| Steady state, k | Orbit type and number | Orbital count, n | Velocity in a pericenter V’n×106 , m×s | Velocity in an apocenter V’a·106, m×s | Pericentral radius, r’п×10-10, m | Apocentral radius, r’а×10-10 , m |
| I | Round | 2,186500611 | 2,186500611 | 0,529177249 | 0,529177249 | |
| II | 1st round 2nd elliptical | 1,093228498 4,080011431 | 1,093228498 0,292931642 | 2,116751219 0,283589719 | 2,116751219 3,949885269 | |
| III | 1st round 2nd elliptical 3rd elliptical | 0,728816306 1,908068681 4,247877841 | 0,728816306 0,278383469 0,125045849 | 4,762707838 1,212793217 0,272382215 | 4,762707838 8,312608374 9,252977104 | |
| IV | 1st round 2nd elliptical 3rd elliptical 4th elliptical | 0,546611523 1,210882086 2,039985368 4,303484883 | 0,546611523 0,246749450 0,146464359 0,069429114 | 8,467047101 2,866620271 1,134367330 0,268862656 | 8,467047101 14,06746452 15,79969878 16,66514681 |
Table 1 (continued)
| Steady state, K | Orbit type and number | Charge count, z' | Length of a large axis
 ×10-10, m
| Length of a small axis
 ×10-10, m
| Full energy, E×10-19, Joules | Orbital period,
 ×10-16, s
|
| I | Round | 1,000026596 | 1,058354498 | 1,058354498 | 21,78687544 | 1,520657574 |
| II | 1st round 2nd elliptical | 1,000006648 1,000013297 | 4,233502438 4,233474988 | 4,233502438 2,116737494 | 5,446501565 5,446573992 | 12,16574593 12,16558416 |
| III | 1st round 2nd elliptical 3rd elliptical | 1,000002954 1,000004432 1,000008865 | 9,525415676 9,525401591 9,525359319 | 9,525415676 6,350267727 3,175119773 | 2,420649477 2,420656632 2,420678093 | 41,05969589 41,05957452 41,05921049 |
| IV | 1st round 2nd elliptical 3rd elliptical 4th elliptical | 1,000001662 1,000002216 1,000003324 1,000006648 | 16,93409420 16,93408479 16,93406611 16,93400946 | 16,93409420 12,70056359 8,467033055 4,233502366 | 1,361611812 1,361613322 1,361616339 1,361625391 | 97,32693805 97,32683021 97,32661453 97,32596751 |
Based on calculations conducted above it is possible to draw the following conclusions. Each orbit is characterized by only two quantum numbers which are k and n. In a hydrogen atom, charge count z is equal to 1 only for the electron which is static to the kernel. For the electrons which are moving on the orbit charge count z is more the 1. For the electrons which are in the same steady state but moving on the orbits with different values of n, lengths of a large axis are different so are the values of full energy. In a hydrogen atom, the parameters of the first Bohr orbit have been experimentally calculated at a very high precision. The parameters of the rest possible orbits can be calculated using equations above at a very high precision either.
In a nonexited atom of the helium, both electrons are in the first steady state and move on the round orbits. The orbital period of the external electron is twice more that the orbital period of the internal electron. Energy consumption to remove an electron from a nonexited helium atom is E = 198310,76 Sn-1 = 39.3933902·10-19 Watt-Second. In this case, the equation (8) takes the following form:
.
Having calculated via this equation the values ze2 = 1.3914422, it is possible to find z'1 = 1.9677965 from 
ratio. Now it is possible to calculate the parameters of the orbits of both electrons in the first steady state with the equations (9-14).
