How We Made Our Decisions

The goal of this game is to introduce players to the nuclides and the fundamental properties that matter most in nuclear chemistry, while staying grounded in correct scientific sources. For that reason, for example, our colour scheme follows the Karlsruhe Nuclide Chart. Several databases could have been used for this game. We decided largely in favour of the data from the Live Chart of Nuclides [1] rather than the data from NNDC (nndc.ornl.gov). These two large, reputable databases often differ by a few decimal places in half-life values. The difference usually comes down to which snapshot of the primary literature was used to fix the values. Larger differences show up in the cross-sections: for cosmogenic radionuclides, NNDC usually does not list cross-sections for the n,γ reaction at all.

Half-life

The half-life values for each nuclide come from the Live Chart of Nuclides [1]. A few adjustments were made for design reasons: half-lives were rounded to two decimal places wherever a more precise figure was available. Values that were not further specified were not padded out to two decimal places with a “0”. The half-life of ⁶⁰Co was converted into years and then rounded. For nuclides with very short half-lives, such as ⁸Be, ²²⁹ᵐTh, and ²⁹⁴Og, the half-life carries a large relative error; for design reasons, that error is not shown on the card. The half-life of ¹⁷⁶Lu likewise carries a large absolute error. For ¹⁰Be, rather than using the value from the Live Chart of Nuclides, which reflects the 2004 data set, we use the significantly different, more recent value [2][3]. ²²⁹ᵐTh presents a particular problem: it is a nuclear isomer whose preferred decay mode, and even its half-life, depend on its chemical environment. The 7 µs given here is the half-life as measured for ²²⁹ᵐTh in the oxidation state ± 0 [4].

Decay energy

In general, the Q value shown is for the most probable decay. The Q value does not describe how much energy the particle radiation (α, β⁻, β⁺) carries; rather, it describes the total energy available for the decay as a whole, corresponding to the mass difference between parent and daughter nuclide. Without this convention, pure electron-capture nuclides such as ⁵³Mn could not be assigned a value at all. Where the Q value exceeds 1022 keV, a parallel beta-plus decay is possible alongside electron capture. More importantly, this value also includes the energy of any subsequent gamma emissions as well as the recoil of the daughter nuclide. A further argument for this choice was ⁶⁰Co, which has a maximum beta energy of only about 300 keV (about 99% of decays), yet is famous for its high-energy gamma lines that follow the beta decay. We felt that reporting the Q value better captures this high-energy character of the beta emitter. The same logic applies to ⁴⁰K, which more often undergoes beta-minus decay. Its other possible decay path, electron capture/beta-plus decay to ⁴⁰Ar, is associated with the well-known 1461 keV gamma line, and it was this line we wanted the decay-energy field to represent – which is why the Q value shown here is for the rarer electron-capture decay. The Q value given for ²²⁹ᵐTh is, in this case, the most precise value currently known for the energy of the state, 8.338 eV [5]. We are aware that the energetic position of an excited state does not necessarily equal the Q value; however, for ²²⁹ᵐTh only transitions into the ground state of the same isotope are known so far. All values were rounded to whole numbers for design reasons. We would nonetheless like to take this opportunity to express our gratitude to the researchers who continue to refine these figures to ever more decimal places.

Gamma lines

The number of gamma lines was taken from the Live Chart of Nuclides [1]. Specifically, we counted the gamma lines listed under “Decay Radiation” with an emission probability of at least 1%, taking into account any branched decay modes of the nuclide. Although an isomeric transition of ²²⁹ᵐTh with emission of gamma radiation in the UV range is in principle possible, internal conversion is favoured for neutral ²²⁹ᵐTh, which emits conversion electrons instead [6].

