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We end up with a solution known as the "Law of Radioactive Decay", which mathematically is merely the same solution that we saw in the case of light attenuation.We get an expression for the number of atoms remaining, N, as a proportion of the number of atoms N, where the quantity l, known as the "radioactive decay constant", depends on the particular radioactive substance.In the previous article, we saw that light attenuation obeys an exponential law.To show this, we needed to make one critical assumption: that for a thin enough slice of matter, the proportion of light getting through the slice was proportional to the thickness of the slice.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.
Let's take a look at an example of how dates are calculated using Libby's method.
Again, we find a "chance" process being described by an exponential decay law.
We can easily find an expression for the chance that a radioactive atom will "survive" (be an original element atom) to at least a time t.
Similarly, in a population which grows exponentially with time there is the concept of "doubling time".
We started the first article by talking about carbon dating and the Dead Sea scrolls.