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In fact, one would expect that the ratio of oranges to apples would change in a very specific way over the time elapsed, since the process continues until all the apples are converted. A particular rock or mineral that contains a radioactive isotope (or radio-isotope) is analyzed to determine the number of parent and daughter isotopes present, whereby the time since that mineral or rock formed is calculated.Of course, one must select geologic materials that contain elements with long half-lives— those for which some parent atoms would remain.Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple: 1. Different schemes have been developed to deal with the critical assumptions stated above.

Such checks include dating a series of ancient units with closely spaced but known relative ages and replicate analysis of different parts of the same rock body with samples collected at widely spaced localities.Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating.In the first place, since the unknown term in radiometric dating is obviously ) rather than through the decay constant λ.In this analogy, the apples would represent radioactive, or parent, atoms, while the oranges would represent the atoms formed, the so-called daughters.Pursuing this analogy further, one would expect that a new basket of apples would have no oranges but that an older one would have many.For a single element, these atoms are called isotopes.Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer (see below Use of mass spectrometers).Given below is the simple mathematical relationship that allows the time elapsed to be calculated from the measured parent/daughter ratio.The age calculated is only as good as the existing knowledge of the decay rate and is valid only if this rate is constant over the time that elapsed.The situation is analogous to the death rate among human populations insured by an insurance company.Even though it is impossible to predict when a given policyholder will die, the company can count on paying off a certain number of beneficiaries every month.

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