isochron

isochron A line joining points of equal time intervals or ages. In geochronology the slope of the isochron may be used to determine the age of a suite of rocks. For example, if it is assumed that all the rocks formed from one magma had the same initial ⁸⁷Sr:⁸⁶Sr ratio (see initial strontium ratio), then there is a simple equation to describe the growth of radiogenic ⁸⁷Sr:⁸⁷Sr = ⁸⁷Sro + ⁸⁷Rb(e^λt− 1) where ⁸⁷Sr_o is the number of atoms of the ⁸⁷Sr isotopes incorporated into the rock at the time of formation, ⁸⁷Sr and ⁸⁷Rb are the numbers of these isotopes after time t, and λ is the decay constant. Because the number of ⁸⁶Sr is constant, we can derive an equation: ⁸⁷Sr:⁸⁶Sr = ⁸⁷Sr_o:⁸⁶Sr + (⁸⁷Rb:⁸⁶Sr)(e^λt− 1) which would give a family of straight lines when plotted on a graph of ⁸⁷Sr:⁸⁶Sr (on the y axis) against ⁸⁷Rb:⁸⁶Sr (on the x axis). All rock specimens belonging to a co-magmatic suite will plot as points on a straight line called an ‘isochron’ because all points on the line represent systems having the same age (t) and the same initial ⁸⁷Sr: ⁸⁶Sr ratio. In order to date co-magmatic igneous rocks by the whole-rock isochron method, a suite of rocks must be collected which span as wide a range of Rb/Sr ratios as possible, so that the slope of the isochron will be well defined. The age of the suite of rocks is obtained from the slope (m) using the equation m = e^λt− 1. Isochrons can also be determined in lead—lead dating by plotting a series of growth curves. See also ISOCHRON MAP.