the isoelectronic series and their ionized states
The following figure shows above polynomials of Figure 1 in linear form. In the ordinate the square root of the ionization energy is plotted in electron volts (eV). From the polynomials of the second degree, the ones Listzin developed, finally become the Mosleyeschen degrees. The relationship between the atomic number and the square root of the ionization energy is not completely linear but the "degrees" show a slightly convex curvature; a fact that already can be seen in this illustration.
For the analyses that are made in this work, the convex structure of the measured values can be neglected, since only the regularities of the isoelectronic series should be considered. Just: the convex nature of the Moseley charts also means that the polynomials which are described by Lisitzin, are not exact polynomials.
Obviously, the first rows follow the linear relationship more clearly than the subsequent rows of larger atomic numbers. The more you move to the right, approaching the larger atomic numbers, the more definite is the convexity of the linear transformation "degrees".
In 1930 Werner Braunbeck has published a work in which he points out the linear relationship between the square root of the ionization energy and the atomic number of the corresponding elements. Thisis motivated by the Moseley Set. At that time there weren’t enough ionization measurements available. So Mr. Braunbeck stops his observations at the 19th element, because "as you know, from the element K (the 19. Element) on the inconstancies regarding the structure of the atoms grows." (Quote from his work). Let me point put here that the regularity of the filling of the shells is caused by the modified periodicity.
So Mr. Braunbeck still assumed that the increase of the degrees within a group is constant. Mrs. Lisitzin showed that the increase of the paraboles - and this also means the degrees of increases within a group then - in each group ends at a maximum value.
Furthermore he realized that the performance of ionization energies of the second and third periods are analog. The first two ionization energies form a subgroup. Apart from this, the six remaining can be devided elements into two groups. It two threesomes, in which the ionization energy increases; this refers to the observation of the s and the p sub-shell.
The result of Mr. Braunbeck’s work is that the shielding performances are linear, referred to the atomic number. From the parallelism of lines, Mr. Braunbeck derives that also the change of the shielding within one period - referred to the isoeletronic rows - is identical.
Further analyzes are conducted by the Lisitzinschen polynomials, because they describe the really measured values.