By Prof.Lefteris Kaliambos (Λευτέρης Καλιαμπός) Τ.Ε. Institute of Larissa Greece.( May 2014)
Despite the enormous success of the Bohr model (1913) and the Schrodinger equation in three dimensions(1926) in the one-electron atoms based on the proton-electron interaction of electromagnetic laws, neither was able to provide a satisfactory explanation of the two-electron atoms (electron-electron attraction) even in the simplest cases of the Hydrogen anion and the Helium atom. Unfortunately Heisenberg and Dirac in 1926 under the influence of the invalid Einstein’s relativity abandoned the electromagnetic laws of the spinning electrons and introduced qualitative approaches of the so-called “exchange interaction”. In 1925 the discovery of the electron spin showed that the peripheral velocity of the electron spin is greater than the speed of light ( u >> c ), which means that two electrons of opposite spin at very short interelectron separations exert stronger magnetic attraction Fm than the electric repulsion Fe.
It is indeed unfortunate that the discovery of the electron spin met much opposition by physicists, including Pauli, who suggested his qualitative “exclusion principle”, which cannot be applied in the simplest nuclear structure (Deuteron). Under this crisis of atomic physics and the later crisis in nuclear physics, due to the discovery of the assumed uncharged neutron (1932), I prepared in 2002 my paper “ Nuclear structure is governed by the fundamental laws of electromagnetism” which contains also the electron-electron attraction of opposite spin in atomic orbitals. The paper was presented at the 12th Symposium of the Hellenic Nuclear Physics Society (2002) and published in Ind.J. Th. Phys. (2003). On the other hand I showed that the enormous peripheral velocity u of the electron spin (u >> c) cannot be affected by the absorptions of photons. Whereas in my discovery of the PHOTON -MATTER INTERACTION I showed that the absorption of photons mass and energy by electrons is responsible for the increase of the electron mass in accelerators leading to the velocity υ < c. (See my HELIUM ATOM in my new FUNDAMENTAL PHYSICS CONCEPTS ).
Therefore the enormous peripheral velocity in two electrons of opposite spin at short distances under the application of the Biot-Savart Law gives a magnetic attraction stronger than the electric repulsion of the Coulomb law able to explain the energies of two-electron atoms and the bonds of nuclei. That is, Einstein’s relativity which in general forbids greater velocities than the speed of light did much to retard the progress of atomic and molecular physics. ( See my LAWS AND EXPERIMENTS INVALIDATE FIELDS AND RELATIVITY ) . In 2008 I published in Ind J. Th. Phys. (2008 ) my paper “Spin-spin interactions….structures” showing that two electrons of opposite spin exert electromagnetic attraction Fem able to explain the electron configurations in atoms and molecular bonds. I also presented the paper at the16th Hellenic symposium on Nuclear Physics (2006) . Here you see my following Abstract.
16th Hellenic Symposium on Nuclear Physics, University of Athens, May 26-27, 2006
SPIN-SPIN INTERACTIONS OF ELECTRONS AND ALSO OF NUCLEONS CREATE ATOMIC MOLECULAR AND NUCLEAR STRUCTURES
ABSTRACT: Fundamental interactions of spinning electrons at an interelectron separation less than 578.8 fm yield attractive electromagnetic forces with S=0 creating vibrations under a motional emf. They explain the indistinguishability of electrons and give a vibration energy able for calculating the ground-state energies of many-electron atoms without using any perturbative approximation. Such forces create two-electron orbitals able to account for the exclusion principle and the mechanism of covalent bonds. In the outer subshells of atoms the penetrating orbitals interact also as pair-pair systems and deform drastically the probability densities of the quantum mechanical electron clouds. Such a dynamics of deformation removes the degeneracy and leads to the deviation from the Bohr shell scheme. However in the interior of atoms the large nuclear charge leads to a spherically symmetric potential with non interacting pairs for creating shells of degenerate states giving an accurate explanation of the X-ray lines. On the other hand considerable charge distributions in nucleons as multiples of 2e/3 and -e/3 determined by the magnetic moments, interact for creating the nuclear structure with p-n bonds. Such spin-spin interactions show that the concept of the untisymmetric wave function for fermions is inapplicable not only in the simple p-n systems but also in the LS coupling in which the electrons interact from different quantum states giving either S=0 or S=l.
