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The concept is further revised in Chemistry book book under Ionization energy and work function.

1.9.1 Background and actual interpretation

The ionization energy has the same significance like ,,the work function” (Wex) defined by Einstein, representing the energy required to remove an electron from his position in the atomic structure. The work function was defined by Einstein for metals; ionization potential is an extension to every known element in periodic system. Ionization, as it is referred to, in this context means the liberating of an electron from an atom. For H which has only a single electron moving around nucleus we will have a single value for the ionization potential. For other elements, a distinct and increasing value of ionization potential is measured from distanced electron to closer electron of nucleus.
In actual theory of atomic structure ionization potential is ignored. The variation of ionization potential of last outer electron is used only as example support for chemical periodicity. The variation of ionization potentials of different electrons from the same element or the variation of ionization potential of the same inner electron from different elements does not present any significance in actual quantum mechanic.

1.9.2 Proposed explanation

It is important to emphasize that ionization potential must play a fundamental role in the atomic structure. This because electrons are arranged in shells, and in every shell again a difference in ionization energy is observed. In quantum mechanic the difference of ionization energy for the electrons on the same shell is given by electron spin energy and eventually interaction between electrons.
In presented theory different value of ionization potential are given due to the different orbits of electrons movements around nucleus.
In our calculus a database with ionization potentials found at following address ... was used.
Without making any supposition about arrangement of electron around nucleus let’s analyze the ionization potential for isoelectronic series. By isoelectronic series we mean the same number of electron but an increasing number of protons respectively neutrons in nucleus. Due to the limited space for display in tab 1 are presented ionization potentials for first 15 elements, but the facts presented for these elements are valid for all elements in periodic system.

Analyzing the ionization potential of first isoelectronic series (one electron around nucleus) we observe a quadratic dependency related to the atomic number Z. The quadratic dependence is easy to be observed for first isoelectronic series but for other series is hidden by a constant factor addition in the energy expression. In order to arrive to a linear dependency we will work with square root of ionization potential and we will make also some simple mathematical tricks.

We define relative ionization potential of kth electron of an element as kth ionization potential divided by ionization potential of hydrogen electron. For example in case of hydrogen the relative potential is 1, and for Helium we have two relative ionization potentials; 1,8 for one electron and 3.99 for the second electron. For other elements the modality of relative ionization potential calculus are the same. In tab 2, are presented square root of relative ionization potentials for the first 15 elements.
With this simple modification, the distribution of square root of relative ionization potential for first electron (first isoelectronic series) in different atoms is linearly related to the atomic number Z and this is observed from tab. 2, even without a graphical representation.

The variation of square root of relative ionization potentials for first 36 isoelectronic series related to the atomic numbers Z is presented in fig 1.17 and 1.18; fig. 1.17 is a detailed part of 1.18 and is presented for a better visualization of ionization potential variations. The same linear dependence is observed also for higher isoelectronic series, but a picture with such amount of information doesn’t give any supplementary information. In pictures the isoelectronic series are positioned from left to right. For first two isoelectronic series, two parallel lines with the same slope are obtained when the number atomic is increased from helium to lead. The second line representing the energy of second electron in different atoms is a little bit shifted related to the first isoelectronic series due to a factor which represent a new appearing interaction. We can observe also a coupling between energy of first electron and the energy of second electron when we change to different elements (different atomic numbers); the slope of energy variation for first two isoelectronic series is constant from Helium to last element (the checking was made up Z= 90).


As it is observed the linear dependency is respected for every electron from these isoelectronic series and also for higher isoelectronic series.
From the graphical representation of ionization energy we can observe that we have a coupling of electrons in pairs of minimum 2 electrons with the same slope of energy variation. We can observe also a coupling in more pairs of two electrons having the same slope for energy dependency. For example after first pair of electrons, a number of four pairs (eight electrons orbit) present the same slope in energy variation. These distributions of ionization potentials contradict quantum mechanic theory and also wave–corpuscular hypothesis. It is impossible for an electron having a complicated movement, given as a probability, to present a linear dependency of ionization potential. Also this linear dependency contradicts the Heisenberg incertitude relations. 

As consequences we can suppose, for the moment, that ,,adding” one or more electrons to a hydrogenoid atom will have as consequences modification of energy interaction with a simple additional term; the variation is related to the atomic number.
In the same time for the Moseley low new explanation can be formulated. The jump of electron from a superior level to another inferior level, with both energy levels linear dependent on atomic number will produce a photon with an energy proportional with this difference. In conclusion the ecranation factor due to other electrons from atoms, actual accepted by quantum mechanic is wrong and the formulation of Moseley low must be corrected.

In conclusion, we have a simple and easy to follow variation of potential ionization in periodic system, but this variation is impossible to be explained in quantum mechanic theories. In the same time this variation supposes a precise trajectory of electron around nucleus which again contradict wave-corpuscle theory and idea of density of electron probability around nucleus.
The linear dependency of relative ionization potential energy is accurate also for so called d layer and f layer in actual quantum mechanic. The only difference observed in distribution of relative ionization potential for different layer is represented by different slope.
A detailed discussion of these aspects will be made at electron arrangements on multielectron atoms.