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You may have heard that the Earth is 4.54 billion years old. If the half-life of a material is 100 years and you have 1 kg of it, 100 years from now you will only have 0.5 kg of it.
This was calculated by taking precise measurements of things in the dirt and in meteorites and using the principles of radioactive decay to determine an age. The rest will have decayed into a different nuclide (called a nuclide).
Several radioactive nuclides exist in nature with half-lives long enough to be useful for geologic dating.
Let’s go through an example of calculating the age of a rock with the radioactive nuclide Rubidium-87 (Rb87).
Meteorites, on the other hand, have been floating around in space since the solar system was formed.
When they come crashing to Earth, analysis of their composition can be geologically analyzed.
The slope of the line can then be solved for \(t\), giving us the age of the rock.
He then took measurements from the deep ocean that fell squarely on the meteorite isochron, suggesting that the Earth and the meteorites were both created at the same time, 4.55 billion years ago.
(You may have learned from COSMOS that he also was among the first to understand the public health risks of lead contamination from leaded gasoline).
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.