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Decay chain of radioactive isotopes

  1. Mar 19, 2012 #1
    How can I efficiently calculate the amount of material decayed after a specific time in a two-step decay chain?

    In my specific example, I have 56Ni -> 56Co -> 56Fe. The half life of the first process is 6.1 days, the second - 77.7 days. How can I accurately calculate the amount of 56Fe that was created after a certain time from a given quantity of 56Ni? Is there a formula for "effective half life" of such a decay, in particular when the objective is to calculate the amount of final substance created after time t, as opposed to the amount of initial substance remaining?
  2. jcsd
  3. Mar 19, 2012 #2
    This problem can be solved using analytical approach since it's a simple linear decay chain(without branching, the coefficients are distinct), I recommand you the paper published by Batman(Solution of a system of differential equations occurring in the theory of radioactive transformations) 100 years ago(the equation that govern this problem is also known as Batman equation).
    For a more general problem(no distinction is needed for coefficients), you can find solution from Jerzy Cetnar's work("General solution of Bateman equations for nuclear transmutations").
    Hope that will help^_^
  4. Mar 19, 2012 #3
    Thank you, Bateman equations are exactly what I was looking for!
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