# Potassium-40

Potassium-40 ($^{40}$K) is a long lived and the main naturally occurring radioactive isotope of potassium. Its half-life is 1.25 billion years. It makes up about 0.012% (120 ppm) of natural potassium.
Potassium-40 undergoes four different types of radioactive decay, including all three main types of beta decay:
* Electron emission (β$^−$) to $^{40}$Ca with a decay energy of 1.31 MeV at 89.6% probability
* Positron emission (β$^+$ to $^{40}$Ar at 0.001% probability
* Electron capture (EC) to $^{40}$Ar$^*$ followed by a gamma decay emitting a photon with an energy of 1.46 MeV at 10.3% probability
* Direct electron capture (EC) to the ground state of $^{40}$Ar at 0.1%.
Both forms of the electron capture decay release further photons, when electrons from the outer shells fall into the inner shells to replace the electron taken from there.
The EC decay of $^{40}$K explains the large abundance of argon (nearly 1%) in the Earth's atmosphere, as well as prevalence of $^{40}$Ar over other isotopes.

## Potassium–argon dating

Potassium-40 is especially important in potassium–argon (K–Ar) dating. Argon is a gas that does not ordinarily combine with other elements. So, when a mineral forms – whether from molten rock, or from substances dissolved in water – it will be initially argon-free, even if there is some argon in the liquid. However, if the mineral contains traces of potassium, then decay of the $^{40}$K isotope present will create fresh argon-40 that will remain locked up in the mineral. Since the rate at which this conversion occurs is known, it is possible to determine the elapsed time since the mineral formed by measuring the ratio of $^{40}$K and $^{40}$Ar atoms contained in it.
The argon found in Earth's atmosphere is 99.6% $^{40}$Ar; whereas the argon in the Sun – and presumably in the primordial material that condensed into the planets – is mostly $^{36}$Ar, with less than 15% of $^{38}$Ar. It follows that most of Earth's argon derives from potassium-40 that decayed into argon-40, which eventually escaped to the atmosphere.

## Contribution to natural radioactivity

The decay of $^{40}$K in Earth's mantle ranks third, after $^{232}$Th and $^{238}$U, in the list of sources of radiogenic heat. Less is known about the amount of radiogenic sources in Earth's outer and inner core, which lie below the mantle. It has been proposed, though, that significant core radioactivity (1–2 TW) may be caused by high levels of U, Th and K.
Potassium-40 is the largest source of natural radioactivity in animals including humans. A 70 kg human body contains about 140 g of potassium, hence about 140g × 0.0117% ≈ 16.4 mg of $^{40}$K; whose decay produces about 3850 to 4300 disintegrations per second (becquerel) continuously throughout the life of an adult person (and proportionally less in young children).

## Banana equivalent dose

Potassium-40 is famous for its usage in the banana equivalent dose, an informal unit of measure, primarily used in general educational settings, to compare radioactive dosages to the amount received by consuming one banana. The radioactive dosage from consuming one banana is around 10$^{−7}$ sievert, or 0.1 microsievert, under the assumptions that all of the radiation produced by potassium-40 is absorbed in the body (which is mostly true, as the majority of the radiation is beta-minus radiation, which has a short range) and that the biological half life of potassium-40 is around 30 days (which is likely too large an estimate, as the body controls potassium levels closely and emits excess potassium quickly through urine). At the estimated 0.1 μSv, one banana equivalent dose is around 1% of the average American's daily exposure to radiation.

## Other naturally occurring potassium isotopes

Besides the long lived potassium-40, there are also trace amounts of potassium-42 in the biosphere. Potassium-42 has a short half life of just over half a day, so exposure to it is usually through the air, but it cannot accumulate in longer lived plants or animals. Potassium-42 is produced by the natural decay of argon-42 with a half-life time of 32.9 years. Argon-42 is in turn produced mostly from nuclear reactions between highly energetic cosmic particles and atmospheric argon-40 in the outermost layers of the earth's atmosphere. Some argon-42 also originates from thermonuclear weapons testing, when the high neutron flux around these weapons lead to double neutron activation of atmospheric argon-40. Production rates are low though, with less than 1 in 10$^{20}$ argon atoms being argon-42.