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There is a definite mathematical relationship between the ratio of the amount of daughter product isotope to the amount of radioactive parent isotope, and the number of half-lives that have elapsed.The relationship is non-linear, involving a logarithmic function.Note that unconformities, which on the diagram above are symbolized by the irregular lines, are indicated by dashed lines in the column below.Also, the formations that appear on the simplified stratrigraphy diagram above are marked in the table with the number that corresponds to the diagram.The same isotope system is used for each pair of samples, but the daughter to parent ratio is different in each sample.How would you use these data to calculate the geologic age indicated by the isotopes in each sample?The table below tracks the decay, half-life by half-life, of a radioactive isotope, and the accumulation of the daughter product isotope that the parent changes into once it decays. There are several different radioactive isotope systems that are used for measuring ages of geologic materials.For more information on these systems, see the isotopes and half-lives section of the Geologic Time Basics page.
(In reality, rocks, minerals and other geologic materials can be checked to see if the isotope system remained closed, rather than assuming so.) At time zero, 100% of the isotopes are the parent isotopes.The Paleozoic strata do not include the Temple Butte Limestone and Surprise Canyon Formation, which are not widespread in the Grand Canyon.Some formations of rock younger than Paleozoic, also not widespread in Grand Canyon, are not included here. There is a major nonconformity, a major angular unconformity and a major disconformity. Below is a stratigraphic sequence for the the Grand Canyon in the form of a table.By the definition of a half-life, the amount of parent isotope at each half-life is half of what it was before the half-life elapsed.
As the amount of parent isotope decreases by radioactive decay, the amount of the daughter isotope increases commensurately.For example, if the age is based on measurements of the amount of uranium-238 ( yr.