Table 2
Orbits of Electrons In The Helium Atom
| Steady state of second electron | Orbit type and number | Charge count | 
| |
| 
| |||
| Round | 1,9677965 | 1,3914422 | ||
| 1st round | 1,9971808 | 1,2043454 | ||
| 2nd round | 1,9991896 | 1,0882210 | ||
| 3rd round | 2,0001251 | 1,0328602 | ||
| 4th round | 2,0001274 | 1,0328613 | ||
| 5th round | 1,9996570 | 0,9998285 | ||
| 1st round | 1,9996874 | 1,1204559 | ||
| 2nd round | 1,9999251 | 1,0551392 | ||
| 3rd round | 1,9998483 | 1,0289134 | ||
| 4th round | 1,9998489 | 1,0289138 | ||
| 5th round | 1,9997306 | 1,0092539 | ||
| 6th round | 1,9997382 | 1,0092577 | ||
| 7th round | 2,0000089 | 1,0000045 |
Table 2 shows similarly calculated count charges of an electron in the helium atom for the cases when the external electron is in the one of three steady states.
Evidently from table 2, the external electron in the helium atom can have only one round orbit in the first steady state, 4 round and 1 elliptical in the second steady state, and 5 round and 2 elliptical orbits in the third steady state. The first orbit of the electron in the second steady state is very stable. Electron’s transfer from this orbit to the orbit in the first steady state is possible only when the atoms collide [15]. Usually, the helium consists of two kinds of atoms. In some atoms, the external electron is moving on the orbit of the first steady state, and on the first orbit of the second steady state in the others. The first atoms are the ones of the parahelium, and the second atoms are the ones of the orthohelium.
For the ions with the equal number of the electrons but different kernel charges, the following equity is valid:
where: En is the ionization potential of the hydrogen atom, En+1, En, and En-1 are the ionization potentials of the ions of three elements located next to one another, n is the number of the element, k is the number of the steady state of the external elements in the ions. By this formula, the ionization potentials and the values for k have been calculated for 24 elements [12]. There is no principal difficulties for calculating the ionization potentials and the parameters of the electron’s orbits for all elements in the Periodical Table.
Table 3
Atoms’ Ionization Potentials
| Number of Electron | Fluorine | Neon | Natrium | |||
| Ionization Energy E, eV | Ionization Energy E, eV | Ionization Energy E, eV | ||||
| Calculation | Reference | Calculation | Reference | Calculation | Reference | |
| 1102,0 | 1101,8 | 1360,5 | 1360,2 | 1646,2 | 1646,4 | |
| 953,43 | 953,5 | 1195,0 | 1195,4 | 1463,7 | 1464,7 | |
| 185,14 | 185,14 | 239,0 | 239,1 | 299,86 | 299,7 | |
| 157,06 | 157,11 | 207,05 | 207,2 | 263,83 | 264,2 | |
| 114,21 | 114,21 | 157,91 | 157,91 | 208,41 | 208,44 | |
| 87,141 | 87,23 | 126,15 | 126,4 | 172,36 | 172,38 | |
| 62,710 | 62,646 | 97,118 | 97,16 | 138,33 | 138,6 | |
| 34,971 | 34,98 | 63,456 | 63,5 | 98,916 | 98,88 | |
| 17,423 | 17,418 | 40,964 | 41,07 | 71,639 | 71,8 | |
| - | - | 21,565 | 21,559 | 47,287 | 47,29 | |
| - | - | - | - | 5,1391 | 5,138 |
Table 3 shows the calculated and the referenced values of the ionization potentials of the fluorine, the neon, and the natruim atoms. Evidently, the calculated values of the ionization potentials conform well to the reference values.
Chemical and a set of physical properties of the elements are stipulated by the energy of binding external electrons with the atoms. The binding energy, and, therefore, the properties are periodically dependent on the number in the Periodical Table. While comparing the ionization potentials of all atoms [13] with the different kernel charges but with the equal number of the electrons, 12 periods shown in table 5 may be neatly discerned for known elements. Table also shows the 13th period for the elements that possibly exist in the Universe in conditions different from ones in the Solar System.
