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By prof. L. Kaliambos (Λευτέρης Καλιαμπός) Τ. Ε. Institute of Larissa Greece ( March 2014 )

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The ionization energies of the Helium is 24.6 eV (1st),  and 54.4  eV (2nd). So the ground state energy of the Helium  having two electrons of opposite spin  is -24.6 – 54.4 = -79  eV which cannot be calculated by using the qualitative approaches of the so-called symmetry properties of atomic theories. Prior to the development of quantum mechanics an atom was portrayed like the solar system, with the electrons representing the planets circulating about the nuclear “sun”.  Even in the simple Bohr model , that analogy is inappropriate. For example the Bohr relation E = -27.2 Z2   for Z =2 gives the wrong result  E = -108.8 eV. 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. In the Helium atom, however the electromagnetic interaction between the spinning electrons and between an electron and the nucleus are almost of the same magnitude, and a perturbation approach is inapplicable.   

In the absence of a detailed knowledge about the magnetic attraction between the electrons of opposite spin, first, it was supposed that the two electrons of the Helium  are on the opposite sides of the nucleus and moving on the same circular orbit. Solving the  equations, the ground state energy (n = 1)  differs from the experimental value. Then  it was supposed another model in which two same-shaped orbital planes are perpendicular to each other. In this model, the electron 1 moves on the X-Y plane, the electron 2 moves on the X-Z plane but the calculations also led to complications. This means that there were used   various different equations approximately without any success because physicists abandoned the natural laws in favor of complicated hypotheses.

Despite the enormous success of the Bohr model (1913) and the Schrodinger equation (1926) based on the well-established electromagnetic laws in explaining the principal features of the spectrum of one-electron atomic systems, neither was able to provide a satisfactory explanation of the two-electron atoms with two-electron orbitals of opposite spin. Note that the discovery of the electron spin (1925) gives a peripheral velocity greater than the speed of light. Therefore under the influence of the invalid relativity physicists developed theories of the so-called qualitative symmetric properties including not the real magnetic attractions between the two electrons  of opposite spin . In fact, in my paper “Nuclear structure is governed by the fundamental laws of electromagnetism (2002)  I discovered that the velocity (u>>c) of the spinning electrons of opposite spin gives a magnetic attraction of short range which overcomes the electric repulsion of long range at short inter-electron separations.

 It is well-known that in 1925 Goudsmit and Uhlenbeck discovered the electron spin

S = [s(s+1)]0.5 (h/2π)   where s  = 1/2

which gives a peripheral velocity u greater than the speed of light (u >> c ) invalidating Einstein’s relativity. Taking into account my discovery of the PHOTON-MATTER INTERACTION I discovered also that the velocity u >>c cannot be related with the absorption of photons in the PHOTOELECTRIC EFFECT OF LAWS . Such an enormous velocity (u >> c ) for two electrons of opposite spin (S=0) gives stronger magnetic attraction than the electric repulsion at a very short  inter-electron separation r  <  578.8/1015 m.

 Thus, in the absence of such a detailed knowledge great theoretical physicists under the strong influence of the invalid relativity abandoned the natural laws of electromagnetism and developed theories with qualitative approaches.  Following the  work, of Pauli (1925) who suggested the qualitative exclusion principle for two electrons of opposite spin, physicists studied the properties of many-electron atoms. Though their efforts shed much light on the subject, the fundamental nature of the forces that contributes to the structure of two-electron atoms remained mysterious. For example Heisenberg tried to explain the ground state energy of the simplest Helium atom but without success.

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N.C.S.R. "Demokritos" (2002)


In other words Einstein’s CONTRADICTING RELATIVITY THEORIES   did much to retard not only the progress of nuclear physics but also the progress of atomic physics. Under this physics crisis I published my papers “ Nuclear structure is governed by the fundamental laws of electromagnetism” (2003) and  “Spin-spin interaction of electrons and also of nucleons create atomic molecular and nuclear structures”.(2008). In that papers I showed theDISCOVERY OF NUCLEAR FORCE AND STRUCTURE and the DISCOVERY OF TWO-ELECTRON ATOMS .

Note 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).  For example in “Helium atom-WIKIPEDIA” one reads: “Unlike for hydrogen a closed -form solution to the Schrodinger equation for the Helium atom has not been found'”.  Under this crisis of atomic physics and the following crisis in nuclear physics, due to the discovery of  the assumed uncharged neutron (1932), we prepared  in 2002 our paper “ Nuclear structure is governed by the fundamental laws of electromagnetism” which contains also the electron-electron attraction of opposite spin in atomic orbitals. . In 2008 we published in Ind J. Th. Phys. (2008 ) our paper “Spin-spin interactions….structures” showing that two electrons of opposite spin exert attraction able to explain the electron configurations in atoms and molecular bonds.  We also presented the paper at the 16th Hellenic symposium on Nuclear Physics (2006) . Here you see the following Abstract:

“Fundamental interactions of spinning electrons at an inter-electron 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=1.”

