Radioactive nuclei decay at random. Nuclear physics tells us the probability that these nuclei will decay per unit time. For instance, half of the 13C in a sample will decay in about 5,500 years. Following ideas from probability theory, this allow to write the equation that governs radioactive nuclei
where N(t) is the number of radioactive nuclei in the sample, k is a constant (probability per unit time), and t the time. The minus sign (-) is reflecting the fact that radioactive nuclei decay in other nuclei species, so that N(t) is bound to diminish. The model is specified by the equation RHS, and the value of k.
This equation is simple to "guess". It is based on simple probability ideas, much alike those that control the tossing of a dice.
The radioactive decay equation can easily be solved exactly since it is one of the simplest differential equation. The solution is
where N0 is the initial number of radioactive nuclei in the sample.
Section 8.1 
Chapter 8 
Section 8.3
TOC
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