##. Is that ok? Or do I need to somehow include the doubling in particle number in there?

    Thanks for any help!
     
  2. jcsd
  3. Dec 8, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    It does not have to. Is there a scintillator thickness given? Otherwise you can just calculate the required length of lead.

    Your second expression grows quadratically with t, that cannot be right. Did you mean "+"? Where does the 0.4 come from?
     
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