18.2 The Age Equation

Sm/Nd isochron plotted of samples from the Great Dyke, Zimbabwe. The age is calculated from the slope of the isochron (line) and the original composition from the intercept of the isochron with the y-axis.

The mathematical expression that relates radioactive decay to geologic time, is

D = D₀ + N(e^λt − 1)

where

t is age of the sample,

D is number of atoms of the daughter isotope in the sample,

D₀ is number of atoms of the daughter isotope in the original composition,

N is number of atoms of the parent isotope in the sample, and

λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2.