Potassium-40

Properties and data of the isotope ⁴⁰K.

Contents

General Data

Radioactive Decay

Isotones und Isobares

Literature

Potassium-40 - symbol ⁴⁰ K - is a naturally occurring, primordial, radioactive isotope of the chemical element potassium with a half-life of 1.25 billion years; Earth's potassium consists of about 0.0117% (117 ppm) of this isotope, which is responsible for the weak natural radioactivity of the alkali metal.

The atomic nucleus of the nuclei consists of ⁴⁰K 21 neutrons and the element-specific 19 protons.

General data

Name of the isotope:Potassium-40; K-40Symbol:⁴⁰K or 4019KMass number A:40 (= number of nucleons)Atomic number Z:19 (= number of protons)Neutrons N:21Isotopic mass:39.9639982(4) u (atomic weight of Potassium-40)Nuclide mass:39.9535754 u (calculated nuclear mass without electrons)Mass excess:-33.53546 MeVMass defect:0.366640644 u (per nucleus)Nuclear binding energy:341.52356004 MeV (per nucleus)
8.538089 MeV (average binding energy per nucleon)Separation energy:S_N = 7.79962(6) MeV (first neutron)
S_P = 7.582(5) MeV (first proton)Half-life:1.248(3) × 10⁹ aDecay constant λ:1.761182124173 × 10^-17 s^-1Specific activity α:271950.94440454 Bq g^-1
7.35002552444 × 10^-6 Ci g^-1Spin and parity:
(nuclear angular momentum)4-Magnetic dipole moment:μ(μ_N) = -1.298100(3)Charge radius:3.4381(28) femtometer fmMirror nucleus:Scandium-40Year of discovery:1935

Radioactive Decay

Potassium-40 is a rare example of an isotope that undergoes both types of beta decay, and these major decay channels are well studied and experimentally verified. However, despite decades of research and great interest in this natural radionuclide, there is uncertainty about the details of ⁴⁰K decay.

In about 89.28% of the events, the nuclide decays with the emission of a beta particle β^- - an electron with the kinetic energy of 0.56018 ± 17 MeV and a neutrino (0.6494 ± 12 MeV) - into the ground state of the isotope Calcium-40:

4019K → 4020Ca + e^- + v_e.
With a probability of 10.72%, after capture of an orbital electron (EE), the decay occurs into an excited ⁴⁰Ar state, which occurs almost simultaneously (T_1/2 = 1.15 picoseconds, spin = 2+) with emission of gamma rays with an energy of 1.460 MeV and a neutrino (0.00506 MeV) into the ground state of the isotope Argon-40 passes:

4019K + e^- → 4018Ar + v_e.
Extremely rarely - in only 0.001% of events - potassium-40 decays, emitting a neutrino v_e and a positron (β⁺-decay) to ⁴⁰Ar [1, 5]. If the positron e⁺ (anti-electron) hits an electron e^-, the two particles undergo pair annihilation with an annihilation energy of 0.511 MeV:

4019K → 4018Ar + e⁺ + v_e.

Another type of decay that has not been confirmed experimentally and is controversial in science:

Based on theoretical considerations, the nuclide ⁴⁰K could radioactively decay from its ground state directly into the ground state of ⁴⁰Ar after electron capture and with a probability of 0.2% . A recent article [Carter et al., 2020] deals with the latest findings and the experimental difficulties in this regard [5]. First evidence for this decay mode was reported in 2023 [7].

The radioactive decay of this potassium isotope explains the large amount of argon of almost one percent in the Earth´s atmosphere as well as the prevalence of ⁴⁰Ar compared to the other argon isotopes; at the same time it is according to ²³⁸Th and ²³⁸U the third most common source of radiogenic heat in the Earth´s mantle.

Half-life T_½ = 1.248(3) × 10⁹ a respectively 3.9356928 × 10¹⁶ seconds s.

Decay mode	Daughter	Probability	Decay energy	γ energy (intensity)
β^-	⁴⁰Ca	89.28(11) %	1.31089(6) MeV
EC/β⁺	⁴⁰Ar	10.72(11) %	1.50440(6) MeV	1.460820(5) MeV 10.66(17) %

Formation

The ⁴⁰K atom nucleus is one of the primordial radionuclides - this means that the terrestrial deposits were already present when they were created and were not replenished in significant quantities through radioactive decay processes or human influences. The potassium-40 therefore comes from stellar processes - particularly supernova explosions - that took place before the Earth was formed. Recent studies of meteorites also indicate that most of the terrestrial potassium (90%) comes from non-carbonaceous matter, the origin of which lies in the interior of the solar system [6].

Occurrence

Potassium-40 is a natural radionuclide found in potassium - but its proportion is only 0.0117%. Since potassium is a mineral found practically everywhere, the radioactive K-40 it contains is the largest source of natural radioactivity in humans, animals and the environment. A human body weighing 70 kg contains approximately 140 g of potassium, which is approximately 0.000117 × 140 g = 0.0164 g of the isotope ⁴⁰ K; The decay causes approximately 4,300 decays per second (Becquerels) within the body continuously throughout life.

