Potassium-40

Last updated
Potassium-40, 40K
Potassium-40.svg
General
Symbol 40K
Names potassium-40, 40K, K-40
Protons (Z)19
Neutrons (N)21
Nuclide data
Natural abundance 0.0117(1)%
Half-life (t1/2)1.251(3)×109 y
Isotope mass 39.96399848(21) Da
Spin 4
Excess energy −33505 keV
Binding energy 341523 keV
Parent isotopes Primordial
Decay products 40Ca (β)
40Ar (EC, γ; β+)
Decay modes
Decay mode Decay energy (MeV)
β1.31109
EC, γ1.5049
Isotopes of potassium
Complete table of nuclides

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.

Contents

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, 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+) and a neutrino. [1]

Potassium–argon dating

Decay scheme Potassium-40-decay-scheme.svg
Decay scheme

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 evolution of Earth's mantle radiogenic heat flow over time: contribution from K in yellow. Evolution of Earth's radiogenic heat.svg
The evolution of Earth's mantle radiogenic heat flow over time: contribution from K in yellow.

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 general 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 exposure to radiation. [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.

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<span class="mw-page-title-main">Radiation</span> Waves or particles moving through space

In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes:

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A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess numbers of either neutrons or protons, giving it excess nuclear energy, and making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transferred to one of its electrons to release it as a conversion electron; or used to create and emit a new particle (alpha particle or beta particle) from the nucleus. During those processes, the radionuclide is said to undergo radioactive decay. These emissions are considered ionizing radiation because they are energetic enough to liberate an electron from another atom. The radioactive decay can produce a stable nuclide or will sometimes produce a new unstable radionuclide which may undergo further decay. Radioactive decay is a random process at the level of single atoms: it is impossible to predict when one particular atom will decay. However, for a collection of atoms of a single nuclide the decay rate, and thus the half-life (t1/2) for that collection, can be calculated from their measured decay constants. The range of the half-lives of radioactive atoms has no known limits and spans a time range of over 55 orders of magnitude.

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Ar
is able to escape the liquid (molten) rock but starts to accumulate when the rock solidifies (recrystallizes). The amount of argon sublimation that occurs is a function of the purity of the sample, the composition of the mother material, and a number of other factors. These factors introduce error limits on the upper and lower bounds of dating, so that the final determination of age is reliant on the environmental factors during formation, melting, and exposure to decreased pressure or open air. Time since recrystallization is calculated by measuring the ratio of the amount of 40
Ar
accumulated to the amount of 40
K
remaining. The long half-life of 40
K
allows the method to be used to calculate the absolute age of samples older than a few thousand years.

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Potassium has 25 known isotopes from 34
K
to 57
K
as well as 31
K
, as well as an unconfirmed report of 59
K
. Three of those isotopes occur naturally: the two stable forms 39
K
(93.3%) and 41
K
(6.7%), and a very long-lived radioisotope 40
K
(0.012%)

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γ
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Banana equivalent dose (BED) is an informal unit of measurement of ionizing radiation exposure, intended as a general educational example to compare a dose of radioactivity to the dose one is exposed to by eating one average-sized banana. Bananas contain naturally occurring radioactive isotopes, particularly potassium-40 (40K), one of several naturally occurring isotopes of potassium. One BED is often correlated to 10−7 sievert ; however, in practice, this dose is not cumulative, as the potassium in foods is excreted in urine to maintain homeostasis. The BED is only meant as an educational exercise and is not a formally adopted dose measurement.

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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.
Lighter:
potassium-39
Potassium-40 is an
isotope of potassium
Heavier:
potassium-41
Decay product of:
Decay chain
of potassium-40
Decays to:
argon-40, calcium-40, Stable