If so, a more efficient version of this page that doesn't present equations as images, and should work with your browser, is available here. In his article Light Attenuation and Exponential Laws in the last issue of Plus, Ian Garbett discussed the phenomenon of light attenuation, one of the many physical phenomena in which the exponential function crops up. In this second article he describes the phenomenon of radioactive decay, which also obeys an exponential law, and explains how this information allows us to carbon-date artefacts such as the Dead Sea Scrolls. In the previous article, we saw that light attenuation obeys an exponential law. Exactly the same treatment can be applied to radioactive decay.
Radioactive atoms decay randomly.
If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval. The steps are the same as in the case of photon survival. This question can be answered using a little bit of calculus. Note that that the domain of F is the interval from zero to 1, which corresponds to the interval of time from zero to infinity. Incidentally, our formula for t gives us an easy way of finding the half-life , the time it takes for half the nuclei in a sample to decay.