Comparison of the natural Potassium isotopes including isotopic abundance (mole fraction of the isotope mixture in percent):

	Atomic Mass m_a	Quantity	Half-life	Spin
Potassium Isotopic mixture	39.0983 u	100 %
Isotope ³⁹K	38.96370649(3) u	93.2581(44) %	stable	3/2+
Isotope ⁴¹K	40.96182526(3) u	6.7302(44) %	stable	3/2+
Isotope ⁴⁰K	39.9639982(4) u	0.0117(1) %	1.248(3) × 10⁹ a	4-

NMR data

Nuclear magnetic properties of the NMR active Nuclide ⁴⁰K

Isotope:⁴⁰K-NMRQuantity:0.0117(1) %Spin:4-Nuclearmagnetic moment
μ/μ_N:-1.298100(3)Gyromagnetic ratio γ:–1.5542854 · 10⁷ rad T^-1 s^-1Nuclear g-factor:g_l = -0.324525Quadrupole moment Q:-0.073(1) barn (100 fm²)Line width parameter (factor):l = 5.23 fm⁴Resonance frequency:v₀ = 2.4737 at 1 TFrequency ratio:Ξ(⁴⁰K) = 5.802018 %Relative Sensitivity:0.00523 (H₀ = const.)
1.5493 (v₀ = const.)
[related to ¹H = 1.000]Reference compound:
(conditions)0.1 M potassium chloride solution in Deuterium Oxide (D₂O).

Radiation Protection

The Radiation Protection Ordinance (European Union), for example, specifies the following limit values for the isotope Potassium-40 (exemption limits, clearance values and other values as a radioactive or highly radioactive source of radiation (HASS)):

Potassium compounds and preparations are ubiquitous in nature, technology and everyday life and are not considered radioactive hazardous substances despite the K-40 content; The radiation emitted by it is too weak for this.

Substances enriched with ⁴⁰K have no practical or technical significance; K-40 is one of the radioactive substances for which even high levels of activity do not lead to classification as a highly radioactive radiation source.

Exemption level:10⁶ BqExemption level per gram:100 Bq/g
Unrestricted handling of solids and liquids.Activity HASS:Unbegrenzt (UL)Surface contamination:10 Bq/cm²Half-life:1.3 × 10⁹ a

Nuclear Isomers

Nuclear isomers or excited states with the activation energy in keV related to the ground state.

Nuclear Isomer	Excitation Energy	Half-life	Spin
^40mK	1643.638(11) keV	0.336(13) μs	0+

Isotones and Isobars

The following table shows the atomic nuclei that are isotonic (same neutron number N = 21) and isobaric (same nucleon number A = 40) with Potassium-40. Naturally occurring isotopes are marked in green; light green = naturally occurring radionuclides.

Z	Isotone N = 21	Isobar A = 40
9	³⁰F
10	³¹Ne
11	³²Na
12	³³Mg	⁴⁰Mg
13	³⁴Al	⁴⁰Al
14	³⁵Si	⁴⁰Si
15	³⁶P	⁴⁰P
16	³⁷S	⁴⁰S
17	³⁸Cl	⁴⁰Cl
18	³⁹Ar	⁴⁰Ar
19	⁴⁰K	⁴⁰K
20	⁴¹Ca	⁴⁰Ca
21	⁴²Sc	⁴⁰Sc
22	⁴³Ti	⁴⁰Ti
23	⁴⁴V	⁴⁰V
24	⁴⁵Cr
25	⁴⁶Mn
26	⁴⁷Fe
27	⁴⁸Co
28	⁴⁹Ni

External data and identifiers

CAS:13966-00-2InChI Key:ZLMJMSJWJFRBEC-OUBTZVSYSA-NInChI Code:[40K]PubChem:ID 6328542Adopted Levels, Gammas:NuDat 40K

Literature and References

[1] - D. W. Engelkemeir, K. F. Flynn, L. E. Glendenin:
Positron Emission in the Decay of ⁴⁰K.
In: Physical Review, 126,1818, (1962), DOI 10.1103/PhysRev.126.1818.

[2] - H. Leutz, G. Schulz, H. Wenninger:
The decay of potassium-40.
In: Zeitschrift für Physik, (1965), DOI 10.1007/BF01387190.

[3] - A. Ažman, A. Moljk, J. Pahor:
Electron capture in potassium 40.
In: Zeitschrift für Physik A, (1968), DOI 10.1007/BF01379914.

[4] - W. Sahm, A. Schwenk:
³⁹K, ⁴⁰K and ⁴¹K Nuclear Magnetic Resonance Studies.
In: Zeitschrift für Naturforschung A, (2014), DOI 10.1515/zna-1974-1208.

[5] - Jack Carter, Ryan B. Ickert, Darren F. Mark et al.:
Production of 40Ar by an overlooked mode of ⁴⁰K decay with implications for K-Ar geochronology.
In: Geochronology, 2(2), 355–365, (2020), DOI 10.5194/gchron-2-355-2020.

[6] - Nicole X. Nie et al.:
Meteorites have inherited nucleosynthetic anomalies of potassium-40 produced in supernovae.
In: Science, 379, 6630, 373-376, (2023), DOI 10.1126/science.abn178.

[7] - L. Hariasz et al.:
Evidence for ground-state electron capture of ⁴⁰K.
In: Physical Review C, 108, 014327, (2023), DOI 10.1103/PhysRevC.108.014327.