# The second degree polynomials of the isoelectronic

In this chapter, some of the functions for the isoelectronic series are written out.

Mrs. Lisitzin`s work shows that the isoelectronic series can be described by second degree polynomials.

As already shown above, it is imperative to the isoelectronic series:

In principle, this notation is up to Moseley's presentation for the X-ray spectra, only that measured energy is described here (not the root of the ionization energy).

The first period of the periodic table includes two rows of identical gradient which is expressed by the coefficient alfa = 13,6 . This also was determined by Werner Braunbeck. The first isoelectric row is the hydrogen row and can be written as;

X_n means to be the atomic number of the n-th element. In this row, X_n starts with number one and ends with the biggest element.

The numerical value of the coefficient corresponds with the ionization energy of the hydrogen atom. In the case of the hydrogen atom, the parameters beta and gamma are number zero.

The second row of the first period is the helium series. It starts with the ionization of neutral helium, with one member less than the hydrogen line. The following represents this series:

X_n start with two and ends with the biggest element. So the first two rows of the first period are fixed.

The second period starts with the lithium series which is the third element of the periodic table.

The essential difference between the rows of the second period is the value of the parameter α of isoelectric rows. α can be written as:

X_n Starts with the 3rd element and ends –like the other rows – with the biggest Element.

The fourth row is the isoelectric Beryllium row, where the continuing development of the parameters goes on.

The parameter α in the second period grows weakly, but noticeable. Regarding beta and gamma there cannot be made any comment at the moment.

The next series is the isoelectronic series of Bor.

Again the continuing development of the parameters goes on until the end of period two.

The third period begins with the sodium series, the 11th element. The eleventh row is written as:

The following polynomials are characterized by the parameter α which can be written as

The parameters beta and gamma, however, show the same behavior as in the second period.

In the next section the Moseley diagrams will be described briefly. After that, the parameters alfa, beta and gamma (polynoms of Liszitin) will be described and analyzed regarding their development.