Methods of dating meteorites
The end result is that the slope of the isochron with Pb207 concentrations graphed against Pb206 (both relative to non-radiogenic Pb204) is equal to: $$ m = \frac \frac$$ Data from several meteorites and from a few terrestrial sources are shown in Figure 3.
The data have been replotted from the tables of .
Claire Patterson was the first to accurately date the crystallization of Earth to 4.55 /- 0.05 billion years ago.
He used a lead isotope isochron method using measurements from three different meteorites (lead-206, lead-207 are the eventual decay products of uranium-238 and uranium-235).
Conveniently, this is very trivial with a few lines of Python.
Using this python program that I wrote, I am able to instantly calculate the age of the Earth to be 4.51 billion years using lead isotopic measurements alone. This is within the uncertainty claimed by Patterson.
It naturally has different concentrations of Rb and Sr in different parts of the rock because these don’t necessarily mix perfectly. Once it cools all the way and crystallizes, it is considered "born" and atoms can no longer come in or out of the system.
Imagine going way back in time and looking at some lava that is cooling to become a rock.
See the decay chain link in the See Also section below for decay chain details. It involves the radioactive nuclide Carbon-14 (aka radiocarbon) decaying to Nitrogen-14 with a 5730 year half-life.
As you can imagine, this half-life is short with respect to the age of the Earth, so it can’t be used to date rocks.
By measuring a few samples of the rock and comparing the relative amounts of Sr87 and Rb87, we can figure out how old the rock is! If you think about it, the equation above is a lot like the formula for a line, \(y=mx b\) with \(y=\text_\), \(m= \left(e^-1 \right)\), \(x=\text_\), and \(b=\text_\).
The mathematics of radioactive decay shows us that the number of Sr87 nuclides that exist after some time t is: $$\text_= \left(e^-1 \right)\text_ \text_ $$ We can measure \(\text_\), \(\text_\), and \(\lambda\), but we can’t measure \(\text_\) (no one was around to measure it back then). Because the rock originally had different mixtures of Rb and Sr, we can expect to get different points for each sample we measure, and if all samples have the same age, then we expect to see a straight line (hence the name isochron).