Radioactive decay age dating
Perhaps a puddle of a certain size will evaporate down to half its original volume in one day.
But on the second day, there is no reason to expect that one-quarter of the puddle will remain; in fact, it will probably be much less than that.
As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5,730 years.
A quantity of carbon-14 will decay to half of its original amount (on average) after 5,730 years, regardless of how big or small the original quantity was.
(In other non-exponential decays, it can increase instead.) The decay of a mixture of two or more materials which each decay exponentially, but with different half-lives, is not exponential.In other words, the probability of a radioactive atom decaying within its half-life is 50%.For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay.Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation.
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In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed.