Georgy Soukhorukov, Edouard Soukhorukov, Roman Soukhorukov
Bohr and Zommerfild definitely proved Rezerfords planetary atomic model [1, 2]. However, as a result of difficulties appeared while explaining the fine atomic structure of hydrogen and complex atomic structure, their theory had been rejected. Now, atomic structure is described by the complex threedimensional Shredingers differential equation [3..5]. Even for hydrogen atom, the solution of this equation cannot be expressed via elementary functions [6]. For atoms which have two or mode electons, Shredingers equation cannot be solved even by numerical way [7]. It takes electronic computers to work for hundreds of hours [8] or several years [9] to compute a spectrum therm.
Our theory is a logical continuation of Bohr and Zommerfields theory. An extensive material concerning the definition of values of the ionization potential and energy of therms of optical and xrays had been used while formation. The referenced values of the ionization potential are given to high precision which reaches 810 decimal points. These data are reliable because they are gotten as a result of summarizing of the experimental material which is available to all mankind. The results of the theoretical research conducted by using techniques developed on a basis of our theory are adjusted with the experimental data above.
The velocity of interaction propagation is equal to the velocity of light. The finiteness of this velocity is determined by presence of the universal medium (ether). Newtons and Koulons laws are precisely applied only to solids which are static for this medium. For mobile solids, the effectiveness of interaction depends on the velocity of their motion relatively to the universal medium. The equations of the motion effect are similar to the equations of Doppler effect in acoustics and optics. In case that both of interacting solids are mobile, the equation takes following form [10, 11]:
where X is the value depending on the motion velocity, C is the velocity of light, V and U are velocities of motion on interacting solids, α_{1} and β_{1} are the angles between directions of motion of the wave source and the receiver and the line joining the point the wave emanated from with the point it met with the receiver. Accented and unaccented letters are given for the values obtained correspondingly taking and not taking into account the motion effect. The motion of atomic nucleus can be neglected, then, the following equations are possible for values characterizing the electron orbital motion:
; , (1)
where a and b are the values which increase of decrease as a result of motion effect.
A velocity of an electron in the atom also depends on motion effect. It can be written as:
. (2)
Having transformed the equation (2) to the following one
(3)
we convince that
. (4)
During the calculation we have to use the values both considering and not considering the motion effect. Using equations (2) and (3) it is possible to switch from one values to another if one of velocity value  either V or V' is known. Considering the equation (4) equations (1) can be written as:
, (5)
(6)
Atoms have planetary structure. When an electron turns from the one steady state to another, the waves are absorbed and emitted. At the same time, in the multielectron atoms, not only the electron that moved from the one orbit to another, but also the rest of electrons have their full energy changed. The lengths of the optical and the roentgen waves emitted by the complex atoms are calculated according the formula [12]:
, (7)
where:
β=1+, m is an electron mass, M is a kernel mass,
are the charge counts and the steady states of a nonexcited atom, are the corresponding values of an exited atom. The electron numbering comes from the kernel to the periphery of the atom. Ridbergs constant m^{1} is the same for all atoms.
The parameters of the orbits of an multielectron atoms can be calculated via the values of the ionization potentials. Here is the sequence of calculations. First, the approximate values of an effective charge counts are calculated via the values of the ionization potentials [13]. Then, the repetition factors of the orbital periods are calculated by the following formulas:
These formulas help to express the charge counts of all electrons via the chare count of the external electron. Then, having put new expressions into the formula (8), we would have an equation with the one unknown value:
. (8)
Now its possible to determine the exact values by sequential accomplishing the tasks for the ions of the given atom which have 2, 3, , i electrons correspondingly. As it is shown above, having known the value z' for the electron, it is possible to determine all parameters of its orbit. In the published issues, the calculated values of the parameters of the electrons orbits are given for all possible ions of the first twelve elements in the Periodic Table. In this article, the examples of calculation of the hydrogen and helium atoms are given.
Parameters of the orbit of complex atoms can be expressed through the parameters of Bohr orbit [12].
If an electron is moving on round orbit, then:
, (9)
and if on elliptical, then
; (10)
, (11)
(12)
where z' is an effective charge count,
is an eccentricity, where n is an orbital count, l and b are lengths of large and small axis of ellipse.
The full energy of an electronatom system is:
. (13)
The orbital period for the electron and the kernel to go around center of mass:
. (14)
Formulas (1) and (2) have helped to determine: r_{n} = 0,529191323×10^{10 m; V}_{n} = 2,186442460×10^{6} m/s; E_{n }= 21,78571660×10^{19} Joules; e = 1,602156024×10^{19} Coulomb; T_{n }= 1,520657574×10^{16} s.
Thus, having known the effective charge count its possible to calculate all magnitudes that characterize the electrons orbital movement in the atom.
Table 1 shows the parameters of an electrons orbit in the hydrogen atom for 4 steady states. Heres the sequence of calculation. Equations (9 11) have been used to calculate the velocities of an electron while moving on round and elliptical orbits. For the hydrogen atom these equations will look like (not considering the motion effect):
; ; .
The table shows real values of the velocity of an electron, i.e. considering the motion effect. These values have been calculated using the following equations:
; ; .
Effective charge counts for the electron which moves on round and elliptical orbits can be determined with the following equations:
, .
The rest of parameters have been calculated using equations (1214).
Table 1
Steady state, k 
Orbit type and number 
Orbital count, n 
Velocity in a pericenter V^{}_{n}×10^{6 }, m×s 
Velocity in an apocenter V^{}_{a}10^{6}, m×s 
Pericentral radius, r^{}_{п}×10^{10, m} 
Apocentral radius, r^{}_{а}×10^{10 }, m 
I 
Round 
1 
2,186500611 
2,186500611 
0,529177249 
0,529177249 
II 
1^{st} round 2^{nd} elliptical 
2 1 
1,093228498 4,080011431 
1,093228498 0,292931642 
2,116751219 0,283589719 
2,116751219 3,949885269 
III 
1^{st} round 2^{nd} elliptical 3^{rd} elliptical 
3 2 1 
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 
1^{st} round 2^{nd} elliptical 3^{rd} elliptical 4^{th} elliptical 
4 3 2 1 
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 
1^{st} round 2^{nd} elliptical 
1,000006648 1,000013297 
4,233502438 4,233474988 
4,233502438 2,116737494 
5,446501565 5,446573992 
12,16574593 12,16558416 
III 
1^{st} round 2^{nd} elliptical 3^{rd} 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 
1^{st} round 2^{nd} elliptical 3^{rd} elliptical 4^{th} 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} = 39.393390210^{19} WattSecond. In this case, the equation (8) takes the following form:
.
Having calculated via this equation the values z^{e}_{2} = 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 (914).
Table 2
Orbits of Electrons In The Helium Atom
Steady state of second electron 
Orbit type and number 
Charge count 







