By Prof. L. Kaliambos (Natural Philosopher in New Energy)

July 11, 2015

After my published paper "Spin-spin interactions of electrons and also of nucleons create atomic molecular end nuclear structures" (2008) today it is well known that the correct electron configuration of Helium atom should be given by this image including the following electron configuration: 1s^{2}. The electron is being removed from the same orbital as in hydrogen's case. It is close to the nucleus and unscreened. The value of the first ionization energy (24.6 eV) of helium is much higher than hydrogen (13.6 eV). It is well known that the energy of 13.6 eV is given by applying the Bohr formula, while for the first ionization energy of 24.6 eV of helium so far no one was able to formulate any successful formula.

Indeed, despite the enormous success of the Bohr model and the quantum mechanics of Schrodinger in explaining the principal features of the hydrogen spectrum and of other one-electron atomic systems, so far neither was able to provide a satisfactory explanation of ionizations of elements related to the chemical properties of atoms. Though such properties were modified by the periodic table initially proposed by the Russian chemist Mendeleev the reason of this subject of ionizations of elements remained obscure under the influence of the invalid theory of special relativity. It is of interest to note that the discovery of the electron spin by Uhlenbeck and Goudsmit (1925) showed that the peripheral velocity of a spinning electron is greater than the speed of light, which is responsible for understanding the electromagnetic interaction of two electrons of opposite spin. So it was my paper of 2008, which supplied the clue that resolved this puzzle.

For understanding better such ionization energies see also my papers about the explanation of ionization energies of elements in my FUNDAMENTAL PHYSICS CONCEPTS. Moreover in “User Kaliambos” you can see my new paper of 2008.

According to the experiments the helium ground state consists of two identical 1s electrons with a ground state energy E(He) = -79 eV. The energy ( E_{1}) required to remove one of them is the highest ionization energy of any atom in the periodic table: E_{1} = 24.6 electron volts. The energy (E_{2}) required to remove the second electron is E_{2} = 54.4 eV, as would be expected by modeling it after the hydrogen energy levels. According to the Bohr model (1913 ) and the well-established Schrodinger equation of the quantum mechanics (1926) the He^{+} ion is just like a hydrogen atom with two units of charge in the nucleus. (Z = 2). Since the hydrogenic energy levels depend upon the square of the nuclear charge, the ground state energy E(He^{+}) in eV of the remaining helium electron or of the He^{+} should be given by

E (He^{+}) = (-13.6057 )Z^{2} = (-13.6057)2^{2 } = -54.4 eV

Therefore E_{2} = 0 - E(He^{+ }) = 0 - (-54.4) = 54.4 eV as observed.

However for the calculation of

E_{1} = 24.6 eV = E (He^{+}) - E(He) = -54.4 - (-79)

in the absence of a detailed knowledge about the electromagnetic force between the two spinning electrons of opposite spin many physicist today using wrong theories cannot explain correctly the ground state energy E(He) = -79 eV.

For example under wrong theories based on qualitative approaches many physicists believe incorrectly that the second electron is less tightly bound because it could be interpreted as a shielding effect; the other electron partly shields the second electron from the full charge of the nucleus. Another wrong way to view the energy is to say that the repulsion of the electrons contributes a positive potential energy which partially offsets the negative potential energy contributed by the attractive electric force of the nuclear charge.

Under such false ideas I published in Ind. J. Th. Phys. (2008) my paper “Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures”. (See it in “User Kaliambos”).

Prior to the development of quantum mechanics, an atom with many electrons was portrayed like the solar system, with the electrons representing the planets circulating about the nuclear “sun”. In the solar system, the gravitational interaction between planets is quite small compared with that between any planet and the very massive sun; interplanetary interactions can, therefore, be treated as small perturbations.

However, In the helium atom with two electrons, the interaction energy between the two spinning electrons and between an electron and the nucleus are almost of the same magnitude, and a perturbation approach is inapplicable.

In 1925 the two young Dutch physicists Uhlenbeck and Goudsmit discovered the electron spin according to which the peripheral velocity of a spinning electron is greater than the speed of light. Since this discovery invalidates Einstein’s relativity it met much opposition by physicists including Pauli. Under the influence of Einstein’s invalid relativity physicists believed that in nature cannot exist velocities faster than the speed of light.(See my FASTER THAN LIGHT).

So great physicists like Pauli, Heisenberg, and Dirac abandoned the natural laws of electromagnetism in favor of wrong theories including qualitative approaches under an idea of symmetry properties between the two electrons of opposite spin which lead to many complications. Thus in the “Helium atom-Wikipedia” one reads: “Unlike for hydrogen a closed form solution to the Schrodinger equation for the helium atom has not been found. However various approximations such as the Hartree-Fock method ,can be used to estimate the ground state energy and wave function of atoms”.