Table 4
Periodical Law
| Period | Element’s Number In The Period | |||||||||||||
| I | H | He | ||||||||||||
| II | Li | Be | B | C | N | O | F | Ne | ||||||
| III | Na | Mg | Al | Si | P | S | Cl | Ar | ||||||
| IV | K | Ca | Sc | Ti | V | Cr | Mn | Fe | Co | Ni | ||||
| V | Cu | Zn | Ga | Ge | As | Se | Br | Kr | ||||||
| VI | Rb | Sr | Y | Zr | Nb | Mo | Tc | Ru | Rh | Pb | ||||
| VII | Ag | Cd | Jn | Sn | Sb | Te | J | Xe | ||||||
| VII | Cs | Ba | La | Ce | Pr | Nd | Pm | Sm | Eu | Gb | To | Dy | Ho | Er |
| IC | Tm | Yb | Lu | Hf | Ta | W | Re | Os | Jr | Pt | ||||
| C | Au | Hg | Tl | Pb | Bi | Po | At | Rn | ||||||
| CI | Fr | Ra | Ac | Th | Pa | U | Np | Pu | Am | Cm | Bk | Cf | Es | Fm |
| CII | Md | No | Lr | Ku | Ns | |||||||||
| CII |
Table 5 shows how the electron layers are filled in the atoms of the elements of the 13th period. The period may give an idea how the electron layers are filled in the atoms of other elements.
The number of layers in the atom corresponds to the number of the period in which it is located. The maximum possible number of the electrons in the layer is equal to the number of elements in the period in which the layer is filled. In the first layer, both electrons are in the first steady state.
Eight electrons in the second layer are in the second steady state, the electrons of the third and the forth layer are in the third, and the electrons of all other layers are in the forth steady state.
Table 5
Electrons Allocation in the Atoms of 13th Period
| Element Number | Layer Number | ||||||||||||
| k=1 | k=2 | k=3 | k=4 | ||||||||||
In a specified periodical table of elements one period contains two elements, six periods contain 8 elements each, four periods contain 10 elements each, and two periods contain 14 elements each. In some periods, there is the same regularity in the change of the element’s properties with the increase of the number of electrons in the atom’s external layer. Thus, the second and the third periods beginning with alkaline elements; the fifth, the seventh, the tenth, and the thirteenth periods beginning with the elements of the copper group; the fourth; the sixth, the ninth, and the twelfth containing 10 elements each; the eighth and the eleventh containing 14 elements each are similar.
The results of calculations on authors’ equations concur to a high precision with the experimental data. Table 6 shows the values of fundamental physical constants obtained experimentally and calculated with equations below:
; 
: 
:
; 
: 
.
Table 6
Physical Constants
| Constant | Calculation | Experiment |
| Ionization Potential E'H, eV | 13.59829218 | 13.5985 |
| Electron Velocity V'H ∙10-6, meters per second | 2.186500601 | - |
| Constant of Fine Structure 1/α'∞, m-1 | 137.0359895 | 137.0359895 |
| Rydberg’s Constant | 1.097373153 | 1.097373153 |
| Orbital Period for Electron | 1.820657574 | - |
| Plank’s Constant | 6.626075438 | 6.6260755 |
As a source data, the values of four constants have been taken [13]:
Velocity of Light c = 2.99792458×108 mps;
Elementary Charge e' = 1.60217733×10-19 Cl;
electron mass m = 9.10938968×10-31 kg;
Bohr radius r'n = 5.29177249×10-11 m.
For hydrogen atom, bn = 1.000544617.
Table 7
Energies of Spectral Therms of Hydrogen Atom
| Therm of an exited state | Therm energy, cm-1; Therm difference, cm-1 | |
| According to equation (7) | Reference Data | |
| 82258,916 0,365 82259,281 | 82258,921 0,365 82259,286 |
| 97491,617 0,108 97491,725 0,036 97491,761 | 97492,213 0,108 97492,321 0,036 97492,357 |
Table 7 shows the values of therms of a hydrogen atom taken from the reference [14] and calculated with the equation (7). The difference between the calculated and the referenced value appears after the fifth or sixth decimal point. This is because last digits of the therm values are given not experimentally, but calculated by the established principles. The differences of the therms characterizing the fine structure of spectrums according to existent and new theory are equal.
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Information about authors:
Georgy I. Soukhorukov
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e-mail: nil_mu@brstu.ru
Edouard G. Soukhorukov
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Roman G. Soukhorukov
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Issue date: 22 August 2000
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