16. ON IONIZATION POTENTIALS of ATOMS
In the tables of experimental values of potentials of ionization a lot of information on a constitution of atoms is enciphered, but, while, this information will not be utilized rather effectively because of absence of constitutive ideas. Knowledge, which one we have obtained from the previous chapters could clear up this problem (qualitatively, these tables are already clear and in them there is no "by abnormal" numerals), but the business strongly is complicated by that the binding energy of a given electron with a nucleus includes not only electrostatic interaction, but also interaction of a given electron with all other electrons and simultaneously effective magnetic interaction. Besides at removal of an electron there is a reorganization of all electronic structure of atom. At the same structure of electrons, with increase of nuclear charge the eccentricity of orbits of electrons, as we have found out on an example of helium, drops at first sharply, then slowly. It gives in strengthening connection of an electron with a nucleus at the expense more nearcircular orbits on the one hand, and to abatement of this connection at the expense of the greater interaction with other electrons, on the other hand. We have an analytical expression only for one of three simultaneously of varying parameters  binding energy of a given electron with a nucleus, which one of the theory of hydrogenlike atoms can be noted so:
_{} (16.1),
where: E_{Z}  potential of ionization of a hydrogenlike atom with nuclear charge Z, and E_{H}  potential of an atomic ionization of hydrogen. Apparently, that here we have that case, when without good mathematical idea to decide a problem about potentials of ionization of atoms it is impossible. And the idea is encompass following (by the way, it has blanket character and can be utilized for a wide range of similar problems). Let's enter into the formula (16.1) concepts of an effective charge:
Z_{eff}=AZ (16.2),
where A reflects combined effect of interaction of electrons among themselves and magnetic interaction. Let's substitute (16.2) in (16.1) and is conversed to a view:
_{} (16.3),
where: E_{Mn}  nth potential of ionization М  similar of atom, E_{M1}  first potential of ionization of Msimilar atom, Z  charge of an ion, which one will be formed at removal of a given electron, A  parameter depending on a constitution of electronic shells of Msimilar atom.
The formula (16.3) will be valid, at A=const, only at Z_{}, since the shape of orbits of electrons depends from Z, especially at small Z. More often in the tables give experimental values of the first ten potentials of ionization and even it completely insufficiently to compute a precise parameter value A in the formula (16.3). To decide this problem, we shall describe experimental values of potentials of ionization Мsimilar of atoms by any empirical expression, but with indispensable by a requirement, that it at Z_{} gave the formula (16.3). Then it is not required to know a major series of potentials of ionization and parameter A it is possible to compute with any precision for anyone Мsimilar of atom.
For example, for the first three periods of the table of the Mendeleyev I tender following semiempirical dependence (deduction it is not given, since does not introduce interest, parameter B in this dependence no object):
_{} (16.4).
The expression (16.4) at Z_{} gives (16.3), that is an indispensable requirement.
For boronlike of atoms (as an example), in (16.4): А=0.63406, В=0.06633. The matching of experimental values of ionization energy with calculation on (16.4) is given in table 16.1. Table 16.1.
Element 
H 
He 
Li 
Be 
B 
A 
1.00000 
0.74271 
0.78910 
0.60122 
0.63406 
Element 
C 
N 
O 
F 
Ne 
A 
0.54574 
0.48029 
0.49382 
0.43789 
0.39704 
Element 
Na 
Mg 
Al 
Si 
P 
A 
0.54411 
0.45078 
0.50804 
0.44081 
0.39181 
Element 
S 
Cl 
Ar 


A 
0.39043 
0.35119 
0.31984 








Boronlike atom 
C^{+1} 
N^{+2} 
O^{+3} 
F^{+4} 
Ne^{+5}

Z 
2 
3 
4 
5 
6 
Е exp. (eV) 
24.376 
47.426 
77.39 
114.21 
157.9 
Е on (57), eV 
24.376 
47.350 
77.25 
114.06 
157.8 
Boronlike atom 
Na^{+6} 
Mg^{+7} 
Al^{+8} 
Si^{+9}