It is of interest to note that in 1993 in Olympia of Greece I presented at the international conference “Frontiers of fundamental physics” my paper “Impact of Maxwell’s equation of displacement current on electromagnetic laws and comparison of the Maxwellian waves with our model of dipolic particles ". The conference was organized by the natural philosophers M. Barone and F. Selleri, who awarded me an award including a disc of the atomic philosoppher Democritus because in that paper I showed that LAWS AND EXPERIMENTS INVALIDATE FIELDS AND RELATIVITY .(EXPERIMENTS REJECTING EINSTEIN) At the same period I tried to find not only the nuclear force and structure but also the coupling of two electrons under the application of electromagnetic laws. For example in the photoelectric effect the absorption of light contributed not only to the increase of the electron energy but also to the increase of the electron mass because the particles of light have mass m = hν/c^{2} .( See my DISCOVERY OF PHOTON MASS ).

However the electron spin which gives a peripheral velocity greater than the speed of light cannot be affected by the photon absorption. Thus after 9 years I published my paper “Nuclear structure is governed by the fundamental laws of electromagnetism" (2003) in which I showed not only my DISCOVERY OF NUCLEAR FORCE AND STRUCTURE but also that the peripheral velocity (u >> c) of two spinning electrons with opposite spin gives an attractive magnetic force (F_{m}) stronger than the electric repulsion (F_{e}) when the two electrons of mass m and charge (-e) are at a very short separation ( r < 578.8 /10^{15} m ). Because of the antiparallel spin along the radial direction the interaction of the electron charges gives an electromagnetic force

F_{em }= F_{e} - F_{m} .

Therefore in my research the integration for calculating the mutual F_{em} led to the following relation:

F_{em }= F_{e} - F_{m} = Ke^{2}/r^{2} - (Ke^{2}/r^{4})(9h^{2}/16π^{2}m^{2}c^{2})

Of course for F_{e} = F_{m} one gets the equilibrium separation r_{o }= 3h/4πmc = 578.8/10^{15} m.

That is, for r < 578.8/10^{15} m the two electrons of opposite spin exert an attractive electromagnetic force, because the attractive F_{m} becomes stronger than the repulsive F_{e} . Here F_{m }is a spin-dependent force of short range. As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the Pauli principle, which cannot be applied in the simplest case of the deuteron in nuclear physics, because the binding energy between the two spinning nucleons occurs when the spin is not opposite (S=0) but parallel (S=1).

According to the experiments in the case of two electrons with antiparallel spin the presence of a very strong external magnetic field gives parallel spin (S=1) with electric and magnetic repulsions given by

F_{em }= F_{e} + F_{m}

So, according to the well-established laws of electromagnetism after a detailed analysis of paired electrons in two-electron atoms I concluded that at r < 578.8/10^{15} m a motional EMF produces vibrations of paired electrons.

Unfortunately today many physicists in the absence of a detailed knowledge believe that the two electrons of two-electron atoms under the Coulomb repulsion between the electrons move not together as one particle but as separated particles possessing the two opposite points of the diameter of the orbit around the nucleus. In fact, the two electrons of opposite spin behave like one particle circulating about the nucleus under the rules of quantum mechanics forming two-electron orbitals in helium, beryllium etc. In my paper of 2008, I showed that the positive vibration energy (Ev) described in eV depends on the Ze charge of nucleus as

Ev = 16.95Z - 4.1

Of course in the absence of such a vibration energy Ev it is well-known that the ground state energy E described in eV for two orbiting electrons could be given by the Bohr model as

E = (-27.2) Z^{2}.

So the combination of the energies of the Bohr model and the vibration energies due to the opposite spin of two electrons led to my discovery of the ground state energy of two-electron atoms given by

E = (-27.2)Z^{2} + (16.95 )Z - 4.1

For example the laboratory measurement of the ionization energy of H^{-} (hydrogen with two electrons) yields an energy of the ground state E = - 14.35 eV. In this case since Z = 1 we get E -27.2 + 16.95 - 4.1 = -14.35 eV. In the same way writing for the helium Z = 2 we get

E = - 108.8 + 32.9 - 4.1 = -79 eV

which is equal to the laboratory measurement. In the same way we can calculate the ground state energies for the Z = 3 : Li^{+} ion , Z = 4 : Be^{2+} beryllium ion, and Z = 5 : B^{3+} boron.

The discovery of this simple formula based on the well-established laws of electromagnetism was the first fundamental equation for understanding the energies of many-electron atoms, while various theories based on qualitative symmetry properties lead to complications.

**CONCLUSIONS**

To explain the ionization energy E_{1} = 24.6 eV one must use for the He^{+} the well known formula of the Bohr model E(He^{+}) = (-13.6) Z^{2 }and for the ground state energy of He my formula E(He) = (-27.2) Z^{2 }+ 16.95Z - 4. That is

E_{1 }= E(He^{+}) - E(He) = (-13.6057)Z^{2 }- [ (-27.2)Z^{2 }+ 16.95Z - 4.1]

Thus for Z = 2 one gets

E_{1 }= -54.4 - (- 79 ) = 24.6 eV .