Potassium-40

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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 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.

Contents

Potassium-40 undergoes four different types of radioactive decay, including all three main types of beta decay: electron emission (β) to 40Ca with a decay energy of 1.31  MeV at 89.6% probability, positron emission (β+ to 40Ar at 0.001% probability [1] , electron capture (EC) to 40Ar* followed by a gamma decay emitting a photon [Note 1] with an energy of 1.46 MeV at 10.3% probability and direct electron capture (EC) to the ground state of 40Ar at 0.1%. [2] [3] [4] Both forms of the electron capture decay release further photons [Note 2] , when electrons from the outer shells fall into the inner shells to replace the electron taken from there.

The EC decay of 40K explains the large abundance of argon (nearly 1%) in the Earth's atmosphere, as well as prevalence of 40Ar over other isotopes.


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 traces of 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 Earth's 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 decay of 40K in Earth's mantle ranks third, after 232Th and 238U, 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. [5] [6]

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; [7] whose decay produces about 3850 [8] to 4300 disintegrations per second (becquerel) continuously throughout the life of an adult person (and proportionally less in young children). [Note 3] [9]

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. [10]

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 1020 argon atoms being argon-42. [11]

See also

Notes

  1. Also called a gamma ray, because it is produced by a transition in the nucleus
  2. Also called x-ray, as they are emitted from transitions of electrons
  3. 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): about 1.507×1022 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.

Related Research Articles

A chemical element is a chemical substance whose atoms all have the same number of protons. The number of protons is called the atomic number of that element. For example, oxygen has an atomic number of 8, meaning each oxygen atom has 8 protons in its nucleus. Atoms of the same element can have different numbers of neutrons in their nuclei, known as isotopes of the element. Two or more atoms can combine to form molecules. Some elements are formed from molecules of identical atoms, e. g. atoms of hydrogen (H) form diatomic molecules (H2). Chemical compounds are substances made of atoms of different elements; they can have molecular or non-molecular structure. Mixtures are materials containing different chemical substances; that means (in case of molecular substances) that they contain different types of molecules. Atoms of one element can be transformed into atoms of a different element in nuclear reactions, which change an atom's atomic number.

<span class="mw-page-title-main">Noble gas</span> Group of low-reactive, gaseous chemical elements

The noble gases are the members of group 18 of the periodic table: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn) and, in some cases, oganesson (Og). Under standard conditions, the first six of these elements are odorless, colorless, monatomic gases with very low chemical reactivity and cryogenic boiling points. The properties of the seventh, unstable, element, Og, are uncertain.

<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:

Radiometric dating, radioactive dating or radioisotope dating is a technique which is used to date materials such as rocks or carbon, in which trace radioactive impurities were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay. The use of radiometric dating was first published in 1907 by Bertram Boltwood and is now the principal source of information about the absolute age of rocks and other geological features, including the age of fossilized life forms or the age of Earth itself, and can also be used to date a wide range of natural and man-made materials.

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.

<span class="mw-page-title-main">Radioactive decay</span> Emissions from unstable atomic nuclei

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha, beta, and gamma decay. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the electromagnetic and nuclear forces.

Potassium–argon dating, abbreviated K–Ar dating, is a radiometric dating method used in geochronology and archaeology. It is based on measurement of the product of the radioactive decay of an isotope of potassium (K) into argon (Ar). Potassium is a common element found in many materials, such as feldspars, micas, clay minerals, tephra, and evaporites. In these materials, the decay product 40
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.

The synthesis of precious metals involves the use of either nuclear reactors or particle accelerators to produce these elements.

Argon–argondating is a radiometric dating method invented to supersede potassium–argon (K/Ar) dating in accuracy. The older method required splitting samples into two for separate potassium and argon measurements, while the newer method requires only one rock fragment or mineral grain and uses a single measurement of argon isotopes. 40Ar/39Ar dating relies on neutron irradiation from a nuclear reactor to convert a stable form of potassium (39K) into the radioactive 39Ar. As long as a standard of known age is co-irradiated with unknown samples, it is possible to use a single measurement of argon isotopes to calculate the 40K/40Ar* ratio, and thus to calculate the age of the unknown sample. 40Ar* refers to the radiogenic 40Ar, i.e. the 40Ar produced from radioactive decay of 40K. 40Ar* does not include atmospheric argon adsorbed to the surface or inherited through diffusion and its calculated value is derived from measuring the 36Ar and assuming that 40Ar is found in a constant ratio to 36Ar in atmospheric gases.

