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"Clock" for geochronological dating readjusted: Accurate determination of the decay constants of potassium-40


Potassium‑40 decays to calcium‑40 by a beta‑minus transition and to argon‑40 by electron capture. Through the potassium‑argon and the particularly accurate argon‑39‑argon‑40 dating methods, potassium‑40 represents one of the most important tools for age determination in geochronology. However, the basis for these dating methods is accurate knowledge of the total half‑life as well as the partial half‑life for decay to argon, which can be derived from the total half‑life and the probability of decay by electron capture. The probability of the latter can also be determined from the probability of beta‑minus decay. We often refer to the so‑called branching ratio instead of the two transition probabilities.

As far back as 2004, PTB published the results of the half‑life determination of potassium‑40, which was achieved by determining the activity by means of liquid scintillation counting [1]. For this purpose, potassium salts with a natural isotopic composition were used, which resulted in only small count rates despite elaborate sample preparation. The evaluation was furthermore based on a branching ratio taken from evaluated data tables that were valid at that time. Although PTB’s experiment was accepted by many scientists as the most accurate half‑life determination of potassium‑40 via activity measurement, leading geochronologists obtained slightly different results by using age comparisons, especially for the partial decay constants. For the age comparison, for instance, rocks whose age can be determined by the uranium‑lead method are used.

In collaboration with other partners, PTB has now published the new results from a very broad series of experiments [2]. In these experiments, two solutions were used where potassium‑40 is enriched reaching a proportion that is about one factor 265 higher than in naturally occurring materials. The number of potassium‑40 nuclei in one of the solutions was very accurately determined by mass spectrometry at the Australian National University (ANU) [3]. This makes the half‑life determination independent of the potassium‑40/potassium ratio in salts with a natural isotopic composition. The specific activity was again determined by liquid scintillation counting. For one of the solutions, the triple‑to‑double coincidence ratio (TDCR) method could be used for the first time in addition to the CIEMAT/NIST method that had been applied successfully before. Improved models for the calculation of the beta spectrum and electron capture were used in the evaluation. However, as previously necessary, the evaluation requires knowledge of the probabilities of the competing decay branches. To be independent of evaluated data, these probabilities were derived from our own experiments. Combining the results from liquid scintillation counting and gamma‑ray spectrometry made it initially possible to determine the probability for the emission of the 1461 keV gamma transitions and hence the probability of the dominant electron‑capture branch. Since in previous experiments a very weak beta‑plus decay has been detected in potassium‑40, the assumption can be made on the basis of theoretical considerations that an electron‑capture branch to the ground state of argon‑40 must exist. This electron‑capture branch has not yet been directly detected by experiments. As a consequence of this consideration, the determination of the probability of gamma‑ray emissions was not sufficient to fully determine the decay scheme of potassium‑40. The missing component could finally be determined by using the spectra from liquid scintillation. The spectra result from a complex superposition of detected events of all decay species involved. Nevertheless, the pure beta‑minus component therein could finally be quantified. For this purpose, the low‑energy fraction of this beta spectrum was modeled using experimentally determined spectra of pure beta emitters. The detection probabilities of individual decay components that are required for the evaluation were determined by an approach similar to the CIEMAT/NIST method.

Based on the now known relative probability of beta‑minus decay, it was finally possible to determine the complete decay scheme (see figure) and subsequently the specific activity of both solutions.

K-40 decay scheme

Figure: Decay scheme of K‑40.

The combination of specific activity and the number of K‑40 nuclei determined by mass spectrometry results in a half‑life of 1.2536(27) billion years. This result and the experimentally determined probabilities for beta minus decay and electron capture do not depend on the uranium 238 half life, the knowledge of which is required for various age comparisons of rocks. The new results are also in good agreement with those of one of the leading research groups in geochronology [4].

If the newly determined branching ratio is used, the measurement results of the earlier PTB publication [1] can also be harmonized with the new measurement as well as with the results of the geochronologists [2].

Thanks to the new determination of potassium‑40 decay data, dating terrestrial and extraterrestrial rocks will be on a more solid basis from now on.


[1]      Kossert, K., Günther, E.: LSC measurements of the half life of 40K. Applied Radiation and Isotopes 60 (2004) 459 464, https://doi.org/10.1016/j.apradiso.2003.11.059

[2]      Kossert, K., Amelin, Y., Arnold, D., Merle, R., Mougeot, X., Schmiedel, M., Zapata, D.: Activity standardization of two enriched 40K solutions for the determination of decay scheme parameters and the half-life. Applied Radiation and Isotopes 188 (2022) 110362, https://doi.org/10.1016/j.apradiso.2022.110362

[3]      Amelin, Y., Merle, R., 2021. Isotopic analysis of potassium by total evaporation and incipient emission thermal ionisation mass spectrometry. Chem. Geol. 559, 119976, https://doi.org/10.1016/j.chemgeo.2020.119976

[4]      Renne, P. R., Balco, G., Ludwig, K. R., Mundil, R., Min, K., 2011. Response to the comment by W.H. Schwarz et al. on “Joint determination of 40K decay constants and 40Ar*/40K for the Fish Canyon sanidine standard, and improved accuracy for 40Ar/39Ar geochronology” by P.R. Renne et al. (2010). Geochim. Cosmochim. Acta 75, 5097–5100, https://doi.org/10.1016/j.gca.2011.06.021


Opens local program for sending emailDr. Karsten Kossert, Department 6.1, 6.14 Fundamentals of Radioactivity