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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.
Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average".
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.
On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is.
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.
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.