Description: A formalism is derived to describe how one radioactive isotope can become another, then another, and so on. We develop first-order, linear differential equations to describe the rates of these simultaneous decay processes, and introduce a few methods of solving them—analytically (the hard way), graphically (the intuitive way, without any math), and using approximations in cases where one decay constant is wildly different than the others. We also go beyond the textbook to introduce “burning” of isotopes, or creation/destruction via nuclear reactions, and show that it can be perfectly modeled using the same equations. Production of medical isotopes and radioisotope thermoelectric generators (RTGs) are modeled using these equations. 

Instructor: Michael Short

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