Year of discovery

The year of discovery was generally taken from the book “Discovery of Isotopes” [7], which discusses the reasoning behind each entry. Two years that are often given differently elsewhere are 1829 for thorium and 1789 for uranium – these are the discovery years for the elements themselves. In the case of thorium, thorium isolated from its mineral happens, for all practical purposes, to be isotopically pure ²³²Th. For the purposes of our game, however, we felt it made more sense to give the year in which concrete information about the isotope's radiation was first published. On that basis, we credit the discovery of ²³²Th to G. C. Schmidt, who was the first to publish that thorium is radioactive [8]. Henri Becquerel discovered and described radioactivity using uranium, so the discovery of ²³⁸U can indirectly be credited to him [9] – even though this is somewhat inconsistent, since neither discoverer actually identified the isotope as such, and natural uranium ore in particular contains more than a single isotope. As a compromise for unambiguous identification of the isotope, the discovery of the other natural uranium isotope, ²³⁵U, is credited to A. J. Dempster [10].

Further inconsistencies came up for ⁹⁹Tc, ⁹⁰Sr, and ¹³⁷Cs.

For ⁹⁹Tc, “Discovery of Isotopes” gives as its source: E. Segrè, G. T. Seaborg, Phys. Rev. 54, 772 (1938) [11]. This is a short publication describing the discovery of ⁹⁹ᵐTc and its transition to the ground state. It gives neither an atomic weight nor a ground-state half-life, but it does correctly and concretely describe the radiation properties.

The situation is quite similar for ⁹⁰Sr and ¹³⁷Cs. Both were discovered as part of the “Plutonium Project,” which was itself part of the Manhattan Project to develop the US atomic bomb – meaning some of the relevant data was classified. That includes the discovery of ⁹⁰Sr and ¹³⁷Cs.

“Discovery of Isotopes” dates the discovery of ⁹⁰Sr to 1951, the publication year of the compilation “Radiochemical Studies: The Fission Products,” which brought together results that had since been declassified. It cites the original contribution, written by R. W. Nottorf in 1943 [12]. Nottorf's report correctly determines the half-life and mass assignment of the isotope and leaves no real room for further dispute regarding its relationship to earlier work. The report can be found as “Paper 77” on page 682 of the compilation.

“Discovery of Isotopes” credits Turkevich with the discovery of ¹³⁷Cs in 1951: he was the first to correctly connect the already-known radiation properties and mass of the isotope and identify it as such [13]. This actually happened back in 1945 but was likewise kept secret, and was only published later in “Radiochemical Studies: The Fission Products.” That same compilation, however, also describes further details of the discovery history of ¹³⁷Cs. The first correct description of the radiation was achieved by L. E. Glendenin and R. P. Metcalf in 1942, who also correctly distinguished its half-life from that of the other long-lived fission-product caesium isotope, ¹³⁵Cs. Their report explicitly references internal communication from 1941 between G. T. Seaborg and M. Melhase, who had clearly distinguished ¹³⁷Cs from ¹³⁴Cs. The text, however, does not draw a clear distinction from the then also-unknown ¹³⁵Cs. In hindsight it is clear that only ¹³⁷Cs can be meant, since fission produces only small amounts of ¹³⁵Cs activity. Although this internal communication is not explicitly documented, we nonetheless credit the discovery of ¹³⁷Cs to G. T. Seaborg and M. Melhase, since this was widely accepted among researchers on the Manhattan Project – including, for instance, Glendenin and Metcalf. Interviews with Mrs. Melhase (later “Mrs. Robert Fuchs”) not only confirm this, but also shed light on the situation of women researchers in the 20th century [14].

The last controversial decision regarding discovery years concerns ²²⁹ᵐTh, for which we settled on 1990. The publication by C. W. Reich and R. G. Helmer [15] was not the first to describe the excited state of thorium, but it was the first to give a narrower energy range for it. At 3.5 ± 1 eV, that value is now known to have been too low. The first description of the excited state, in 1975 [16], only inferred its existence from a discrepancy in the gamma spectrum. Neither publication could establish a clear separation from the ground state, since the half-life was not yet known. The precise determination of the energy level has since been achieved and is, without question, a scientific milestone [17] – but in our view, it ultimately still builds on those earlier, imprecise results [15].

Cross-section

Following the example of the Karlsruhe Nuclide Chart, when we say “cross-section” we mean the cross-section of the n,γ reaction at the nucleus of the listed nuclide with thermalised neutrons (Ekin = 25 meV). Where applicable, the cross-section shown is summed over the individual cross-sections leading to isomeric states of the product. Although some nuclides in the nuclide chart list cross-sections with a “less than” (<) sign, we do not carry that inequality sign over into our value, since experimental data in these cases generally shows only minor deviations. For some nuclides, no cross-section data exists at all; these are marked with a dash. For gameplay purposes, that field should be treated as zero, even though the actual value is not “0” but simply unknown.

