The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms () of the parent remaining at any time gives rise to the following expression: Converting this proportion to an equation incorporates the additional observation that different radioisotopes have different disintegration rates even when the same number of atoms are observed undergoing decay.
In other words, each radioisotope has its own decay constant, abbreviated λ, which provides a measure of its intrinsic rapidity of decay.
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.
Fortunately for geochronology the study of radioactivity has been the subject of extensive theoretical and laboratory investigation by physicists for almost a century.
The results show that there is no known process that can alter the rate of radioactive decay.
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.
This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom. In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known. The measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age.
In short, the process of radioactive decay is immutable under all known conditions.
Although it is impossible to predict when a particular atom will change, given a sufficient number of atoms, the rate of their decay is found to be constant.
Proportion 1 becomes: Stated in words, this equation says that the rate at which a certain radioisotope disintegrates depends not only on how many atoms of that isotope are present but also on an intrinsic property of that isotope represented by λ, the so-called decay constant.
Values of λ vary widely—from 10 is the time elapsed since time zero.
Radioactive decay can be observed in the laboratory by either of two means: (1) a radiation counter (parent atoms.