atoms, in which there is the lower phase velocity of electromagnetic waves that exhibit greater instability. Use of
this result will be discussed just a little bit later.
The nuclear binding energy per nucleon slightly decreases with increasing atomic number (starting from the
first radioactive element bismuth, 83Bi, 7.848 MeV, to the ununoctium, 118Uuo, 7.074 MeV, about 0.31% de-
crease for each of the 35 atoms in that area ). Physically this means that the boundary between stable and
unstable areas is not emphasized. Mathematically it allows that between the two areas there exists so-called
transition area, Figure 5. This is, at the moment, the most accurate way to determine the boundary between sta-
ble atoms and the others. Indeed, the first unstable atom must be located on that border. This is a key fact to de-
termine the structural constant s0 of the atom.
Before calculating, we observe the first derivative F ‘(χ) of the curves of normalized phase velocity F(χ) of
electromagnetic waves in an atom (Figure 5). When this derivative is greater than 1, it means that the phase ve-
locity rapidly declines, that is a zone of unstable atoms (2 < χ < 2.1295317). It should be noted that the situation
χ ≤ 2 is theoretically impossible because then there is no Lecher’s line.
When the second derivative F’’(χ) of the normalized phase velocity F(χ) is greater than 1, it means that the
phase velocity starts to rapidly decline (Figure 5), this is a transition zone (2.129 531 7 < χ < 2.382 788).
The border crossing from the transition zone to the stable zone (i.e., χ0 = 2.382 788), in accordance with the
experiments, , is closest to the bismuth atom. Bismuth atom (83Bi) is the first unstable atom, in the entire
chain of stable atoms, which ends with lead (82Pb). The corresponding value of the structural coefficient in that
place is σ(χ0) = 0.825402, Figure 5. Bismuth is a chemical element with atomic number Z = 83, with half–life
more than a billion times the estimated age of the universe. Even though charges in reality take discrete values
(e, 2e, 3e, Ze), theoretical value of Z in Equation (49) can be within the range Zth = 83 ± 1/2. Thus, according to
Equation (49) we get the structural constant of the atom [0.825402 × (83 ± 1/2)]1/2, i.e., 8.252 < s0 < 8.302, with
a mean value 8.277 and with sample standard deviation ±0.035355 or as a percentage s0 = 8.277 ± 0.43%. Com-
paring with the fine structure constant we get s0 = 8.277 56, which is consistent with the calculation performed
here (the relative difference is less than 0.0068%).
6. System of the Elements
After calculating the structural constants s0 the structural coefficient
of each element can be determined. For
this purpose we use Equations (46) and (49), Figure 6, i.e.,
It can be seen that there is a maximal atomic number, 137, just as it is defined in Equation (75). Recently dis-
covered element (Z = 118) is ununoctium [Joint Institute for Nuclear Research (JINR) by Yuri Oganessian and
his group in Dubna, Russia, 2002].
A century well-known behavior of hydrogen atoms describing Equations (70) and (72) if we put n±1 = n+1 (in
the case of n±1 = 1 we get Lyman series, in case of n±1 = 2 Balmer series, n±1 = 3 Paschen series, n±1 = 4 Brackett
series, n±1 = 5 Pfund series).
Interestingly, the same Equations (70) and (72) describe behavior of neutron, hyperon Λ0 and hyperon Ξ0 if
we put n±1 = n–1 (i.e., n±1 = 1/125.886339 for neutron n0, n±1 = 1/137.03543 for hyperon Λ0, n±1 = 1/137.03587
for hyperon Ξ0). This is the reason that all three of these particles are in the same place as hydrogen (Figure 6),
To the similar results regarding the elementary particles otherwise on original way came Giuseppe Bellotti,
[22,23]. He was also given new periodic classification of the elements on the basis of standing waves in the
atom, using wave equation of potentials of the electron and positron, similar to the Equation (77) of electric and
magnetic fields in this paper.
Maxwell’s equations, together with the Lorentz equations, proved to suffice for the construction of a model of
the atom. This model is made by analogy with the transmission line (Lecher’s line). Using this model laws