Decay chain of radioactive isotopes

beee

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?

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Physic_fun

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^_^

beee

Thank you, Bateman equations are exactly what I was looking for!

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