On the Composition of the Atomic Nucleus in Connection with Its Decay

(W. Kossel. Über die Zusammensetzung des Atomkerns und seine Neigung zum Zerfall. Phys. ZS. 20 p. 265, 1919).

In the periodic system of the elements it is very often the case that elements differing in ordinal number by 2 units differ in atomic weight by 4. The result is a picture as though, in the transition from one element to another, a helium nucleus (having weight 4 and charge 2)¹ were emitted from its nucleus. Since this picture is common to a very large number of elements, the author makes the assumption that the nuclei of the elements consist, either exclusively or predominantly, of \(He\) nuclei²), and considers the consequences of this hypothesis.

For a number of elements belonging to the first members of the periodic system, Kossel’s rule is well fulfilled.

This series thus consists only of \(He\) nuclei.

Proceeding further, we meet an element which ought to consist of 9 \(He\) nuclei, but no such element occurs in nature. There are 2 elements that have a nucleus consisting of 10 \(He\) nuclei, namely \(Ca\), consisting of 10 nuclei and having ordinal number 20, and argon, having ordinal number 18. Kossel assumes that in argon, besides the \(He\) nuclei, which give 20 positive charges, there are 2 electrons in the nucleus, so that

¹) The numbers of positive charges correspond to the ordinal number of the element in the periodic system.

²) As Fajans shows (K. Fajans. Radioaktivität. 1919), the atomic weights of the elements are of a value close to either \(A = 4n - 3\) (azote is an exception, having atomic weight equal to \(A = 4n + 2\), and beryllium, having atomic weight \(A = 4n + 1\)).

in all there is obtained the number of positive charges and, consequently, the ordinal number 18.

Generally speaking, if Kossel’s rule is regarded as general, then the number of electrons occurring in the nucleus must be equal to \(Z=\dfrac{A}{2}-N\) (\(A\)—atomic weight, \(N\)—ordinal number).

This quantity \(Z\), as Kossel finds, has a definite functional connection with the atomic weight, and with increasing \(A\), \(Z\) also increases. At the beginning of the periodic system a number of elements contain no electrons in the nucleus (\(Z=0\)), and in the decay of the atom no emission of \(\beta\)-particles can occur. Only beginning with atomic weight 40 does the possibility arise of emission of \(\beta\)-rays, and here indeed there is encountered for the first time an element giving such radiation, namely \(K\). The series \(K\), according to Kossel, depending on the isotope of it, with atomic weight 43, is expressed thus:

\[ \begin{array}{cccc} & \beta & \beta & \alpha \\ K & \longrightarrow Ca & \longrightarrow Sc & \longrightarrow K \\ 43 & 43 & 43 & 39 \end{array} \]

As is easy to understand, \(K\) (43) and \(K\) (39) must have one and the same number of charges in the nucleus and, consequently, exactly the same number of electrons surrounding them, which determine their chemical properties, and must be identical. For the element their chemical and optical properties must be identical.

We must assume, in order to obtain the true atomic weight of \(K\), that the heavier component \(K\) (39) contains a very heavy isotope \(K\) (43) in the amount of \(\dfrac{1}{40}\). \(Ca\), written in the preceding scheme, must be the heavy isotope of \(Ca\). To represent the relation of \(Z\) and \(A\), Kossel gives this formula, which approximates the experimental ratios fairly well:

\[ (Z-28)^2 = 0{,}04A^2 + 734 \]

Comparing further the isotopes of radioactive elements with one another, Kossel comes to the conclusion that “the relatively greater the content of electrons in the atom \(\left(\dfrac{\text{number of }\beta\text{-particles}}{\text{number of }\alpha\text{-particles}}=\dfrac{Z}{A}\right)\), the more readily decay of the nucleus with emission of \(\beta\)-rays occurs and the less probable is the emission of \(\alpha\)-rays.”

As an example one may cite the uranium series. The member of this series with the greatest content of electrons is \(Ur\,X_1\); it emits \(\beta\)-rays and its period is \(\tau=23{,}6\) days. The next member of the series already emits \(\alpha\)-rays and decays very slowly (\(Th,\tau=2{,}5\,10^{10}\) years),

P. Lazarev.