Z 
7 
8 
9 
10 

Е exp. (eV) 
208.44 
256.84 
330.1 
401.3 

Е on (57), eV 
208.37 
256.83 
330.1 
401.3 

Table 16.2.
The parameter values A for elements of the first three periods are given in table 16.2.
As the error does not exceed 0.2 %, we shall consider expression (16.4) satisfactory for practical use.
For all remaining elements the expression (16.4) does not allow any more enough precisely to compute parameter A because completely of other constitution of shells (see tab. 15.1) and other empirical expression is required, which one us now to interest will not be, as the principle is clear.
Because of that parameter A is liberated from influence of interaction of an electron with a nucleus and its value does not depend on a constitution Мsimilar
of atom (including from reorganization of electronic structure at removal of a given electron), apparently, that the electrons forms the same shell of atom and which are taking place from its nucleus on same distance should have and identical ionization energy E_{0}:
_{} (16.5).
It is clearly, that in the first short period E_{0}=13.595 eV, i.e. is peer to ionization energy of atom of hydrogen. Really, for helium: E_{0 }= E_{He1}×A^{2 }= 24.58/0.74271^{2 }= 13.559 eV, therefore value 24.58 – 13.559 = 11.021 eV is stipulated, in basic, magnetic interaction of two electrons in atom of helium (if not to take into consideration gravidynamic interaction). For elements of the second period E_{0}=3.3535 eV, and third period E_{0}=1.5771 eV. Substituting these values in (16.5), we shall discover the first potentials of ionization of these elements; they are shown in table 16.3.
Element 
Li 
Be 
B 
C 
N 
Е exp. (eV) 
5.39 
9.32 
8.296 
11.264 
14.54 
Е on (16.5), (eV) 
5.39 
9.28 
8.341 
11.259 
14.54 
Element 
O 
F 
Ne 
Na 
Mg 
Е exp. (eV) 
13.614 
17.418 
21.559 
5.138 
7.644 
Е on (16.5), (eV) 
13.752 
17.493 
21.273 
5.327 
7.761 
Element 
Al 
Si 
P 
S 
Cl 
Е exp. (eV) 
5.984 
8.149 
10.55 
10.357 
13.01 
Е on (16.5), (eV) 
6.110 
8.116 
10.27 
10.346 
12.79 
Element 
Ar 


