A Graphical Study of the Stability Relations of Atom Nuclei

Graphical Study of the Electrical Properties of Atomic Nuclei and their Relation to Stability.—The properties considered are: $P$ the number of positive electrons in the nucleus, which is taken to be numerically equal to the atomic weight, $M$ the net positive charge which is equal to the atomic number, $N$ the number of negative electrons which is equal to ($P-M$), $\left[\right(\frac{N}{P})-\frac{1}{2}]$ the excess of the relative negativeness $\frac{N}{P}$ over the minimum ½, and $n$ the isotopic number which is equal to ($P-2M$) and also to ($N-M$). The relations between each of these five quantities and each of the others for the various atomic nuclei are shown in ten two-dimensional plots which clearly bring out the stability relations and are of particular interest because of the limited region in each plot where atoms are found. Except in the case of hydrogen and of the helium isotope $P=3\mathrm{}$, $\frac{N}{P}$ is never less than ½ and $\frac{M}{P}$ is never greater than ½; in fact for 85 per cent. of the atoms composing the crust of the earth, both these ratios are equal to ½ and $n$ is equal to zero. As the atomic number, that is the net positive charge increases, the relative negativeness necessary to stability increases above ½, more and more; that is, as alpha particles are added extra cementing electrons are required to overcome the increasing mutual repulsion of the positive units of the nucleus. An alpha ray transformation does not change $n$ but increases $\frac{N}{P}$, while a beta ray change decreases $n$ by 2 units and also decreases $\frac{N}{P}$; we therefore find that in each group of isotopes, the ones with larger values of $\frac{N}{P}$ show greater beta-ray and less alpha-ray instability. Stability considerations also help explain the fact that the number of isotopes is on the whole smaller for the lighter atoms. The curves bring out other interesting relations. The number of isotopes is larger for even than for odd numbered elements, especially for $M\geqq 30$. Also for most atoms, $M$, $n$ and $P$ are either all even or all odd, but $N$ is usually even. The curve for the frequency of occurrence of atoms as a function of $n$ shows periodic maxima four units apart, while as a function of $M$ (or of $N$) the periodic maxima are two units apart. These regularities make it possible to predict the existence of the more abundant isotopes of elements whose mean atomic weights are accurately known; for instance, in the cases of lithium and boron predictions made in 1920 were later verified by Aston and by Dempster.