Abstract:
For investigation of equilibrium conditions of electrons in an atom, and Ionization
Energies of Elements, a simplified deterministic static model is proposed.
The electrons are initially uniformly and sparsely arranged on the outer
surface of nucleus. Then, by taking into account the nucleus-electron interaction
(attractive and repulsive) and the mutual electron-electron repulsions,
and by a simple step-by-step nonlinear static analysis program, all the electrons
are found to equilibrate on the outer surface of the same sphere, which
is concentric and larger than nucleus. In a second stage, starting from an equilibrium
sphere of electrons, one of the electrons is subjected to gradual forced
removal, radially and outwards with respect to nucleus. Within each removal
step, the produced work increment is determined and the increments are
summed. When no more significant attraction is exerted by nucleus to removed
electron, the total work gives the Ionization Energy. After removing of
single electron, the remaining electrons fall on a lower shell, that is, they equilibrate
on the outer surface of a smaller concentric sphere. For nucleus-electron
interaction, an L-J (Lennard-Jones) type curve, attractive and
repulsive, is adopted. When the parameter of this curve is n > 1.0, the Ionization
Energy exhibits an upper bound. As parameter n increases from 1.0 up to
2.0, the attractive potential of L-J curve is gradually weakened. The proposed model is applied on Argon. It is observed that, as the number of electrons increases,
the radius of equilibrium sphere increases, too, whereas the attractive
nucleus-electron potential is reduced; thus the Ionization Energy is reduced,
too. Particularly, as the number of electrons and the radius of equilibrium
sphere exceed some critical values, the above two last quantities exhibit abrupt
falls. A regular polyhedron is revealed, which can accommodate Elements up
to atomic number Z = 146, that is 28 more than Z = 118 of existing last Element,
as guide for initial locations of electrons in the above first program.
