RADIOACTIVITY OF POTASSIUM*

G. Hevesy, Copenhagen

The discovery of the phenomenon of artificial radioactivity, consisting in the fact that many elements, under the action of α-particles, neutrons, and other fast particles, and in some cases even under the action of X-rays, can be brought into a radioactive state, has shed new light on the much-discussed problem of the natural radioactivity of potassium. Fermi and his co-workers¹ found that potassium subjected to neutron irradiation emits, along with the ordinary β-rays, harder β-rays; moreover, the artificial radioactivity caused by neutrons decays with a half-life of 16 hours. On the other hand, the author of the present article² succeeded in isolating from neutron-irradiated scandium an isotope of potassium of mass 42, which can be shown to be identical with the isotope obtained by Fermi and his co-workers from ordinary potassium. From this coincidence it follows that the formation of the isotope \(^{42}\mathrm{K}\) occurs when a neutron is captured by the nucleus \(^{41}\mathrm{K}\), in accordance with the following equation:

\[ {}^{41}_{19}\mathrm{K} + {}^{1}_{0}\mathrm{n} = {}^{42}_{19}\mathrm{K}^{*}. \]

\(^{41}\mathrm{K}\) is the less abundant isotope of potassium and constitutes, as Aston showed, 7% of ordinary potassium, whereas 93% is accounted for by \(^{39}\mathrm{K}\). This now suggests the idea that, like \(^{41}\mathrm{K}\), the nuclei of \(^{39}\mathrm{K}\) also capture neutrons when irradiated by them, but the formation of \(^{40}\mathrm{K}\) cannot be proved by radioactive measurements only because the product formed decays too slowly. Proof of the existence of artificial radioactivity is based on the fact that the newly formed atoms are radioactive and decay with the emission of negative or positive electrons sufficiently rapidly. Thus, for example, the transformation of \(^{42}\mathrm{K}\), with the emission of β-rays, into Ca, occurring according to the equation \(^{42}_{19}\mathrm{K} = {}^{42}_{20}\mathrm{Ca} + \beta\), proceeds sufficiently rapidly for the number of emitted β-particles to be readily established with a counter. If, however, the decay period of \(^{42}\mathrm{K}\), instead of 16 hours, were 16 years, the existence of this isotope

* Naturwiss., 23, 583, 1935; trans. L. Grochev.

could not have been established, because in that case the number of atoms decaying per unit time would have been too small for them to be detected with the aid of a counter.

Of course, in the case under consideration the difficulty might have been eliminated by subjecting the irradiated preparation to the action of neutrons not for 24 hours, as in the cases analyzed above, but for many weeks. However, if we are dealing with such atoms as have a decay period of many millions of years, as we must assume for \(^{40}\mathrm{K}\), then even prolonged neutron irradiation can be of no help, since even the longest laboratory experiments take place over a vanishingly small interval of time in comparison with the enormous periods mentioned above. Under laboratory conditions, therefore, it is not possible to obtain \(^{40}\mathrm{K}\); the situation is different in space. At the time when the elements in the corresponding regions of world space were subjected to the action of neutrons and similar particles, the mixture of basic substances contained atoms of all kinds which we can now create artificially in the laboratory. However, after the cessation of the action of the named agents, all unstable elements quickly disappeared, and only the lifetime of \(^{40}\mathrm{K}\) and \(^{86}\mathrm{Rb}\) proved sufficiently long for these elements, along with uranium and thorium, to be found billions of years later. We must therefore accept that the radioactivity of potassium may be ascribed to the radioactive isotope \(^{40}\mathrm{K}\), which arose in the period before the formation of the Earth. In what follows we shall investigate how far this conclusion is confirmed by our knowledge of the radioactivity of potassium.

Conclusion from the Results on Isotope Separation

The most direct way of resolving the question of which isotope of potassium is radioactive would consist in separating the isotopes of potassium, for example with an Aston apparatus adapted for quantitative separation, followed by testing for radioactivity the strips coated with the separated isotopes.