Е exp. (eV) 
15.755 


Е on (16.5), (eV) 
15.416 

Table 16.3
Structural parameter A completely correlates with that electronic constitution of atoms, which one we have established earlier. As well as it was necessary to expect, the constitution of atom completely determines energy of connections of electrons in its composition. Shell arrangement of electrons around of a nucleus was confirmed. Is shown the essential influence of magnetic interaction to electronbinding energy with atom (in which one is included and gravidynamic interaction, but it in this case is insignificant). The experimental potentials of ionization completely correspond to a constitution of atoms enunciated in this book.
16.1. Ion structure
On a figure 16.1.1 the relation of an ionization energy of ions of different elements to total of electrons, inherings to an ion is shown. At 10 electrons the electronic configuration of ions corresponds to a neon, and at 18 electrons  argon. Therefore at the subsequent ionization of such ions the sharp increase of an ionization energy is watched, since it is necessary to shatter filled electronic shell of inert gases. The similarity of curves of a fig. 16.1.1 demonstrates a similarity of electronic structure of the applicable ions. Here only it is necessary to add, that though the electronic structures of ions with the same total number of electrons are similar, but electrons are arranged much closer to a nucleus for multicharge ions, that is quite natural.
In a fig. 16.1.2 for the electronic configuration of ions applicable to argon, the ionization energies E are adduced depending on nuclear charge of an ion (curve 1) and same values which have been counted up on the formula (curve 2). In matching from a dashed straight line it is visible, that with increase of nuclear charge at the same configuration of electrons the ionization energy is proportional to a square of nuclear charge. The more charge of an ion, the more precisely is executed quadratic relation, i.e. the interplay of electrons among themselves in
16.2. Calculation of ionization potentials
Who though once saw spectra of composite atoms, that can sympathize to the astronomers, which one are compelled to be disassembled in thousand spectral lines not only given element, but also in their mixture with other elements, as it is substantially watched in space objects. In outcome before eyes of the explorer there is such bar code in which one practically it is impossible to be disassembled. Let's presume, that we have a set of spectra of all suspected elements existing on investigated object. Then the modern computer equipment can section a spectrum of a complex mixture into spectra of separate elements. But here there is one more severe difficulty: we do not know spectra of multicharge ions. For example, in a corona of the Sun the bright green line of ions Fe^{+13} (it is watched assigned to a new element «coronium»). And what all spectrum of this ion and similar to it? It cannot be played back in laboratory conditions, and to make idealized calculation, it is necessary, at least to know potentials of ionization of transition Fe^{+12}_{}^{ }_{}Fe^{+13}_{}Fe^{+14}, which one also cannot be defined experimentally. The given chapter will help to leave from this desperate situation and to calculate potentials of ionization of any multicharge ions with a high accuracy.
New physics introduces formation of atomic spectra thus. All electrons of atom are in a ground state and nothing beam. For each electron this condition is strict individually. If atom properly to jolt, the obtained energy is reallocated between all electrons and they will take everyone the personal exited state. At returning in a ground state each electron will beam some serials of spectral lines, number of lines in each serial, basically, is indefinite. Only limit of each serial indicates, that the electron again has taken a ground state. At increase of nuclear charge density of power condition near to a ground state is augmented, therefore spacing interval between spectral lines changes. But as though electronbinding energy with a nucleus was not great, near to a ground state it will beam photons optical and infrared diapason. On the basis of the set up mechanism of formation of atomic spectra there is a understandable occurrence of spectra, inclusive many thousand of lines.
In chapter 16 the empiricalformula dependences for calculation of potentials of ionization are adduced, but they cannot be recognized satisfactory. In chapter 16.1 (the figure 16.1.1) is shown, that of ions structure with identical number of electrons is lookalike, and on a figure 16.1.2 is shown, what the ionization energy in a degree 1/2 begin with Z+5 and is higher practically linearly depends on nuclear charge (at the same number of electrons). At a charge < Z+5 interplays of electrons among themselves (magnetic and electrostatic) are reduces a potential of ionization, as far as the potential of ionization in each particular case decreases it is impossible to count up, as it is impossible to decide a manybody problem. At rather large nuclear charge the interplay of electrons among themselves practically does not influence interplay with a nucleus, therefore function E(ion)^1/2 ~ Z becomes linear.
Поэтому расчетная формула будет №14: E_{14}=(1,302Z14,783)^{2}. Мы в эту формулу должны подставить Z=26. В результате получим искомый потенциал ионизации 363,63 эв. Для иона Fe^{+14} аналогичные расчеты по формуле 12 дадут 460,92 эв.
The author, using the data «the reference Book of the chemist», т.1, 1963, page 325327 was not too lazy to compound computational equations for all of elements, the data on an ionization energy (eV) which one are accessible. The outcomes are shown in table 16.2.1. In the first column  character of an element, in the second column  nuclear charge of this element, in the third column  formula for calculation of an ionization energy of any ions, which one contain quantity of electrons, equal number of the formula (and only this quantity!), in the subsequent columns matching experimental value of an ionization energy of ions with calculation under the indicated formula is resulted. For example, we shall count up an ionization energy of an ion Fe^{+12}. The nuclear charge iron 26, in the indicated ion is contained 2612=14 electrons. Therefore this ion attributes to Sisimilar atoms (by analogy with hydrogenlike atoms inclusive one electron). Therefore calculated formula will be №14: E_{14}=(1.302Z14.783)^{2}. We in this formula should substitute Z=26. In outcome we shall receive a required potential of ionization 363.63 eV. For an ion Fe^{+14} the similar calculations under the formula 12 will give 460.92 eV.
Table 16.2.1.
Symbol of element 
Nuclear charge Z

