# Historical Geology/K-Ar dating

In this article we shall examine the basis of the K-Ar dating method, how it works, and what can go wrong with it.

## Decay of $^{40}$K

$^{40}$K (potassium-40) is rather a peculiar isotope, in that it can undergo decay in three different ways: by beta minus decay into $^{40}$Ca (calcium-40); by electron capture into $^{40}$Ar (argon-40); and by beta plus decay into $^{40}$Ar again. It is possible to measure the proportion in which $^{40}$K decays, and to say that about 89.1% of the time it decays to $^{40}$Ca and about 10.9% of the time to $^{40}$Ar. $^{40}$K has a half-life of 1.248 billion years, which makes it eminently suitable for dating rocks.

## K-Ar dating

Potassium is chemically incorporated into common minerals, notably hornblende, biotite and potassium feldspar, which are component minerals of igneous rocks.
Argon, on the other hand, is an inert gas; it cannot combine chemically with anything. As a result under most circumstances we don't expect to find much argon in igneous rocks just after they've formed. (However, see the section below on the limitations of the method.)
This suggests an obvious method of dating igneous rocks. If we are right in thinking that there was no argon in the rock originally, then all the argon in it now must have been produced by the decay of $^{40}$K. So all we'd have to do is measure the amount of $^{40}$K and $^{40}$Ar in the rock, and since we know the decay rate of $^{40}$K, we can calculate how long ago the rock was formed. From the equation describing radioactive decay, we can derive the following equation:
    t = h × log$_2$(1 + R/c)
where
* t is the age of the rock in years;
* h is the half-life of $^{40}$K in years;
* c is the proportion of $^{40}$K which decays to $^{40}$Ar rather than to $^{40}$Ca (about 10.9%);
* R is the measured ratio of $^{40}$Ar to $^{40}$K.

## Limitations of K-Ar dating

There are a number of problems with the method. One is that if the rocks are recent, the amount of $^{40}$Ar in them will be so small that it is below the ability of our instruments to measure, and a rock formed yesterday will look no different from a rock formed fifty thousand years ago. The severity of this problem decreases as the accuracy of our instruments increases. Still, as a general rule, the proportional error in K-Ar dating will be greatest in the youngest rocks.
A second problem is that for technical reasons, the measurement of argon and the measurement of potassium have to be made on two different samples, because each measurement requires the destruction of the sample. If the mineral composition of the two sample is different, so that the sample for measuring the potassium is richer or poorer in potassium than the sample used for measuring the argon, then this will be a source of error.
Another concern with K-Ar dating is that it relies on there being no $^{40}$Ar in the rock when it was originally formed, or added to it between its formation and our application of the K-Ar method. Because argon is inert, it cannot be chemically incorporated in the minerals when they are formed, but it can be physically trapped in the rocks either during or after formation. Such argon is known as excess argon.
If the source of this argon is atmospheric contamination, then we can correct for this. The reasoning is as follows: the atmosphere does not only contain $^{40}$Ar, but also $^{36}$Ar. There is 298 times as much $^{40}$Ar as $^{36}$Ar in the atmosphere, and there is no reason why an atom of $^{40}$Ar should be preferentially incorporated into rocks rather than an atom of $^{36}$Ar, or vice versa. So this means that for every atom of $^{36}$Ar we find in our sample, we can discount 298 atoms of $^{40}$Ar as being atmospheric argon.
However, this only works if all the excess argon did indeed come from the atmosphere. But consider what happens if the argon came from deep within the Earth, where it was formed by $^{40}$K decay, and was then trapped in magma or transported into the rock by hydrothermal fluid. Then the excess argon will not have the same $^{40}$Ar/$^{36}$Ar ratio as is found in the atmosphere, and the formula that corrects for atmospheric carbon will not correct for this.
Finally, we must consider the possibility of argon loss. When a rock undergoes metamorphism, some or all of its argon can be outgassed. If all the argon was lost, this would reset the K-Ar clock to zero, and dating the rock would give us the time of metamorphism; and if we recognized the rock as metamorphic this would actually be quite useful. However, we cannot rely on all the argon being lost, and if it is not then when we apply K-Ar dating this will give us an essentially arbitrary date somewhere between the formation of the rock and the metamorphosis event.
For these reasons K-Ar dating has largely been superseded by Ar-Ar dating, which will be the subject of the next article.
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