# Carbon dating exercises

*13-Sep-2017 09:32*

We could be sure that a mineral containing parentium originally had no daughterium.If the mineral contained 1 part per million Parentium-123 and 3 parts per million Daughterium-123, we could be sure all the Daughterium-123 was originally Parentium-123.A minimum age is the youngest the object can possibly be.A maximum age is the oldest the object can possibly be. But they obviously have to have been made first, so 1920 is the maximum age of the burial.Suppose, in repaving your driveway, you find a stash of old coins buried in the ground. Of course there are more outlandish explanations, like somebody counterfeiting 1920 coins in 1900 (and successfully anticipating any changes in design in the meantime), or secretly tearing up part of the driveway after 1950, but unless someone comes up with really persuasive evidence, we're justified in ignoring these hypotheses.The driveway was poured in 1950, and the coins are all dated 1920. Radiometric dating generally requires that a system be closed - in other words, has not had material added or removed.Potassium-argon dating is very susceptible to resetting because the argon decay products are merely held in place mechanically by surrounding atoms.

The most common dating methods for rocks are based on radioactive isotopes of potassium, rubidium, uranium, and thorium.Sedimentary rocks are generally hard to date because common cements like silica don't have datable radioisotopes, and minerals like glauconite that are common in sedimentary rocks are very prone to resetting.If only there were long-lived isotopes of silicon, calcium, and magnesium!When t = 0, ln N(0) = C Taking exponentials of both sides, we get N(t) = N(0)exp(-Kt) If t = one half life, then N(t)/N(0) = 1/2 = exp(-Kt), and: ln(1/2) = -ln2 = -Kt, so t = ln2 / K So what we do in practice is determine the decay constant and calculate half life from it.

If the decay constant is very small, even tiny amounts of contamination by other radioactive materials can be very significant.

So accurate determinations require very pure samples, very accurate and selective detectors, or both.