Mathematical Modelling of Alpha Radioactive Decay by Ordinary Differential Equations

Alpha radioactive decay is one of the most classical processes in nuclear physics and can be naturallydescribed by an ordinary differential equation. In this work, a mathematical model for alpha decay isderived from a balance law for the number of unstable nuclei. The exponential decay law is obtainedanalytically, and related quantities such as activity, half-life, cumulative decay, and asymptotic behaviourare deduced. The model is also interpreted from a discrete point of view, showing the passage from finitedifferences to the continuous decay law through a limit process. The resulting formulation illustrates howdifferential equations can explain the temporal evolution of unstable nuclei in a simple and rigorous way.