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.The formula for the fraction remaining is one-half raised to the power given by the number of years divided by the half-life (in other words raised to a power equal to the number of half-lives)."In a billion years [from now], it seems, intelligent life might be as different from humans as humans are from insects . To change from a human being to a cloud may seem a big order, but it's the kind of change you'd expect over billions of years." Freeman Dyson, Statement made in 1986, quoted in Asimov's Book of Science and Nature Quotations, p. [American mathematician.]"Slowness has really nothing to do with the question.An event is not any more intrinsically intelligible or unintelligible because of the pace at which it moves.

And when I look at the Wikipedia article, the discussion is so technical and defensive that I can't actually picture what is going on. You are right: there is no decay of 40-Ar into 39-Ar. The difference between measured 40-Ar and 40-Ar at formation is used in the procedure.

If we knew the fraction of a radioactive element still remaining in a mineral, it would be a simple matter to calculate its age by the formula To determine the fraction still remaining, we must know both the amount now present and also the amount present when the mineral was formed.

Contrary to creationist claims, it is possible to make that determination, as the following will explain: By way of background, all atoms of a given element have the same number of protons in the nucleus; however, the number of neutrons in the nucleus can vary.

The Washington Post article Scientists discover hundreds of footprints left at the dawn of modern humanity describes the geological dating of stratified layers of mud by analyzing and dating minerals within each layer.

But since floods jumble materials of different origins and ages together, that meant the scientists had to date dozens of different minerals.