Calculated formula 
Nuclear charge 
Z+4 
Z+5 
Z+6

Z+7

Z+8

Z+9

H 
1 
E1=(3.688Z)2 
Е(experiment) 
340.03 
489.65 
666.47 
870.49 
1101.71 
1360.13 
Е(calculation) 
340.03 
489.65 
666.47 
870.49 
1101.71 
1360.13 

He 
2 
E2=(3.701Z2.441)2

Е(experiment) 
391.99 
551.93 
739.11 
953.8 
1195.4 
1464.7 
Е(calculation) 
390.65 
550.65 
738.05 
952.83 
1195 
1454.5 

Li 
3 
E3=(1.852Z3.062)2

Е(experiment) 
97.86 
138.08 
185.14 
239.1 
299.7 
367.2 
Е(calculation) 
98.05 
138.16 
185.12 
238.95 
299.64 
367.18 

Be 
4 
E4=(1.857Z4.182)^{2}

Е(experiment) 
113.87 
157.12 
207.2 
264.2 
328 
398.6 
Е(calculation) 
113.93 
157.03 
207.01 
263.9 
327.68 
398.36 

B 
5 
E5=(1.869Z6.134)^{2}

Е(experiment) 
114.21 
157.9 
208.44 
265.84 
330.1 
401.3 
Е(calculation) 
114.21 
157.65 
208.08 
265.49 
329.89 
401.28 

C 
6 
E6=(1.881Z7.59)^{2}

Е(experiment) 
126.4 
172.4 
225.3 
285.13 
351.8 
425.4 
Е(calculation) 
125.89 
171.64 
224.46 
284.36 
351.34 
425.39 

N 
7 
E7=(1.881Z8.918)^{2}

Е(experiment) 
138.6 
186.8 
241.8 
304 
372.8 
448.5 
Е(calculation) 
138.6 
186.43 
241.34 
303.32 
372.37 
448.51 

O 
8 
E8=(1.891Z10.806)^{2}

Е(experiment) 
141.23 
190.42 
246.41 
309.3 
378.9 
455.3 
Е(calculation) 
141.28 
189.8 
245.49 
308.32 
378.3 
455.44 

F 
9 
E9=(1.905Z12.404)^{2}

Е(experiment) 
153.8 
205.1 
263.3 
328.4 
400.3 
479 
Е(calculation) 
152.79 
203.52 
261.5 
326.74 
399.24 
479 

Ne 
10 
E10=(1.915Z13.94)^{2}

Е(experiment) 
166.73 
220.41 
280.99 
348.5 
422.6 
503.8 
Е(calculation) 
165.64 
218.6 
378.89 
346.52 
421.48 
503.78 

Na 
11 
E11=(1.303Z11.524)^{2}

Е(experiment) 
65.01 
88 
114.2 
143.4 
176 
211.3 
Е(calculation) 
64.34 
86.94 
112.93 
142.32 
175.11 
211.29 

Mg 
12 
E12=(1.296Z12.227)^{2}

Е(experiment) 
72.5 
96.6 
123.9 
154.3 
187.9 
224.9 
Е(calculation) 
72.4 
96.14 
123.23 
153.69 
187.5 
224.67 

Al 
13 
E13=(1.293Z13.719)^{2}

Е(experiment) 
67.8 
91.3 
117.9 
143.3 
180.2 
216.9 
Е(calculation) 
68.26 
91.3 
117.68 
147.4 
180.47 
216.88 

Si 
14 
E14=(1.302Z14.783)^{2}

Е(experiment) 
75 
99.4 
127.9 
159.2 
193.1 
230.2 
Е(calculation) 
74,87 
99.1 
126.72 
157.73 
192.13 
229.92 

P 
15 
E15=(1.319Z15.977)^{2}

Е(experiment) 
82.6 
109 
139 
172 
206 
246 
Е(calculation) 
82.52 
108.22 
137.4 
170.07 
206.21 
245.83 

