The potassium-argon (K-Ar) isotopic dating method is especially useful for determining the age of lavas. Developed in the 1950s, it was important in developing the theory of plate tectonics and in calibrating the geologic time scale.

## Potassium-Argon Basics

Potassium occurs in two stable isotopes (^{41}K and ^{39}K) and one radioactive isotope (^{40}K). Potassium-40 decays with a half-life of 1250 million years, meaning that half of the ^{40}K atoms are gone after that span of time. Its decay yields argon-40 and calcium-40 in a ratio of 11 to 89. The K-Ar method works by counting these radiogenic ^{40}Ar atoms trapped inside minerals.

What simplifies things is that potassium is a reactive metal and argon is an inert gas: Potassium is always tightly locked up in minerals whereas argon is not part of any minerals. Argon makes up 1 percent of the atmosphere. So assuming that no air gets into a mineral grain when it first forms, it has zero argon content. That is, a fresh mineral grain has its K-Ar "clock" set at zero.

The method relies on satisfying some important assumptions:

- The potassium and argon must both stay put in the mineral over geologic time. This is the hardest one to satisfy.
- We can measure everything accurately. Advanced instruments, rigorous procedures and the use of standard minerals ensure this.
- We know the precise natural mix of potassium and argon isotopes. Decades of basic research has given us this data.
- We can correct for any argon from the air that gets into the mineral. This requires an extra step.

Given careful work in the field and in the lab, these assumptions can be met.

## The K-Ar Method in Practice

The rock sample to be dated must be chosen very carefully. Any alteration or fracturing means that the potassium or the argon or both have been disturbed. The site also must be geologically meaningful, clearly related to fossil-bearing rocks or other features that need a good date to join the big story. Lava flows that lie above and below rock beds with ancient human fossils are a good—and true—example.

The mineral sanidine, the high-temperature form of potassium feldspar, is the most desirable. But micas, plagioclase, hornblende, clays, and other minerals can yield good data, as can whole-rock analyses. Young rocks have low levels of ^{40}Ar, so as much as several kilograms may be needed. Rock samples are recorded, marked, sealed and kept free of contamination and excessive heat on the way to the lab.

The rock samples are crushed, in clean equipment, to a size that preserves whole grains of the mineral to be dated, then sieved to help concentrate these grains of the target mineral. The selected size fraction is cleaned in ultrasound and acid baths, then gently oven-dried. The target mineral is separated using heavy liquids, then hand-picked under the microscope for the purest possible sample. This mineral sample is then baked gently overnight in a vacuum furnace. These steps help remove as much atmospheric ^{40}Ar from the sample as possible before making the measurement.

Next, the mineral sample is heated to melting in a vacuum furnace, driving out all the gas. A precise amount of argon-38 is added to the gas as a "spike" to help calibrate the measurement, and the gas sample is collected onto activated charcoal cooled by liquid nitrogen. Then the gas sample is cleaned of all unwanted gasses such as H_{2}O, CO_{2}, SO_{2}, nitrogen and so on until all that remains are the inert gasses, argon among them.

Finally, the argon atoms are counted in a mass spectrometer, a machine with its own complexities. Three argon isotopes are measured: ^{36}Ar, ^{38}Ar, and ^{40}Ar. If the data from this step is clean, the abundance of atmospheric argon can be determined and then subtracted to yield the radiogenic ^{40}Ar content. This "air correction" relies on the level of argon-36, which comes only from the air and is not created by any nuclear decay reaction. It is subtracted, and a proportional amount of the ^{38}Ar and ^{40}Ar are also subtracted. The remaining ^{38}Ar is from the spike, and the remaining ^{40}Ar is radiogenic. Because the spike is precisely known, the ^{40}Ar is determined by comparison to it.

Variations in this data may point to errors anywhere in the process, which is why all the steps of preparation are recorded in detail.

K-Ar analyses cost several hundred dollars per sample and take a week or two.

## The ^{40}Ar-^{39}Ar Method

A variant of the K-Ar method gives better data by making the overall measurement process simpler. The key is to put the mineral sample in a neutron beam, which converts potassium-39 into argon-39. Because ^{39}Ar has a very short half-life, it is guaranteed to be absent in the sample beforehand, so it's a clear indicator of the potassium content. The advantage is that all the information needed for dating the sample comes from the same argon measurement. Accuracy is greater and errors are lower. This method is commonly called "argon-argon dating."

The physical procedure for ^{40}Ar-^{39}Ar dating is the same except for three differences:

- Before the mineral sample is put in the vacuum oven, it is irradiated along with samples of standard materials by a neutron source.
- There is no
^{38}Ar spike needed. - Four Ar isotopes are measured:
^{36}Ar,^{37}Ar,^{39}Ar, and^{40}Ar.

The analysis of the data is more complex than in the K-Ar method because the irradiation creates argon atoms from other isotopes besides ^{40}K. These effects must be corrected, and the process is intricate enough to require computers.

Ar-Ar analyses cost around $1000 per sample and take several weeks.

## Conclusion

The Ar-Ar method is considered superior, but some of its problems are avoided in the older K-Ar method. Also, the cheaper K-Ar method can be used for screening or reconnaissance purposes, saving Ar-Ar for the most demanding or interesting problems.

These dating methods have been under constant improvement for more than 50 years. The learning curve has been long and is far from over today. With each increment in quality, more subtle sources of error have been found and taken into account. Good materials and skilled hands can yield ages that are certain to within 1 percent, even in rocks only 10,000 years old, in which quantities of ^{40}Ar are vanishingly small.