THE GROUND STATE ENERGY OF THE HYDROGEN ANION
In the absence of a detailed knowledge of the electron-electron electromagnetic attraction Fem one observes a great confusion about the simplest atoms of Hydrogen anion and Helium atom. For example in “Helium - WIKIPEDIA” (electron configuration) one sees that the two electrons of opposite spin occupy the same orbital but they are placed far apart, though the experiments showed that there is a strong tendency to pair off electrons which also give zero magnetic field and are responsible for the covalent bonds in molecules. An obvious confusion is observed in Google (images of the Helium atom), because in many cases the two electrons are placed far apart in the same orbital, while in other cases one sees the electrons placed in two different sub-orbitals so as to keep them as far apart as possible.
Looking also the images of the negative hydrogen ion (hydrogen with two electros) on can observe the same confusion. So to overcome this crisis we present here the electromagnetic attraction
Fem = Fe - Fm
at an interelectron separation R on the spinning electrons with mass M and charge e of opposite spin after the application of the Coulomb and the Biot –Savart laws. In my FORCE AND STRUCTURE OF NUCLEUS one can see how I derived the equation (52)
Fem = Fe - Fm = K e2 / R2 - ( K e2 / R4 )( 9 h2/16 π2 M 2 c2)
So for Fe = Fm one gets Ro = 3h / 4π Μ c = 0.5788 / 10 12 m
That is for R < Ro the electrons exert an attractive electromagnetic force Fem . As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the exclusion principle. Note that in the presence of an external magnetic field the electrons operate with S = 1 giving
Fem = Fe + Fm
which cannot allow such a pairing of electrons. Whereas for two paired electrons of opposite spin at R < Ro a motional EMF produces vibrations of the two electrons. As a result the electrons under such vibrations seem to be indistinguishable particles, restricted between two potential barriers. So they behave like one particle forming two-electron orbitals. After the ionizations a detailed analysis showed that the vibration energy Ev in eV is given by
Ev = 16.95Z - 4.1 where Z is the number of protons.
Thus, in the absence of such a vibration energy the ground state energy of an atom with Z protons and two electrons in the ground state (1s2) according to the Bohr model should be given by
E = 2(-13.6)Z2 because the two electrons behave like one particle.
As a result the total energy in eV of the ground state will be
E = -27.2 Z 2 + (16.95Z - 4.1)
Under this discovery the energy of the ground state energy of the negative hydrogen ion or hydrogen anion (atom with Z =1 having two electrons) is
E = -27.2 +16.95 - 4.1 = - 14.35 eV which is the experimental value.
That is, for the electron configuration of the negative hydrogen ion (1s2) we may use the same image of the electron configuration 1s1 of the “Hydrogen-WIKIPEDIA” because in the same position is a pair of two electrons. Since the two electrons behave like one particle we apply the same Schrodinger equations as those of the one-electron atoms for the ground state energy.
In other words, in the quantum mechanics, we may use the same image of the “Hydrogen atom-WIKIPEDIA” which shows the first orbital s with l = 0. (principal quantum number n = 1, l = 0), because the pair of two electrons in the negative hydrogen ion replaces the one electron of the ordinary hydrogen.
In the same way the ground state energy of the Helium atom with Z = 2 having two electrons is
E = (-27.2)4 + (16.95) 2 - 4.1 = -79 eV which is the experimental value.
Since the one electron of the positive helium ion behaves like the one electron of the ordinary hydrogen, then in the same way the two electrons of the helium atom behave like the two electrons of the negative hydrogen ion leading to the quantum mechanics of the two-electron orbitals.