S 
16 
E16=(1.311Z16.995)^{2}

Е(experiment) 
84 
111 
141 
174 
209 
249 
Е(calculation) 
85.1 
111 
140.35 
173.13 
209.35 
249 

Cl 
17 
E17=(1.321Z18.16)^{2}

Е(experiment) 
91.8 
119 
151 
185 
221 
262 
Е(calculation) 
91.8 
118.85 
149.4 
183.44 
220.97 
261.99 

Ar 
18 
E18=(1.33Z19.27)^{2}

Е(experiment) 
99.8 
128.9 
161.1 
196.4 
234.4 
276.9 
Е(calculation) 
99.8 
128.14 
160.02 
195.44 
234.4 
276.89 

K 
19 
E19=(1.362Z23.176)^{2}

Е(experiment) 
65.2 
90.6 
120 
151 
185.9 
224 
Е(calculation) 
66.42 
90.48 
118.24 
149.72 
184.91 
223.8 

Ca 
20 
E20=(1.38124.525)^{2}

Е(experiment) 
73 
100 
130 
163 
200 
241 
Е(calculation) 
74.29 
100 
129.53 
162.87 
200.02 
240.99 

Sc 
21 
E21=(1.4Z26.272)^{2}

Е(experiment) 
76 
103 
133 
168 
206 
247 
Е(calculation) 
76.18 
102.58 
132.89 
167.13 
205.29 
247.37 

Ti 
22 
E22=(1.515Z30.497)^{2}

Е(experiment) 
79 
109 
143 
182 
224 
271 
Е(calculation) 
79.08 
108.33 
142.16 
180.58 
223.59 
271.19 

V 
23 
E23=(1.542Z32.601)2

Е(experiment) 
82 
113 
148 
188 
231 
280 
Е(calculation) 
81.59 
111.83 
146.82 
186.57 
231.07 
280.33 

Cr 
24 
E24=(1.528Z33.879)^{2}

Е(experiment) 
79 
109 
144 
183 
226 
274 
Е(calculation) 
79.3 
108.85 
143.06 
181.95 
225.51 
273.74 

Mn 
25 
E25=(1.529Z35.193)^{2}

Е(experiment) 
83 
114 
149 
189 
234 
282 
Е(calculation) 
83.69 
114 
148.99 
188.65 
232.99 
282 

Fe 
26 
E26=(1.549Z37.156)^{2}

Е(experiment) 
86 
118 
155 
196 
241 
291 
Е(calculation) 
86.75 
118 
154.06 
194.91 
240.56 
291 

Co 
27 
E27=(1.557Z38.75)^{2}

Е(experiment) 
90 
123 
160 
202 
248 
300 
Е(calculation) 
90.57 
122.63 
159.54 
201.3 
247.9 
299.36 

Ni 
28 
E28=(1.338Z32.854)^{2}

Е(experiment) 
93.4 
127.5 
155 
193 
234 
277 
Е(calculation) 
99.24 
127.69 
159.72 
195.33 
234.52 
277.29 

Cu 
29 
E29=(1.061Z27)^{2}

Е(experiment) 
62.9 
82.1 
103 
126 
150 
177 
Е(calculation) 
64.21 
82.34 
102.72 
125.35 
150.23 
177.37 

Zn 
30 
E30=(1.102Z29.148)^{2}

Е(experiment) 
68.3 
88.6 
111 
136 
162 
191 
Е(calculation) 
69.22 
88.77 
110.75 
135.16 
162 
191.27 

Ga 
31 
E31=(1.073Z29.767)^{2}

Е(experiment) 
59.7 
78.5 
99.2 
122.3 
146.2 
173 
Е(calculation) 
60.65 
78.52 
98.68 
121.15 
145.93 
173 

Ge 
32 
E32=(1.119Z32.233)^{2}

Е(experiment) 
64.7 
84.4 
106 
129 
154 
186 
Е(calculation) 
64.82 
84.09 
105.86 
130.14 
156.93 
186.21 

As 
33 
E33=(1.053Z30.298)^{2}

Е(experiment) 
71 
90.8 
116 
139 
165 
194 
Е(calculation) 
75.05 
94.4 
115.97 
139.76 
165.77 
193.99 

