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Consider a mixture of a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of 1 year.In a couple of minutes, almost all atoms of element A will have decayed after repeated halving of the initial number of atoms, but very few of the atoms of element B will have done so as only a tiny fraction of its half-life has elapsed.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.Mathematically, the sum of two exponential functions is not a single exponential function.A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different half-lives.For example, if there is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" left after one second.

In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay".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.However, unlike in an exponential decay, the half-life depends on the initial quantity, and the prospective half-life will change over time as the quantity decays.There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.The decay of many physical quantities is not exponential—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule.

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