Deriving the Decay Equation
Channel: Dominik Hezel
Date: 2019-10-25

*check out all videos and much more on metbase.org in the 'Resources' section*
At each time step a certain fraction of the available parent nuclides – N(t), with N amount of available parent nuclides, and t time – decays, i.e., the amount decayed is: DN/Dt, with DN being the amount of parent nuclides that decayed, and Dt the time interval during which this decay happens. In the next time step, the amount of available parent nuclides is correspondingly smaller, as part of it already decayed, i.e., N(t) is smaller in the next step. The fraction of parent nuclides that decay in this next step is, however, the same. Therefore the proportionality is N(t) ~ DN/Dt. The exact fraction of decaying parent nuclides at each time step depends on the specific parent nuclide. This fraction (lambda) is multiplied with DN/Dt, which then becomes the equation N(t) = lambda DN/Dt, and lambda is called the decay constant. This equation is a differential equation that, if solved, results in N(t) = N0 e^(-lamda*t).