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Electromagnetic shower energy spectrum

  1. Mar 11, 2017 #1
    1. The problem statement, all variables and given/known data
    The energy of a daughter particle in electromagnetic shower is approximated by, ##E(t)=\frac{E_0}{2^t}##. Show that the energy falls off like approximately ##E^{-2}##, for small ##E##.

    2. Relevant equations
    Nothing really. Just a matter of knowing how to differentiate.

    3. The attempt at a solution
    I have that the rate of change of the energy is given by ##\frac{dE}{dt}=-\frac{\ln(2)E_0}{2^t}##. However, I'm not sure how to approximate this by ##-E^{-2}=-\frac{2^{2t}}{E_0^2}##, which is what I think I'm supposed to be doing.
     
  2. jcsd
  3. Mar 12, 2017 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    How can the energy fall off with increasing energy? Is that really the precise problem statement?
    That is just the initial equation squared, inverted and with a minus sign on both sides. I don't think that is the goal.
     
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