The radioactive decay of a sample of atoms is characterized by the half-life of those atoms. The half-life is the time it takes for half of the atoms of a sample of radionuclides to decay. Thus, if the half-life of 1000 atoms was 1 day, then after 1 day we would expect 500 atoms would remain undecayed. After 2 days, we would expect 250 atoms would remain undecayed. After 3 days, we would expect 125 atoms would remain undecayed. And so on.

If we had a sample that contained N_{0} atoms at time t=0, then it can be shown that the number of
atoms of a sample at some time
t is given by

where t_{1/2} is the half-life of the atoms in the sample. The number e is a mathematical constant,
approximately equal to 2.71828. We can also define a
characteristic for the atoms in the sample
called the decay constant (λ)
which is given by

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