[1] IAEA, "Live Chart of Nuclides – Nuclear Structure and Decay Data," can be found under https://nds.iaea.org/relnsd/vcharthtml/VChartHTML.html, 2026 (accessed January 31, 2026).

[2] J. Chmeleff, F. von Blanckenburg, K. Kossert, and D. Jakob, "Determination of the ¹⁰Be Half-Life by Multicollector ICP-MS and Liquid Scintillation Counting," Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 268 (2010): 192–199, https://doi.org/10.1016/j.nimb.2009.09.012.

[3] G. Korschinek, A. Bergmaier, T. Faestermann, et al., "A New Value for the Half-Life of ¹⁰Be by Heavy-Ion Elastic Recoil Detection and Liquid Scintillation Counting," Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 268 (2010): 187–191, https://doi.org/10.1016/j.nimb.2009.09.020.

[4] B. Seiferle, L. von der Wense, and P. G. Thirolf, "Lifetime Measurement of the ²²⁹Th Nuclear Isomer," Physical Review Letters 118 (2017): 042501, https://doi.org/10.1103/PhysRevLett.118.042501.

[5] P. G. Thirolf, S. Kraemer, D. Moritz, and K. Scharl, "The Thorium Isomer ²²⁹ᵐTh: Review of Status and Perspectives after More than 50 Years of Research," The European Physical Journal Special Topics 233 (2024): 1113–1131, https://doi.org/10.1140/epjs/s11734-024-01098-2.

[6] B. Seiferle, "Characterization of the Th-229 Nuclear Clock Transition" (PhD diss., Ludwig-Maximilians-Universität München, 2019), https://edoc.ub.uni-muenchen.de/25340/.

[7] M. Thoennessen, The Discovery of Isotopes (Cham: Springer International Publishing, 2016), https://doi.org/10.1007/978-3-319-31763-2.

[8] G. C. Schmidt, "Über die von den Thorverbindungen und einigen anderen Substanzen ausgehende Strahlung," Annalen der Physik und Chemie 65 (1898): 141–151.

[9] H. Becquerel, "Sur les radiations émises par phosphorescence," Comptes Rendus de l'Académie des Sciences 122 (1896): 420–421.

[10] A. J. Dempster, "Isotopic Constitution of Uranium," Nature 136 (1935): 180, https://doi.org/10.1038/136180a0.

[11] E. Segrè and G. T. Seaborg, "Nuclear Isomerism in Element 43," Physical Review 54 (1938): 772, https://doi.org/10.1103/PhysRev.54.772.2.

[12] R. W. Nottorf, "Paper 77," in Radiochemical Studies: The Fission Products, National Nuclear Energy Series IV, vol. 9 (New York: McGraw-Hill, 1951), 682.

[13] A. Turkevich et al., "Paper 153," in Radiochemical Studies: The Fission Products, National Nuclear Energy Series IV, vol. 9 (New York: McGraw-Hill, 1951), 1070.

[14] D. D. Patton, "Part 5: The Discovery of Cesium 137: The Untold Story," Academic Radiology 1 (1994): 51–58, https://doi.org/10.1016/S1076-6332(05)80785-8.

[15] C. W. Reich and R. G. Helmer, "Energy Separation of the Doublet of Intrinsic States at the Ground State of Th 229," Physical Review Letters 64 (1990): 271–273.

[16] L. A. Kroger and C. W. Reich, "Features of the Low-Energy Level Scheme of ²²⁹Th as Observed in the α-Decay of ²³³U," Nuclear Physics A 259 (1976): 29–60, https://doi.org/10.1016/0375-9474(76)90494-2.

[17] C. Zhang, T. Ooi, J. S. Higgins, et al., "Frequency Ratio of the ²²⁹ᵐTh Nuclear Isomeric Transition and the ⁸⁷Sr Atomic Clock," Nature 633 (2024): 63–70, https://doi.org/10.1038/s41586-024-07839-6.