But while the difficulties of single life may be intractable, the challenge of determining the age of prehistoric artifacts and fossils is greatly aided by measuring certain radioactive isotopes.

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- Radiocarbon dating - Wikipedia.

Until this century, relative dating was the only technique for identifying the age of a truly ancient object. By examining the object's relation to layers of deposits in the area, and by comparing the object to others found at the site, archaeologists can estimate when the object arrived at the site.

Though still heavily used, relative dating is now augmented by several modern dating techniques.

## Measuring the Age of the Earth

Radiocarbon dating involves determining the age of an ancient fossil or specimen by measuring its carbon content. Carbon, or radiocarbon, is a naturally occurring radioactive isotope that forms when cosmic rays in the upper atmosphere strike nitrogen molecules, which then oxidize to become carbon dioxide.

Parts of the rock that have more Rb87 will end up with more Sr 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! The mathematics of radioactive decay shows us that the number of Sr87 nuclides that exist after some time t is: So what do we do?

## The Age of the Earth

We use something called an isochron. 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. We plot all our measurements and then fit a line through them. The animation in Figure 2 shows the flat line and how it increases with time. Note that the values of the axes are actually normalized by Sr86 because the mass spectrometers used to take these measurements are much more accurate at relative values than they are at absolutes.

It works because Sr86 is stable and not radiogenic and therefore stays constant with time. The isochron method can determine the age of any rock, but new rocks are formed all the time. So to figure out the age of the Earth, we have to look somewhere else Earth has a molten magma layer and plate tectonics, so the "closed system" requirement of these radiometric dating methods is sometimes difficult to satisfy for Earth itself.

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. Claire Patterson was the first to accurately date the crystallization of Earth to 4. He used a lead isotope isochron method using measurements from three different meteorites lead, lead are the eventual decay products of uranium and uranium 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.

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.

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Many other methods have been used to date the Earth, with many different sets of radioactive nuclides and other methods. This is how we know how old the Earth is. The mathematical details of the lead-lead isotopic clock are less straightforward than those of the Rb-Sr method. On the other hand, since only lead is involved instead of two chemical species , the lead-lead clock is resilient against situations where the samples were recently weathered or otherwise "opened". We will skip the isochron derivation, but you can find it elsewhere[1].

The end result is that the slope of the isochron with Pb concentrations graphed against Pb both relative to non-radiogenic Pb is equal to: Data from several meteorites and from a few terrestrial sources are shown in Figure 3.

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- How Carbon-14 Dating Works?
- Carbon Dating.

The data have been replotted from the tables of [2]. The Pb-Pb isochron of several meteorites and deep Earth samples. Since this determines the age of the Earth, it is also known as the Geochron. The best-fit line shown in Figure 3 has a slope of 0.

## Radiocarbon dating

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. This is within the uncertainty claimed by Patterson. Note that Uranium decays to Lead and that Uranium decays to Lead See the decay chain link in the See Also section below for decay chain details.

Carbon dating is often discussed.

It involves the radioactive nuclide Carbon aka radiocarbon decaying to Nitrogen with a year half-life. But, it is unmatched in its ability to date things that used to be living bones, wood, food, paper, etc.

When a living thing dies, its body stops uptaking carbon.