Potassium-40

Potassium-40 (40K) is a radioactive isotope of potassium which has a long half-life of 1.25 billion years. It makes up about 0.012% (120 ppm) of the total amount of potassium found in nature.

Potassium-40, 40K
General
Symbol40K
Namespotassium-40, 40K, K-40
Protons (Z)19
Neutrons (N)21
Nuclide data
Natural abundance0.0117(1)%
Half-life (t1/2)1.251(3)×109 y
Isotope mass39.96399848(21) Da
Spin4−
Excess energy−33505 keV
Binding energy341523 keV
Parent isotopesPrimordial
Decay products40Ca (β−)
40Ar (EC, γ; β+)
Decay modes
Decay modeDecay energy (MeV)
β−1.31109
EC, γ1.5049
Isotopes of potassium
Complete table of nuclides

Potassium-40 undergoes three types of radioactive decay. In about 89.28% of events, it decays to calcium-40 (40Ca) with emission of a beta particle (β−, an electron) with a maximum energy of 1.31 MeV and an antineutrino. In about 10.72% of events, it decays to argon-40 (40Ar) by electron capture (EC), with the emission of a neutrino and then a 1.460 MeV gamma ray.[Note 1] The radioactive decay of this particular isotope explains the large abundance of argon (nearly 1%) in the Earth's atmosphere, as well as prevalence of 40Ar over other isotopes. Very rarely (0.001% of events), it decays to 40Ar by emitting a positron (β+) and a neutrino.[1]

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 any potassium, then decay of the 40K 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 40K and 40Ar atoms contained in it.

The argon found in Earth's atmosphere is 99.6% 40Ar; whereas the argon in the Sun – and presumably in the primordial material that condensed into the planets – is mostly 36Ar, with less than 15% of 38Ar. It follows that most of the terrestrial argon derives from potassium-40 that decayed into argon-40, which eventually escaped to the atmosphere.

Contribution to natural radioactivity

The radioactive decay of 40K in the Earth's mantle ranks third, after 232Th and 238U, as the source of radiogenic heat. The core also likely contains radiogenic sources, although how much is uncertain. It has been proposed that significant core radioactivity (1–2 TW) may be caused by high levels of U, Th, and K.[2][3]

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 40K;[4] whose decay produces about 3850[5] to 4300 disintegrations per second (becquerel) continuously throughout the life of the person.[Note 2][6]

Banana equivalent dose

Potassium-40 is famous for its usage in the banana equivalent dose, an informal unit of measurement, primarily used in generalized educational settings, to compare radioactive dosages to the amount received by consuming one banana. The radioactive dosage from consuming one banana is generally agreed to be 10−7 sievert, or 0.1 microsievert, which is 1% of the average American's daily radioactive intake.[7]

See also

Notes
  1. This photon would be called an x-ray if emitted from an electron. In nuclear physics, it is common to name photons according to their origin rather than their energy, high energy photons produced by electrical transitions are called "x-rays" while those emitted from atomic nuclei are called "gamma rays" irrespective of their energy.
  2. The number of radioactive decays per second in a given mass of 40K is the number of atoms in that mass, divided by the average lifetime of a 40K atom in seconds. The number of atoms in one gram of 40K is the Avogadro constant 6.022×1023 mol−1 divided by the atomic weight of potassium-40 (39.96 g/mol), which is about 0.1507×1023 per gram. As in any exponential decay, the average lifetime is the half-life divided by the natural logarithm of 2, or about 56.82×1015 seconds.

References
  1. Engelkemeir, D. W.; Flynn, K. F.; Glendenin, L. E. (1962). "Positron Emission in the Decay of K40". Physical Review. 126 (5): 1818. Bibcode:1962PhRv..126.1818E. doi:10.1103/PhysRev.126.1818.
  2. Wohlers, A.; Wood, B. J. (2015). "A Mercury-like component of early Earth yields uranium in the core and high mantle 142Nd". Nature. 520 (7547): 337–340. Bibcode:2015Natur.520..337W. doi:10.1038/nature14350. PMC 4413371. PMID 25877203.
  3. Murthy, V. Rama; Van Westrenen, Wim; Fei, Yingwei (2003). "Experimental evidence that potassium is a substantial radioactive heat source in planetary cores". Nature. 423 (6936): 163–5. Bibcode:2003Natur.423..163M. doi:10.1038/nature01560. PMID 12736683. S2CID 4430068.
  4. "Radioactive Human Body". Harvard Natural Sciences Lecture Demonstrations.
  5. Connor, Nick. "What is Potassium-40 – Characteristics – Half-life – Definition". Radiation Dosimetry.
  6. Bin Samat, S.; Green, S.; Beddoe, A. H. (1997). "The 40K activity of one gram of potassium". Physics in Medicine and Biology. 42 (2): 407–13. Bibcode:1997PMB....42..407S. doi:10.1088/0031-9155/42/2/012. PMID 9044422. S2CID 250778838.
  7. Nick Connor (14 December 2019). "What is Banana Equivalent Dose – BED – Definition". Radiation Dosimetry.
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