# Historical Geology/Radiocarbon dating

In this article we shall discuss how radiocarbon dating works, the conditions under which it can be applied, and the limitations of the method.

## The isotopes

There are three important isotopes underlying the process of radiocarbon dating.
$^{14}$N (nitrogen-14) is converted to $^{14}$C (carbon-14) in the upper atmosphere as a result of bombardment by neutrons in so-called cosmic rays: high-energy particles bombarding the Earth's atmosphere from outer space. Such an isotope is said to be cosmogenic. On formation, the newly-born carbon atom quickly oxidizes to form a molecule of carbon dioxide (CO$_2$).
$^{14}$C is an unstable isotope of carbon, and so decays back to $^{14}$N via beta decay with a half-life of about 5730 years. Because the quantity of $^{14}$C being produced annually is more or less constant, whereas the quantity being destroyed is proportional to the quantity that exists, it can be shown that the quantity in the atmosphere at any given time will be more or less constant: the processes of production and decay of $^{14}$C produces an equilibrium.
Also of importance is the stable carbon isotope $^{12}$C; this makes up 98.89% of atmospheric carbon, as opposed to only 0.0000000001% $^{14}$C. The balance is made up by the stable isotope $^{13}$C, which need not concern us in this article.

## The terrestrial carbon cycle

The terrestrial carbon cycle is fairly simple: plants get their carbon from the atmosphere via the process of photosynthesis; herbivores get their carbon from plants, and carnivores from the herbivores. After the death of the organism, processes of decay will return its carbon to the atmosphere, unless it is sequestered — for example in the form of coal.
This means that when an organism is alive, its ratio of $^{14}$C/$^{12}$C will be the same as the ratio in the atmosphere. But of course when the organism dies it is cut off from the source of atmospheric carbon, the $^{14}$C will start to decay to $^{14}$N, and the ratio will begin to change.

## The method

This immediately suggests a method of dating organic remains. If we measure the amount of $^{12}$C and the amount of $^{14}$C in an organic sample, then since we know the atmospheric ratio and the amount of $^{12}$C present, we can deduce how much $^{14}$C was present originally. And then since we know how much was present originally, since we can measure how much is present now, and since we know the decay rate of $^{14}$C, it is trivial to compute the age of the sample.
This method is variously known as radiocarbon dating, carbon dating, $^{14}$C dating, or C-C dating.
One of the nice things about this method is that we don't have to worry about carbon being lost from the sample. Because we are measuring the abundance of two isotopes of carbon, and because isotopes of the same element will be chemically identical, no ordinary process can preferentially remove $^{12}$C or $^{14}$C, and so any process of carbon removal will leave the $^{12}$C/$^{14}$C ratio the same, and the method will still work.

## Limitations of the method

The method has various limitations. First of all, the quantity of $^{14}$C is going to be small enough to begin with, being only 0.0000000001% of atmospheric carbon, and then as the decay process progresses it's going to get smaller and smaller. After about 60,000 years the quantity will be too small for our instruments to measure accurately, and the best we'll be able to say is that the sample is about 60,000 years old or more. For this reason radiocarbon dating is of more interest to archaeologists than to geologists.
Two effects also interfere with the dating of very recent samples. The testing of thermonuclear weapons produced an increase in atmospheric $^{14}$C, peaking in the mid-1960s; and the burning of fossil fuels has been causing an increase in atmospheric $^{12}$C; this has not been accompanied by a corresponding increase in $^{14}$C because as the carbon in coal and oil is old, the amount of $^{14}$C they contain is infinitesimal. Fortunately it is rarely necessary to use radiocarbon methods to date very recent samples.
Thirdly, it is in the nature of the method that it can only be applied to organic remains: it makes no sense to apply it to rocks or to mineralized fossils.
Fourthly, the carbon in the organic remains does have to originate with the terrestrial carbon cycle and with plants performing photosynthesis. If this is not the case, it is sometimes possible to correct for the fact; in other cases it makes dating impossible.
For example, marine carbon behaves quite differently from carbon in the terrestrial cycle. The residence time of carbon in the ocean can be measured in hundreds of thousands of years (where the residence time of carbon is defined as the average time an atom of carbon will stay in the ocean). This increases the apparent age of the sample by about 400 years, depending on where in the ocean the organism lived and died. Given a latitude and longitude, an appropriate correction to the date is supplied by the Marine Reservoir Database.
Since humans eat seafood, this can also affect the carbon dating of humans, and what is worse it does so in an inconsistent manner, since human consumption of seafood varies with location and culture. However, the marine component of diet can be estimated by measuring the ratio of the stable isotopes $^{15}$N/$^{13}$C in the sample: this will be higher the more seafood the individual consumed. This allows archaeologists to estimate the magnitude of this effect and correct for it.
Another source of carbon we have to take into account is the weathering of limestone. The result of this is to supply streams, rivers, and lakes with a source of dissolved calcium carbonate; if freshwater shellfish (for example) use this to construct their shells, then they are using a source of carbon which is millions of years old. Clearly applying radiometric dating in such a case is pointless. Another source of old carbon is the outgassing from volcanoes: in locations where this is a significant source of CO$_2$, plants growing in the area will appear older than they actually are.
Even participation in the terrestrial carbon cycle does not quite guarantee the date: we could, for example, imagine termites eating their way through the wood of a 200 year old house; these termites would date to 200 years old or more (depending on the age of the tree). By and large, however, organisms tend to consume fresh vegetation or fresh meat, so this problem is unlikely to arise in practice.

## Comparison with known dates

One way we can check the efficacy of radiocarbon dating is to compare the dates it produces with dates known on historical grounds, to ensure that it does indeed give us the right answer.
We can also compare radiocarbon dates with dates known on other grounds. For example, we have discussed the use of varves for dating; now since varves incorporate organic material as they are formed, we can check that when we radiocarbon date a varve, we get the same date for it as we obtain by counting the varves.
Also it is obviously possible to carbon-date one of the growth rings of a tree, and to compare the date produced by radiocarbon dating with the date produced by dendrochronology. Such dates typically agree to within 1 or 2 per cent.

## Calibrated dating

Although the radiocarbon dates agree closely with dendrochronology, they do not agree exactly. It is generally agreed that the dendrochronological dates should be considered the more accurate. The proportion of $^{14}$C in the atmosphere is not absolutely constant; for example, it can be reduced by volcanic activity, since the carbon dioxide emitted by volcanoes is richer in $^{12}$C than atmospheric carbon dioxide. By comparison the behavior of the genera of trees used in dendrochronology is more reliable and consistent.
It is therefore standard procedure to tweak the raw radiocarbon dates to bring them in line with dendrochronology, producing what are known as calibrated radiocarbon dates. This allows us to combine the greater accuracy of dendrochronology with the wider applicability of radiocarbon dating.
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