ABSTRACT
This chapter considers a mathematical description of the nuclear decay of unstable isotopes including electron capture, beta-minus, beta-plus decay, and other decay modes. It is worth noting that the exponential form of the decay curve is due to the independent and random process of nuclear decay. That is, any one decay event is completely unrelated to the decay events that happened before it or the ones that will occur after it. It is difficult to measure or quantify the number of nuclei, N, in a sample. An easier quantity to work with is the activity of the sample, i.e. the number of decays per second, since this can be measured through the decay products that emerge. The decay constant (and half-life) are determined by the stability of the nucleus; less stable nuclei will have more decays per second or a larger decay constant. The final quantity to consider is mean-life, sometimes referred to as average life.