Such a complete separation of the isotopes of potassium has not yet been achieved. In order to obtain an answer to the question posed, the author, together with Logstrup, carried out a partial separation of the isotopes of potassium several years ago. After a large number of “ideal” distillations, in which the difference in the evaporation rates of the isotopes was used, a final fraction was obtained enriched in \(^{41}\mathrm{K}\) and depleted in \(^{39}\mathrm{K}\). The degree of enrichment could be judged from the results of measuring the atomic weight, which make it possible to indicate to what extent the fraction had been enriched with the isotope \(^{41}\mathrm{K}\). Data on the enrichment of the fraction with the radioactive isotope were obtained by comparing the radioactivity of ordinary and heavy potassium; in doing so the samples were compared, for example, in the form of \(\mathrm{KCl}\). The degree of enrichment depends, under otherwise identical conditions,

only on the difference between the atomic weights of the isotope being enriched and \(^{39}\mathrm{K}\). If \(^{41}\mathrm{K}\) is the radioactive isotope, then the radioactivity of the heavy fraction will increase to the same extent as the enrichment of the fraction in the isotope \(^{41}\mathrm{K}\); if the radioactive isotope is heavier than \(^{41}\mathrm{K}\), then the increase in the radioactivity of the heavy fraction will be greater than its enrichment in the isotope \(^{41}\mathrm{K}\), and, finally, if the radioactive isotope were \(^{40}\mathrm{K}\), we should obtain a smaller increase in radioactivity as compared with the enrichment of the fraction in \(^{41}\mathrm{K}\). Comparison of the radioactivities of different samples with sufficient accuracy presents no difficulty. It was carried out in Hofmann’s laboratory\(^6\) with the aid of a Hofmann electrometer and at the institute in Freiburg with the aid of a Geiger–Müller counter, and showed\(^7\) that the heavy fraction had an activity increased by \(4.4\%\) in comparison with the activity of ordinary potassium. Determination of the atomic weight is a considerably more difficult task. However, the atomic weight of our heavy fraction was determined both in the Munich\(^8\) and in the Harvard\(^9\) laboratories working in this field. Both determinations gave the same values, namely 39.109. The difference between this value and the value of the atomic weight formerly accepted for normal potassium (39.104) is 0.005 units. If this value is taken as the basis of the calculation, as the author did earlier, then an increase in the radioactivity of the heavy fraction is obtained corresponding to its enrichment in the isotope \(^{41}\mathrm{K}\). This leads to the conclusion that the radioactive isotope of potassium is \(^{41}\mathrm{K}\). However, we now know that the atomic weight of ordinary potassium\(^ {10}\) differs appreciably from the value given above and is 39.096. Hence there follows a much greater enrichment for the isotope \(^{41}\mathrm{K}\) (0.013 units) than for the radioactivity, i.e. the radioactive isotope is separated with more difficulty than \(^{41}\mathrm{K}\), and therefore lies closer to \(^{39}\mathrm{K}\) than to \(^{41}\mathrm{K}\). This gives unambiguous proof that the isotope responsible for the radioactivity of potassium is \(^{40}\mathrm{K}\).

Half-life of \(^{40}\mathrm{K}\)

We know the number of \(\beta\)-particles emitted by 1 g of potassium per unit time. From this number it follows that half of the potassium existing at some moment of time decays only after \(1.5 \cdot 10^{13}\) years. It is assumed here that all potassium atoms will sooner or later take part in the decay. If only the atoms of \(^{40}\mathrm{K}\) take part in the decay, then the above-mentioned number of \(\beta\)-particles must be divided by the concentration of \(^{40}\mathrm{K}\) in ordinary potassium. If the concentration of \(^{40}\mathrm{K}\) were extremely small, then the activity would have a very short half-life. In that case the activity of potassium would have disappeared long ago. Therefore the period of \(^{40}\mathrm{K}\) must be considerable. Although we are not in a position to indicate its value, we can nevertheless set limits within which it lies. From the fact that neither Aston\(^ {11}\) nor Bainbridge\(^ {12}\) could prove the presence in the mass spectrum of the potassium isotope of mass 40, it follows that the concentration

