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Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.
The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not.
It comes from cosmic rays that rain down on the earth (and us) from outer space.
You probably have seen or read news stories about fascinating ancient artifacts.
The carbon-14 undergoes radioactive decay once the plant or animal dies, and measuring the amount of carbon-14 in a sample conveys information about when the plant or animal died.
Imagine we have an undiscovered element, Parentium, that has a radioactive isotope, Parentium-123, which decays to stable Daughterium-123.
(Whatever you're being treated for is the greater danger.) The half-life is just long enough for the doctors to have time to take their pictures.
I do not have the decay constant but, by using the half-life information, I can find it.Since there is now only 1/4 of the original amount of Parentium-123, we know that two half-lives of Parentium-123 have elapsed.