1 
Round 
1,9677965 
1,3914422 
2 
2 
1^{st} round 
1,9971808 
1,2043454 
22 
2^{nd} round 
1,9991896 
1,0882210 
27 

3^{rd} round 
2,0001251 
1,0328602 
30 

4^{th} round 
2,0001274 
1,0328613 
30 

5^{th} round 
1,9996570 
0,9998285 
32 

3 
1^{st} round 
1,9996874 
1,1204559 
86 
2^{nd} round 
1,9999251 
1,0551392 
97 

3^{rd} round 
1,9998483 
1,0289134 
102 

4^{th} round 
1,9998489 
1,0289138 
102 

5^{th} round 
1,9997306 
1,0092539 
106 

6^{th} round 
1,9997382 
1,0092577 
106 

7^{th} round 
2,0000089 
1,0000045 
108 
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. Electrons 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 En1 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 electrons 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 

1 
1102,0 
1101,8 
1360,5 
1360,2 
1646,2 
1646,4 
2 
953,43 
953,5 
1195,0 
1195,4 
1463,7 
1464,7 
3 
185,14 
185,14 
239,0 
239,1 
299,86 
299,7 
4 
157,06 
157,11 
207,05 
207,2 
263,83 
264,2 
5 
114,21 
114,21 
157,91 
157,91 
208,41 
208,44 
6 
87,141 
87,23 
126,15 
126,4 
172,36 
172,38 
7 
62,710 
62,646 
97,118 
97,16 
138,33 
138,6 
8 
34,971 
34,98 
63,456 
63,5 
98,916 
98,88 
9 
17,423 
17,418 
40,964 
41,07 
71,639 
71,8 
10 
 
 
21,565 
21,559 
47,287 
47,29 
11 
 
 
 
 
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 13^{th} period for the elements that possibly exist in the Universe in conditions different from ones in the Solar System.
Table 4
Periodical Law
Period 
Elements Number In The Period 


1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
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 
106 
107 
108 
109 
110 




CII 
111 
112 
113 
114 
115 
113 
117 
118 






Table 5 shows how the electron layers are filled in the atoms of the elements of the 13^{th} 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 13^{th} Period
Element Number 
Layer Number 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 

k=1 
k=2 
k=3 
k=4 

111 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
1 
112 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
2 
113 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
3 
114 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
4 
115 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
5 
116 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
6 
117 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
7 
118 
2 
8 
8 
10 
8 
10 
8 
14 
10 
8 
14 
10 
8 
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 elements properties with the increase of the number of electrons in the atoms 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∙106, meters per second 
2.186500601 
 
Constant of Fine Structure 1/α'_{∞}, m^{1} 
137.0359895 
137.0359895 
Rydbergs Constant 
1.097373153 
1.097373153 
Orbital Period for Electron 
1.820657574 
 
Planks Constant 
6.626075438 
6.6260755 
As a source data, the values of four constants have been taken [13]:
Velocity of Light c = 2.99792458×10^{8} 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, b_{n} = 1.000544617.
Table 7
Energies of Spectral Therms of Hydrogen Atom
Therm of an exited state 
Therm energy, cm1; Therm difference, cm1 


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
42A, Naymoushina Str., 8
Bratsk 665709
Russian Federation
Phone: +7 (3953) 379529 (home)
email: nil_mu@brstu.ru
Edouard G. Soukhorukov
10, Studencheskaya Str., 802
Bratsk 665709
Russian Federation
Phone: +7 (3953) 379155
Roman G. Soukhorukov
53, Yubileynaya Str., 98
Bratsk 665730
Russian Federation
Phone: +7 (3953) 331803
Issue date: 22 August 2000
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