Doesn t carbon dating work rocks
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.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.If you don't have minerals with those elements, you can't date the rock.In particular, quartzites and carbonate rocks almost always don't have enough to permit dating.Crystallization of a mineral is a good way to close a system. Any disturbance of the system effectively resets the clock to zero by allowing decay products to escape or reshuffling the abundances of elements.
It is one of the simplest examples of a differential equation.
Rubidium-strontium dating is more robust, and uranium-lead dating can survive fairly significant metamorphism without resetting.
If a system gains or loses isotopes in a predictable way, it may be possible to estimate the loss and correct the age.
In other words there was originally 4 parts per million Parentium-123 and 0 parts per million Daughterium-123.
Since there is now only 1/4 of the original amount of Parentium-123, we know that two half-lives of Parentium-123 have elapsed.Furthermore, Parentium and Daughterium are so different in chemical properties that they don't otherwise occur together.