Fig. 4. Ionization potentials of a neon and argon

Subject to degree of ionization

Let's verify the validity of formula (19). But for this purpose it is necessary to determine radius of external electron shell as precisely as possible.

For this purpose as it was already shown, the best variant is of an electron shell with only one electron. Therefore radius of the external shell of neon atom is determined on the bases of the eighth degree ionization potential

(21)

There are other methods of calculation of radius which also give close results.

Having substituted concrete values in (19), we obtain

(22)

Thus, the right and the left parts of (19), really, are close to each other. Results of similar calculations for other noble gases are shown in table 4.

Òàáëèöà 4

Atom	φ8, eV	R/RÁ	Calc. Σφi, eV	Exper. Σφi, eV	Calc/Exper.
10 (Ne)	239,1	0,455	956,48	953,89	1,003
18 (Ar)	143,4	0,759	573,39	577,64	0,993
36 (Kr)	126	0,863	504,29	508,16	0,992
54 (Xe)	126	0,863	504,29	484,43	1,041

External shell of halogens atoms has only one electron less, than noble gases; therefore we can expect exact fit of calculations and experiments in this case too. However, formulas are "to be corrected" accordingly:

(23)

(24)

Calculations output and actual values are represented in table 5.

Table 5

Atom	φ7, eV	R/RÁ	Calc. Σφi, eV	Exper. Σφi, eV	Calc/Exper.
9 (F)	185,14	0,514	648,25	658,75	0,984
17 (Cl)	114,2	0,834	399,52	408,61	0,978
35 (Br)	103	0,924	360,6	367,94	0,98
53 (J)	104	0,915	364,15	362,44	1,005

As we see, calculations output and actual values for external electron shells of halogens (as well as noble gases) correspond with each other.

Whether these laws are also distinctly valid for internal atom shells? To answer this question, let us make similar calculations for the filled shells which are directly under external shells of univalent and bivalent atoms.

Here also quite obvious changes in formulas are required. First we write down these formulas for atoms with only one electron on an external shell:

(25)

(26)

Similarly we can modify formulas for atoms with two electrons on an external shell:

(27)

(28)

Calculations output and actual values are represented accordingly in tables 6 and 7.

Thus, made analysis convincingly shows, that electrons in atoms really concentrate layer-by-layer in spherical electron shells.

Exact correspondence of calculation results to experimental data also testifies high accuracy of determining of electron shells radiuses.

Table 6

Atom	φ9, eV	R/RÁ	Calc. Σφi, eV	Exper. Σφi, eV	Calc/Exper.
11 (Na)	299,7	0,408	1333,33	1299,31	1,026
19 (K)	176	0,695	782,73	769,01	1,018
37 (Rb)	150	0,816	666,67	660,76	1,009
55 (Cs)	150	0,816	666,67	621,7	1,072

Table 7

Atom	φ10, eV	R/RÁ	Calc. Σφi, eV	Exper. Σφi, eV	Calc/Exper.
12 (Mg)	367,2	0,370	1764,32	1702	1,037
20 (Ca)	211,3	0,644	1013,66	982	1,032
38 (Sr)	177	0,768	850	830,4	1,024

In conclusion of electron shells structure analysis it is necessary shortly talk about so-called "shielding action" on the charge of a nucleus (or atomic core) by shells electrons.

What is the mechanism of "screening effect"? The model of spherical electron shells enables to specify this question.

According to Gauss theorem [5] each subsequent charged sphere is exposed to the electricfield of the total charge which sits inside of this sphere. So, the charge of shells of greater radius cannot influence shells of smaller radius (according to the model of spherical electron shells, fig. 5).

However in this simple scheme there is one not so obvious feature. The matter is that each charged sphere besides has “self-action”. The charges being on sphere surface are subjected to electric field equal to the half value of the field created by this charged sphere close to the external surface:

(29)

This formula can be deduced by integration of contributions of all elementary charges located on a surface of sphere.