Se 
34 
E34=(1.08Z32.476)^{2}

Е(experiment) 
71.6 
93 
116 
141 
167 
195 
Е(calculation) 
73.34 
93.01 
115 
139.33 
166 
195 

Br 
35 
E35=(1.19Z37.663)^{2}

Е(experiment) 
77 
99.4 
124 
153 
183 
216 
Е(calculation) 
76.51 
98.74 
123.81 
151.71 
182.44 
216 

Kr 
36 
E36=(1.123Z35.535)^{2}

Е(experiment) 
82.3 
110.4 
131 
161 
192 
225 
Е(calculation) 
88.08 
110.42 
135.28 
162.66 
192.57 
225 

Rb 
37 
E37=(1.252Z44.25)^{2}

Е(experiment) 
50 
67 
94 
119 
147 
178 
Е(calculation) 
50.15 
69.45 
91.89 
117.46 
146.17 
178 

Sr 
38 
E38=(1.239Z44.558)^{2}

Е(experiment) 
61.2 
76 
100 
126 
155 
187 
Е(calculation) 
55.95 
76.02 
99.16 
125.37 
154.65 
187.01 

Y 
39 
E39=(1.238Z45.46)^{2}

Е(experiment) 
59 
81 
105 
132 
162 
195 
Е(calculation) 
60.43 
81.22 
105.06 
131.97 
161.95 
194.99 

Zr 
40 
E40=(1.263Z47.604)^{2}

Е(experiment) 
63 
85 
111 
139 
170 
204 
Е(calculation) 
63.49 
85.21 
110.12 
138.23 
169.52 
204 

Nb 
41 
E41=(1.277Z49.256)^{2}

Е(experiment) 
67 
90 
116 
146 
178 
213 
Е(calculation) 
67.39 
89.98 
115.84 
144.96 
177.34 
212.98 

Mo 
42 
E42=(1.28Z50.754)^{2}

Е(experiment) 
66 
89 
115 
144 
176 
211 
Е(calculation) 
66.03 
88.47 
114.19 
143.18 
175.46 
211 

Tc 
43 
E43=(1.293Z52.404)^{2}

Е(experiment) 
70 
94 
121 
151 
184 
220 
Е(calculation) 
70 
93.32 
119.97 
149.96 
183.3 
219.99 

Ru 
44 
E44=(1.308Z54.191)^{2}

Е(experiment) 
73 
98 
126 
157 
192 
229 
Е(calculation) 
73.84 
98.03 
125.64 
156.67 
191.13 
229.01 

Rh 
45 
E45=(1.335Z56.663)^{2}

Е(experiment) 
77 
103 
132 
164 
200 
238 
Е(calculation) 
76.6 
101.75 
130.46 
162.74 
198.58 
237.99 

Pd 
46 
E46=(1.273Z54.015)^{2}

Е(experiment) 
91 
119 
149 
182 
218 
256 
Е(calculation) 
92.83 
116.98 
148.38 
181.01 
216.88 
256 

Ag 
47 
E47=(1.065Z46.328)^{2}

Е(experiment) 
63.8 
83 
104 
126 
150 
158 
Е(calculation) 
63.79 
81.94 
102.35 
125.04 
150 
177.21 

Cd 
48 
E48=(0.944Z40.963)^{2}

Е(experiment) 
66 
83 
102 
122 
144 
165 
Е(calculation) 
66.02 
82.25 
100.26 
120.06 
141.63 
164.99 

In 
49 
E49=(0.938Z41.289)^{2}

Е(experiment) 
71 
89 
108 
127 
151 
172 
Е(calculation) 
70.98 
87.67 
106.11 
126.31 
148.28 
172 

Sn 
50 
E50=(1.023Z47.629)^{2}

Е(experiment) 
57 
74 
93 
114 
137 
162 
Е(calculation) 
57.96 
74.58 
93.3 
114.1 
137.01 
162 