\(^{40}\mathrm{K}\) is in any case less than \(1/300\), and, consequently, the half-life is less than \(5 \cdot 10^{10}\) years. Geochemical considerations lead us to the establishment of a lower limit. If we first assumed that the period is \(6 \cdot 10^7\) years, then the content of \(^{40}\mathrm{K}\) in ordinary potassium would be \(4 \cdot 10^{-7}:1\). This value refers to the present time. Millions of years ago the fraction of \(^{40}\mathrm{K}\) would have been much greater, and a billion years ago, when a solid earth’s crust already existed, the mixed element potassium would have consisted chiefly of \(^{40}\mathrm{K}\); we would have had \(^{40}\mathrm{K}\) in an amount 25 times greater than the total quantity of potassium now encountered.

The decay of \(^{40}\mathrm{K}\) according to the equation

\[ {}^{40}_{19}\mathrm{K} = {}^{40}_{20}\mathrm{Ca} + \beta \]

leads to the formation of the most widespread isotope of calcium, \(^{40}\mathrm{Ca}\), and all the \(^{40}\mathrm{K}\) which has decayed over a period of \(10^9\) years must now exist in the earth’s crust in the form of \(^{40}\mathrm{Ca}\). Such enormous quantities of calcium, however, have not been found; the concentration [[unclear: obscured by pasted correction slip]] \(\cdot 10^{-2}\) g per 1 g of the earth’s crust) only slightly exceeds [[unclear: obscured]] \(\cdot 10^{-2}\) g per 1 g). Therefore the period [[unclear: obscured]].

[[unclear: continuation obscured by pasted correction slip]] in ordinary [[unclear]].

[[unclear: beginning of line obscured]] would have been richer [[unclear]] by a much greater radioactivity, [[unclear]] role played by the heat liberated during [[unclear]] decay, played in the thermal balance of the earth. The indication that the heat liberated in the decay of potassium plays a noticeable role had already been made by Holmes and Lawson\(^{13}\). At the present time this heat is, of course, smaller (approximately by a factor of ten) than the heat liberated in the decay of the elements of the thorium and uranium series; however, millions of years ago this ratio was shifted in favor of potassium, and if the half-life of potassium should lie closer to the lower than to the upper of the limits indicated above, then the heat liberated in the decay of \(^{40}\mathrm{K}\) was very considerable. The same applies to the intensity of the \(\beta\)- and \(\gamma\)-radiation emitted by potassium.

Half-life of \(^{40}\mathrm{K}\) and the hardness of the emitted \(\beta\)-radiation

The greater the energy of the emitted \(\alpha\)-radiation, the greater the rate of decay of the elements emitting this radiation. This connection between the energies of \(\alpha\)-particles and rapidity of decay was established by Geiger and Nuttall. Between the energy of \(\beta\)-radiation and the half-life there is an analogous relation, if one compares the energies of the upper limit of continuous \(\beta\)-spectra\(^{14}\). In the \(\beta\)-spectrum of potassium there is still noticeable a component of energy \(700\,000\ \mathrm{eV}\)\(^{15}\), which

corresponds, as experiments with other elements undergoing β-decay show, to a very rapidly disintegrating element. If the radiation of potassium is compared with the radiation of RaE and RaC, then for the half-life period one obtains a value equal to 25 days. However, such a short decay period is in sharp contradiction with the considerations presented above. Recently Klemperer \(^{16}\) pointed out a possibility that makes it possible to clarify this contradiction. In the decay of RaE, RaC, and certain other radioactive elements, the difference between the spins of the nucleus of the decaying atom and of the newly formed atom is \(\pm 1\) \(^{17}\). Klemperer established with sufficient probability that the difference between the nuclear spins of \(^{40}\mathrm{K}\) and \(^{40}\mathrm{Ca}\) is substantially greater and is about 4 units. A large difference in the nuclear spins of the decaying and the formed nuclei reduces the probability of decay, and in order to take this reduction into account, it is necessary to multiply the calculated decay period of 25 days by \(10^4\). The period thus obtained, amounting to about \(10^7\) years, does not contradict the limits for the period established above.