 THE GROUND STATE ENERGY OF HELIUM ATOM

The helium ground state consists of two identical 1s electrons. The energy required to remove one of them is the highest ionization energy of any atom in the periodic table: 24.6 electron volts. The energy required to remove the second electron is 54.4 eV, as would be expected by modeling it after the hydrogen energy levels. The He+ ion is just like a hydrogen atom with two units of charge in the nucleus. Since the hydrogenic energy levels depend upon the square of the nuclear charge, the energy of the remaining first electron should be just 4x(-13.6 eV) = -54.4 eV as observed.

The fact that the second electron is less tightly bound it was supposed incorrectly a shielding effect; the other electron partly shields the second electron from the full charge of the nucleus. Its energy can be used incorrectly to model the effective shielding ζ  as follows.

 Second electron (-13.6) ζ2  = -24.6 eV. Thus  ζ = 1.34

 In  the absence of a detailed knowledge of the electron-electron electromagnetic attraction one observes a great confusion about the 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 physics crisis we present here the electromagnetic attraction

Fem  =  Fe  - F

at an inter-electron 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 the FORCE AND STRUCTURE OF NUCLEUS (User Kaliambos ) one can see how we 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  =  578.8 / 10 15   m

That is, for R < Ro the electrons exert an attractive electromagnetic force . So 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. Hence they behave like one particle forming a two-electron orbital. After the ionizations a detailed analysis of many  atoms showed that the vibration energy  Ev  in eV is given by

 Ev = 16.95 Z  - 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)

 For example the energy of the ground state energy of the negative hydrogen ion (atom  with Z =1 having two electrons) is

 E = -27.2 +16.95 - 4.1 = - 14.35 eV which is equal to the experimental value.

That is, for the electron configuration of the negative hydrogen ion (1s2) we may use the same image of the one-electron configuration 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 equal to 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.

 

INTERPRETATION OF THE SINGLET AND TRIPLET ENERGY LEVELS OF HELIUM

According to the  wrong atomic theories based on qualitative approaches of the so-called symmetry properties of the electronic wave function, if one of the two electrons is raised to a higher energy level the energy difference  between singlet states (S=0)  and triplet states (S=1) was based incorrectly on the wrong qualitative symmetry properties. It was supposed incorrectly that the energy is lower in the S=1 state because the electrons tend to avoid one another without any magnetic repulsion of laws ( thereby reducing their electrostatic repulsion).

In fact, we discovered that the electromagnetic repulsion Fem of the two electrons of parallel spin is Fem = Fe + Fm  is stronger  than the electromagnetic repulsion Fem = Fe - Fm of the  two electrons of opposite spin. In this case since the inter-electron separation is greater than 578.8/1015 m one observes an electromagnetic repulsion because the electric repulsion Fe of long range is stronger than the magnetic attraction Fm of short range. 

In other words the 1s12s1 weak repulsion with opposite spin (S =0) contributes to a smaller deformation of the spherical symmetry than that of the 1s12s1 repulsion with S = 1 .  So under the effective ζ0 for the S = 0  and the effective ζ1 for the S = 1 the  energy levels are given by

E(ζ0) = (-13.6)ζ02/22    and  E(ζ1) = (-13.6) ζ12/22

Since the experiments showed that  E(ζ0) = - 3.93 eV     and   E(ζ1) =  - 4.76  eV  one gets

  ζ0 = 1.156    and   ζ1 = 1.183

Here we do not describe the very small energy leves  of the triplet system which are split  by the spin-orbit interaction.

Notice hat for a sufficiently large  n the non- penetrating orbitals of both cases cannot deform  the spherical symmetry, Also at large distances the magnetic force  of short range is very small.

Therefore ζ0 = ζ1 = Z -1 = 2-1 = 1    That is the singlet (S=0) and triplet states (S=1) of the one-electron orbitals for large n behave like the electron orbitals of Hydrogen.

 

CONCLUSIONS

Under the influence of the invalid Einstein’s relativity theoretical physicists abandoned the electromagnetic  laws of the Bohr model and of  the Schrodinger equations. So in vain they tried to solve the problems of two-electron orbitals under fallacious theories based on approximations of perturbation theories. For example in the “Helium atom-WIKIPEDIA” one sees various approximations, which lead to complications such as the Hartree-Fock method, the Thomas-Fermi method, and the Variational method. Under this crisis of atomic physics we took into account the peripheral velocity u>>c of the discovery of the electron spin and applied carefully the laws of Coulomb and Biot-Savard on the spinning electrons. In my paper "Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures" one sees that the applications of electromagnetic laws under the rules of the quantum mechanics lead to the enormous success for describing atomic and molecular structures.