Sb 
51 
E51=(1.041Z49.383)^{2}

Е(experiment) 
62 
80 
100 
122 
146 
171 
Е(calculation) 
61.97 
79.44 
99.08 
120.89 
144.86 
171.01 

Te 
52 
E52=(1.056Z51.263)^{2}

Е(experiment) 
62 
80 
100 
122 
147 
173 
Е(calculation) 
61.98 
79.73 
99.7 
121.9 
146.34 
173 

J 
53 
E53=(1.066Z52.638)^{2}

Е(experiment) 
66 
85 
106 
129 
154 
181 
Е(calculation) 
66 
84.46 
105.18 
128.19 
153.46 
181.01 

Xe 
54 
E54=(1.06Z53.105)^{2}

Е(experiment) 
70 
89 
111 
135 
161 
187 
Е(calculation) 
70.14 
89.02 
110.14 
133.52 
159.14 
187.01 

NO DATA 
Е(experiment) 







Е(calculation) 







Tu 
69 
E69=(1.075Z71.767)^{2}

Е(experiment) 
45 
61 
79 
99 
121 
146 
Е(calculation) 
45 
60.57 
78.46 
98.66 
121.18 
146 

Yb 
70 
E70=(1.088Z73.583)^{2}

Е(experiment) 
48 
65 
89 
104 
127 
153 
Е(calculation) 
48.01 
64.27 
82.9 
103.9 
127.26 
152.99 

Lu 
71 
E71=(1.091Z74.671)^{2}

Е(experiment) 
51 
68 
88 
109 
133 
159 
Е(calculation) 
51.18 
67.98 
87.16 
108.72 
132.66 
158.99 

Hf 
72 
E72=(1.1Z76.216)^{2}

Е(experiment) 
54 
72 
92 
114 
139 
166 
Е(calculation) 
54.52 
71.98 
91.85 
114.15 
138.86 
166 

Ta 
73 
E73=(1.123Z78.933)^{2}

Е(experiment) 
57 
75 
96 
120 
145 
173 
Е(calculation) 
56.82 
75.01 
95.73 
118.96 
144.72 
173 

W 
74 
E74=(1.126Z80.458)^{2}

Е(experiment) 
55 
73 
94 
117 
142 
169 
Е(calculation) 
54.32 
72.18 
92.58 
115.52 
140.99 
169 

Re 
75 
E75=(1.123Z81.066)^{2}

Е(experiment) 
58 
77 
98 
112? 
148 
176 
Е(calculation) 
58.54 
76.98 
97.95 
121.44 
147.45 
175.99 

Os 
76 
E76=(1.144Z83.712)^{2}

Е(experiment) 
61 
81 
103 
127 
154 
183 
Е(calculation) 
60.96 
80.14 
101.93 
126.34 
153.36 
183.01 

Ir 
77 
E77=(1.157Z85.718)^{2}

Е(experiment) 
64 
84 
107 
132 
160 
190 
Е(calculation) 
63.98 
83.83 
106.36 
131.56 
159.44 
190 

Pt 
78 
E78=(1.137Z84.883)^{2}

Е(experiment) 
69.7 
94.4 
112 
138 
166 
197 
Е(calculation) 
69.74 
90.02 
112.89 
138.34 
166.38 
197.01 

Au 
79 
E79=(Z75.51)^{2}

Е(experiment) 
56 
73 
91 
111 
133 
156 
Е(calculation) 
56.1 
72.08 
90.06 
110.04 
132.02 
156 

Hg 
80 
E80=(0.999Z76.105)^{2}

Е(experiment) 
61 
78 
97 
117 
140 
164 
Е(calculation) 
61.01 
77.62 
96.22 
116.81 
139.4 
163.99 

Tl 
81 
E81=(0.98Z76.158)^{2}

Е(experiment) 
51 
67 
84 
103 
123 
145 
Е(calculation) 
51.01 
65.97 
82.85 
101.65 
122.37 
145.01 

Pb 
82 
E82=(0.996Z78.226)^{2}

Е(experiment) 
55 
71 
89 
109 
130 
154 
Е(calculation) 
55.2 
71 
88.77 
108.53 
130.28 
154.01 