Calcium (20Ca) has 26 known isotopes, ranging from 35Ca to 60Ca. There are five stable isotopes, plus one isotope (48Ca) with such a long half-life that it is for all practical purposes stable. The most abundant isotope, 40Ca, as well as the rare 46Ca, are theoretically unstable on energetic grounds, but their decay has not been observed. Calcium also has a cosmogenic isotope, 41Ca, with half-life 99,400 years. Unlike cosmogenic isotopes that are produced in the air, 41Ca is produced by neutron activation of 40Ca. Most of its production is in the upper metre of the soil column, where the cosmogenic neutron flux is still strong enough. 41Ca has received much attention in stellar studies because it decays to 41K, a critical indicator of solar system anomalies. The most stable artificial isotopes are 45Ca with half-life 163 days and 47Ca with half-life 4.5 days. All other calcium isotopes have half-lives of minutes or less.

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%)

Argon (18Ar) has 26 known isotopes, from 29Ar to 54Ar, of which three are stable. On Earth, 40Ar makes up 99.6% of natural argon. The longest-lived radioactive isotopes are 39Ar with a half-life of 268 years, 42Ar with a half-life of 32.9 years, and 37Ar with a half-life of 35.04 days. All other isotopes have half-lives of less than two hours, and most less than one minute.

Absolute dating is the process of determining an age on a specified chronology in archaeology and geology. Some scientists prefer the terms chronometric or calendar dating, as use of the word "absolute" implies an unwarranted certainty of accuracy. Absolute dating provides a numerical age or range, in contrast with relative dating, which places events in order without any measure of the age between events.

<span class="mw-page-title-main">Thermochronology</span> Study of the thermal evolution of a region of a planet

Thermochronology is the study of the thermal evolution of a region of a planet. Thermochronologists use radiometric dating along with the closure temperatures that represent the temperature of the mineral being studied at the time given by the date recorded to understand the thermal history of a specific rock, mineral, or geologic unit. It is a subfield within geology, and is closely associated with geochronology.

<span class="mw-page-title-main">Primordial nuclide</span> Nuclides predating the Earths formation (found on Earth)

In geochemistry, geophysics and nuclear physics, primordial nuclides, also known as primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed. Primordial nuclides were present in the interstellar medium from which the solar system was formed, and were formed in, or after, the Big Bang, by nucleosynthesis in stars and supernovae followed by mass ejection, by cosmic ray spallation, and potentially from other processes. They are the stable nuclides plus the long-lived fraction of radionuclides surviving in the primordial solar nebula through planet accretion until the present; 286 such nuclides are known.

<span class="mw-page-title-main">Banana equivalent dose</span> Informal measurement of ionizing radiation exposure

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.

<span class="mw-page-title-main">Radiogenic nuclide</span> Nuclide produced by radioactive conversion from other nuclide

A radiogenic nuclide is a nuclide that is produced by a process of radioactive decay. It may itself be radioactive or stable.

<span class="mw-page-title-main">Earth's internal heat budget</span> Accounting of heat created within the Earth

Earth's internal heat budget is fundamental to the thermal history of the Earth. The flow of heat from Earth's interior to the surface is estimated at 47±2 terawatts (TW) and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantle and crust, and the primordial heat left over from the formation of Earth.

Potassium–calcium dating, abbreviated K–Ca dating, is a radiometric dating method used in geochronology. It is based upon measuring the ratio of a parent isotope of potassium to a daughter isotope of calcium. This form of radioactive decay is accomplished through beta decay.

References

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  2. Stukel, M.; et al. (KDK Collaboration) (2024). "Rare 40K Decay with Implications for Fundamental Physics and Geochronology". Physical Review Letters. 131 (5): 052503. doi:10.1103/PhysRevLett.131.052503.
  3. Hariasz, L.; et al. (KDK Collaboration) (2024). "Evidence for ground-state electron capture of 40K". Physical Review C. 108 (1): 014327. doi:10.1103/PhysRevC.108.014327.
  4. "Physicists Observe Rare Nuclear Decay of Potassium Isotope". Sci.News. 2024-05-08. Retrieved 2024-05-08.
  5. 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.
  6. 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.
  7. "Radioactive Human Body". Harvard Natural Sciences Lecture Demonstrations.
  8. Connor, Nick. "What is Potassium-40 – Characteristics – Half-life – Definition". Radiation Dosimetry.
  9. 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.
  10. Nick Connor (14 December 2019). "What is Banana Equivalent Dose – BED – Definition". Radiation Dosimetry.
  11. Barabash, A.S.; Saakyan, R.R.; Umatov, V.I. (2016). "On concentration of 42Ar in the Earth's atmosphere". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. doi:10.1016/j.nima.2016.09.042.
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