# The math behind radioactive carbon dating

The two curves cross each other at half life = 1.00.

At this point the fraction of Rb87 = Sr87 = 0.500; at half life = 2.00, Rb87 = 25% and Sr87 = 75%, and so on. 131, Strahler, Science and Earth History: Points are taken from these curves and a plot of fraction Sr-87/Sr-86 (as ordinate) vs. It turns out to be a straight line with a slope of -1.00.

Rubidium-Strontium dating: The nuclide rubidium-87 decays, with a half life of 48.8 billion years, to strontium-87.

Strontium-87 is a stable element; it does not undergo further radioactive decay.

Radioactive elements "decay" (that is, change into other elements) by "half lives." If a half life is equal to one year, then one half of the radioactive element will have decayed in the first year after the mineral was formed; one half of the remainder will decay in the next year (leaving one-fourth remaining), and so forth.

Carbon-14 dating: See Carbon 14 Dating in this web site.The corresponding half lives for each plotted point are marked on the line and identified.It can be readily seen from the plots that when this procedure is followed with different amounts of Rb87 in different minerals, if the plotted half life points are connected, a straight line going through the origin is produced. The steeper the slope of the isochron, the more half lives it represents.The amount of strontium-86 in a given mineral sample will not change.Therefore the relative amounts of rubidium-87 and strontium-87 can be determined by expressing their ratios to strontium-86: Rb-87/Sr-86 and Sr87/Sr-86 We measure the amounts of rubidium-87 and strontium-87 as ratios to an unchanging content of strontium-86.