Bi 
83 
E83=(1.01Z80.192)^{2}

Е(experiment) 
59 
76 
95 
115 
138 
162 
Е(calculation) 
58.95 
75.48 
94.05 
114.66 
137.31 
162 

Po 
84 
E84=(1.01Z81.215)^{2}

Е(experiment) 
59 
76 
94 
115 
137 
? 
Е(calculation) 
58.75 
75.26 
93.8 
114.38 
137.01 
? 
16.3 Values of coefficients in the formulas of an ionization energy
Values of coefficients in the formulas of an ionization energy of a kind E_{Z}=(AZB)^{2} of chapter 16.2.
On a figure 16.3.1 the course of change of a factor A is shown depending on nuclear charge, and on a figure 16.3.2  similar course of change of a factor B. As the factor B, on the average, is proportional to nuclear charge, on a figure 16.3.2 the broken line of direct ratio is conducted. From table 16.3.1 and graphs the correlation of factors A and B with degree of fullness of electronic envelopes and subenvelopes of table 15.1 of chapter 15 is legiblly visible and it proves the new form of the table of the Mendeleyev.
Z at E numerically is equal to number of the formula of chapter 16.2, which one is peer to nuclear charge of this element (Z brackets) minus a charge of any ion of this element. Z 
A 
B 
Z 
A 
B 
Z 
A 
B 
Comment 
1 
3,688 
0,000 
25 
1,529 
35,193 
49 
0,938 
41,289 
In brackets the number of electrons in a envelope or sub envelope of table 15.1 is indicated 
2 
3,701 (2) 
2,441 
26 
1,549 
37,156 
50 
1,023 
47,629 

3 
1,852 
3,062 
27 
1,557 
38,750 
51 
1,041 
49,383 

4 
1,857 
4,182 
28 
1,338 (8) 
32,854 
52 
1,056 
51,263 

5 
1,869 
6,134 
29 
1,061 
27,000 
53 
1,066 
52,638 

6 
1,881 
7,590 
30 
1,102 (2) 
29,148 
54 
1,060 (6) 
53,105 
For elements with z=55 up to z=68 there are no data 
7 
1,881 
8,918 
31 
1,073 
29,767 
69 
1,070 
71,767 

8 
1,891 
10,806 
32 
1,119 
32,233 
70 
1,088 
73,583 

9 
1,905 
12,404 
33 
1,053 
30,298 
71 
1,091 (16) 
74,871 

10 
1,915 (8) 
13,940 
34 
1,080 
32,476 
72 
1,100 
76,216 

11 
1,303 
11,524 
35 
1,190 
37,663 
73 
1,123 
78,933 

12 
1,296 
12,227 
36 
1,123 (6) 
35,535 
74 
1,126 
80,458 

13 
1,293 
13,719 
37 
1,252 
44,250 
75 
1,123 
81,066 

14 
1,302 
14,783 
38 
1,239 (2) 
44,558 
76 
1,144 
83,712 

15 
1,319 
15,977 
39 
1,238 
45,460 
77 
1,157 
85,718 

16 
1,311 
16,995 
40 
1,263 
47,604 
78 
1,137 
84,883 

17 
1,321 
18,160 
41 
1,277 
49,256 
79 
1,000 (8) 
75,510 

18 
1,330 (8) 
19,270 
42 
1,280 
50,754 
80 
0,999 
76,105 

19 
1,362 
23,176 
43 
1,293 
52,404 
81 
0,980 (2) 
76,158 

20 
1,381 (2) 
24,525 
44 
1,308 
54,191 
82 
0,996 
78,226 

21 
1,400 
26,272 
45 
1,335 
56,663 
83 
1,010 
80,192 

22 
1,515 
30,497 
46 
1,273 (8) 
54,015 
84 
1,010 
81,215 

23 
1,542 
32,601 
47 
1,065 
46,328 




24 
1,528 
33,879 
48 
0,944 (2) 
40,963 



