The 87Rb isotope has a long half-life (4.88 X 1010 years). This isotope emits negative beta radiation (as discussed in Section 4.4.2), producing an 87Sr isotope. Similarly to the ratio of 40K/40Ar, the age of geological formations can be determined by the ratio of 87Rb/87Sr. The problem with this approach, however, is that the source of an 87Sr isotope is not the decay of 87Rb alone; it was present at the time of the rock for­mation (t = 0). Thus, the quantity of Sr ( — N) can be expressed as:

Sr-87N = Sr-87Nt=0 + Rb-87N (eARb-87t — 1) (4.72)

where Sr-87Nt=0 is the quantity of Sr-87 at the time of the formation of the rock (at t = 0), Rb-87N is the quantity of Rb-87, ARb-87 is the decay constant of Rb-87,

and t is the age of the rock. Since the initial quantity of the Sr-87 is not known, for dating purposes, it also has to be determined. This problem is solved by incorporat­ing the quantity of Sr-86 into Eq. (4.72). Sr-86 is a stable isotope, the quantity of which does not change over time. By dividing Eq. (4.72) by the constant quantity of Sr-86 (Sr-86N), we obtain:

When the quantities of Sr-86, Sr-87, and Rb-87 are determined in different rocks or minerals with the same genetics, and the ratio of Sr-87N/Sr-86N is plotted as a function of Rb-87N/Sr-86N, a straight line is obtained. The slope of this straight line is (eARb-87t — 1), and the intercept is Sr_87Nt=0/Sr"86N, which shows the initial ratio of the strontium isotopes. The age can be determined from the slope of the straight line. The line is called an “isochron,” which means “similar age.” The method has been used to determine the age of igneous, metamorphic, and sedimentary rocks, and it is used frequently to date meteorites.