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If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict when that particular atom might decay.It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.Radioactive elements "decay" (that is, change into other elements) by "half lives." If a half life is equal to one year, then one half of the radioactive element will have decayed in the first year after the mineral was formed; one half of the remainder will decay in the next year (leaving one-fourth remaining), and so forth.The formula for the fraction remaining is one-half raised to the power given by the number of years divided by the half-life (in other words raised to a power equal to the number of half-lives).It takes a certain amount of time for half the atoms in a sample to decay.It then takes the same amount of time for half the remaining radioactive atoms to decay, and the same amount of time for half of those remaining radioactive atoms to decay, and so on. The amount of time it takes for one-half of a sample to decay is called the half-life of the isotope, and it’s given the symbol: It’s important to realize that the half-life decay of radioactive isotopes is not linear.The rate of decay (given the symbol λ) is the fraction of the 'parent' atoms that decay in unit time.

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Understand how decay and half life work to enable radiometric dating.

An atom with the same number of protons in the nucleus but a different number of neutrons is called an isotope.