# Radiometric dating half life definition

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.The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right).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".

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There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.

The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below).

Half-lives must therefore be known with great accuracy for precise dating and should range from about 10 years.

In addition, there should be no loss or gain of parent or daughter isotope during the time the ‘radioactive clock’ is operating; if this condition is only partly satisfied, allowances must be made.