Since the discovery of the radioactivity of potassium by Campbell in 1907, various assumptions have been made regarding its causes; among them it is necessary to note the suggestion expressed by Meitner \(^{18}\). Her considerations are based on the examination of isobaric elements having the same mass at different atomic numbers, for example \(^{40}\mathrm{Ar}\) and \(^{40}\mathrm{Ca}\). Isobars always differ from one another in atomic number by two units; at the same time, the third isobar lying between them is unknown and must be a very unstable element. Likewise, in radioactive series consisting of three isobars, the middle one always has the shortest decay period. On the basis of these considerations Meitner came to the conclusion that the radioactivity of potassium must be ascribed to the unstable and therefore radioactive element \(^{40}\mathrm{K}\).

Summary

Potassium and rubidium are the only radioactive elements with β-decay that lie outside the radioactive families. An explanation of the existence of such isolated elements with β-decay has until now encountered a whole series of difficulties. After the discovery of artificial radioactivity these difficulties disappear. The new radioactive atoms arising under the action of neutrons and similar particles form isolated elements which in most cases decay with the emission of β-rays. In the periods preceding the formation of the earth, along with many other radioactive elements, there also appeared an isotope of potassium with mass 40 and an isotope of rubidium with mass 86; whereas during the time that has elapsed since then, the first of the named elements have had time to decay completely, the second have remained in detectable quantities, which are the cause of the radioactivity of potassium and rubidium.

Our knowledge of the radioactivity of potassium, and in particular the results of the partial separation of potassium isotopes, is in the best agreement with the conclusions stated above.

References

1. Amaldi, D’Agostino, Fermi, Pontecorvo, Rasetti & Segré, Ric. Sci., 2 December 1934.
2. J. v. Hevesy, Nature, 19 January 1935.
3. J. v. Hevesy, l. c.; F. H. Newman and H. J. Walke, Nature, 19 January 1935, p. 98; J. Hurst, Nature, 1 June 1935.
4. J. v. Hevesy and M. Lögsrup, Z. anorg. u. allg. Chem. 171, 1, 1928.
5. J. Brönsted and J. v. Hevesy, Z. physik. Chem. 124, 22, 1922.
6. M. Biltz and H. Ziegert, Physik. Z. 29, 197, 1928.
7. J. v. Hevesy, W. Seith and M. Pahl, Z. physik. Chem., Bodenstein-Festb., p. 309, 1931.
8. J. Hönigschmid and Joubeau, Z. anorg. u. allg. Chem. 163, 93, 1917.
9. J. P. Baxter and Ch. M. Alter, J. Am. Chem. Soc. 55, 3270, 1933.
10. O. Hahn, Atomgewichtsbericht, 1935.
11. F. W. Aston, Mass Spectra and Isotopes, 2nd ed., p. 111, 1933.
12. K. T. Bainbridge, J. Frank. Inst. 212, 3–8, 1931.
13. A. Holmes and R. W. Lawson, Nature (Lond.) 117, 620, 1926.
14. B. W. Sargent, Proc. Roy. Soc. Lond. 140, 659, 1933.
15. Bocciarelli, R. C. 17, 833, 1933.
16. O. Klemperer, Proc. Roy. Soc. Lond. 148, 646, 1935.
17. Cp. G. Gamow, Physik. Z. 35, 533, 1934.
18. L. Meitner, Naturwiss. 14, 719, 1926.