Potassium naturally occurs in 3 isotopes - 39K (93.2581%), 40K (0.0117%), 41K (6.7302%). The radioactive isotope 40K decays with a half-life of 1.248x109 (1.248 billion) years. Conversion to stable 40Ca occurs via electron emission beta decay occurs in 89.1% of decay events. Conversion to stable 40Ar occurs via positron emission beta decay or electron capture in 10.9% of decay events.
Calcium is common in the crust, with 40Ca being the most common isotope. Despite 40Ca being the favored daughter nuclide, its usefulness in dating is limited since a great many decay events are required for a small change in relative abundance.
The 40Ar content of a rock is determined by mass spectrometry of the gasses released when a sample is melted. The amount of 40K is determined using flame photometry or atomic absorption spectroscopy. The ratio of the amount of 40Ar to 40K is related to the time elapsed since the rock was cool enough to trap the Ar by:
In the foregoing, t is time elapsed, t1/2 is the half life of 40K, Kf is the amount of 40K remaining in the sample, and Arf is the amount of 40Ar found in the sample. The scale factor 0.109 corrects for the unmeasured fraction of 40K which decayed into 40Ca; the sum of the measured 40K and the scaled amount of 40Ar gives the amount of 40K in the original unaged sample. In practice, each of these values is scaled to the total potassium fraction as only relative, not absolute, quantities are required.
Extraneous argon is commonly incorporated into the cooling sample. The above equation may be corrected for the presence of non-radiogenic by subtracting from the measured 40Ar value the amount originally present as determined by the 40Ar/36Ar ratio. Ordinarily, 40Ar is 295.5 times more plentiful than 36Ar, though this may need to be adjusted if the sample cooled in an isotopically enriched or depleted region. The amount of the measured 40Ar that resulted from 40K decay is then: decayed = measured - 295.5 * measured.
Both flame photometry and mass spectrometry are destructive tests, so particular care is needed to ensure that the aliquots used are truly representative of the sample. Argon-argon dating is a similar technique which compares isotopic ratios from the same portion of the sample to avoid this problem.
Some additional information about the history and composition of a sample is required before K-Ar isotopic comparison may be used to produce accurate dates. Great care is needed in selecting a sample for dating, as many potential samples have been contaminated by various means. The sample must have remained a closed system since it cooled enough to retain argon, neither admitting nor emitting either of the isotopes of interest. A deficiency of 40Ar in a sample of a known age can indicate a full or partial melt in the thermal history of the area. Molten magma can be contaminated by inclusion of older xenolithic material such as chilled deep sea basalts that may not completely outgas preexisting 40Ar before cooling. Reliability in the dating of a geological feature is increased by sampling disparate areas which have been subjected to slightly different thermal histories.
Accuracy relies on the isotopic ratios included in the sample being representative since 40K is usually not measured directly, but is assumed to be 0.0117% of the total potassium. Unless some other process is active at the time of cooling, this is a very good assumption for terrestrial samples. Accuracy also requires that the nuclear decay rate be unaffected by external conditions such as temperature and pressure. Because of the energy scales involved, this is a very good assumption, though the 40K electron capture partial decay constant may be enhanced at ultrahigh pressure.
Due to the long half-life, the technique is most applicable for dating minerals and rocks more than 100,000 years old. K-Ar dating was instrumental in the development of the geomagnetic polarity time scale. Although it finds the most utility in geological applications, it plays an important role in archaeology. One archeological application has been in bracketing the age of archeological deposits at Olduvai Gorge by dating lava flows above and below the deposits. It has also been indispensable in other early east African sites with a history of volcanic activity such as Hadar, Ethiopia. The K-Ar method continues to have utility in dating clay mineral diagenesis. Clay minerals are less than 2 microns thick and cannot easily be irradiated for Ar-Ar analysis because Ar recoils from the crystal lattice.