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Knowing the level of activity of a sample of organic material enables us to deduce how much C-14 there is in the material at present.
Since we also know the ratio of C-14 to C-12 originally, we can find the time that has passed since carbon exchange ceased, that is, since the organic material "died".
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.
Exactly the same treatment can be applied to radioactive decay.
However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). 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.
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.
On average, how much time will pass before a radioactive atom decays?
He graduated in 1977 with a BSc Honours in Applied Physics from the University of Lancaster, and obtained an MSc in Medical Physics from the University of Leeds in 1987.
He is interested in various theoretical aspects of radiation and radiological physics, with an interest in mathematical modelling in general.
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.