Long-Lived Chronometers

Basic Principles Long-lived radioactive isotopes, defined here as those that have half-lives in excess of a few hundred million years, have been utilized for chronology since the early part of the twentieth century. The decay of a radioactive (‘‘parent’’) isotope involves its spontaneous transformation, sometimes through other intermediate radioisotopes, into a stable (‘‘daughter’’) isotope at a rate proportional to the number of atoms of the radioisotope at any given time, such that (Formula Presented) where P is the number of atoms of the parent isotope remaining at present, P₀ the initial abundance of the parent isotope at the time of isotopic closure, t the time elapsed since isotopic closure (e.g., crystallization age for a rock) and l the decay constant. Equation (1) may be rewritten in terms of the abundance of the radiogenic daughter isotope (D*) as follows: (Formula Presented) However, since the total number of atoms of the daughter isotope (D) is the sum of the radiogenic (D*) and the nonradiogenic (D₀) components, (Formula Presented) Normalizing to a stable isotope of the daughter element (Formula Presented) As such, the slope in an isochron plot for a long-lived chronometer (i.e., where D/D_s is plotted versus P/D_s) is given by (e^lt-1), from which the age (t) may be determined. The past several decades have seen significant improvements in the precision and accuracy of chronological information based on the decay of long-lived radioisotopes. These have resulted particularly from advances in the mass spectrometric techniques for measurement of isotope ratios and better constriants....