Сlassification of chemical elements according to the electronic structure of their atoms

Original article

Структурирование химических элементов по электронному строению атомов

Борис Владимирович Гусев* ©, Александр Сергеевич Тертерян

Российская инженерная академия, 125009, Москва, Газетный пер., 9, стр. 4, Российская Федерация

• *    Автор, ответственный за переписку: e-mail: info-rae@mail.ru

AННОТАЦИЯ

Как известно, химия развивалаcь и развивается, прежде всего, благодаря открытию Д.И. Менделеева и существующей уже более 150 лет Периодической таблице химических элементов. Рассматривается новое видение структурирования химических элементов в виде объемной матрицы. Это позволяет прогнозировать новые элементы с обозначением ядерных масс и электронным строением оболочек. Сформулированы новые закономерности по цикличности и блочности строения горизонтальных рядов, уточнено строение вертикальных групп и их физическое осмысливание. Из представленного материала следует, что в Периодическом законе важным является система двух уравнений. Согласно этим уравнениям, энергия блоков возрастает, циклически приближаясь от отрицательных значений к значениям, близким к нулю в блоке под названием «8s».

Nanotechnologies in construction      2026; 18 (4):

Нанотехнологии в строительстве     537–544

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES

Nanob

Гусев Б.В., Тертерян А.С. Структурирование химических элементов по электронному строению атомов. Нанотехнологии в строительстве. 2026;18(4):537–544. – EDN: PMJDVU.

The theory of the electronic structure of atoms was developed by N. Bohr and W. Pauli [1, 2].

Tables 1 and 2 present energy sequences of atomic orbitals, where:

• n    is the principal quantum number, which reflects the distance of the electron from the nucleus;

l is the orbital quantum number, which determines the orbital angular momentum of the electron’s momentum and the energy state of the electrons in the atom;

• s , p, d, f are the atomic orbitals for the following states:

l = 0 – one orbital;

l = 1 – three orbitals;

l = 2 – five orbitals;

l = 3 – seven orbitals.

According to the authors, the energy of the levels for the most fundamental element in nature, the hydrogen atom, and for other atoms as well, is determined by the formula [1, 2]:

E = –13.6 eV / n ²,

where n is the period number and the corresponding number of the level boundary ( n = 1, 2, 3, 4, 5, 6, 7, 8). Thus:

E₀ = –13.6–13.6 = –27.2 eV

E1 = –13.6/12 = –13.6/1 = –13.6 eV

E2 = –13.6/22 = –13.6/4 = –3.4 eV

E3 = –13.6/32 = –13.6/9 = –1.51 eV

E4 = –13.6/42 = –13.6/16 = –0.85 eV

E5 = –13.6/52 = –13.6/25 = –0.54 eV

E6 = –13.6/62 = –13.6/36 = –0.38 eV

E7 = –13.6/72 = –13.6/49 = –0.28 eV

E8 = –13.6/82 = –13.6/64 = –0.21 eV

Energy sequence of orbitals in isolated atoms [2]:

The energies of the level boundaries are represented by thick lines in Figures 1, 2, and 3.

Each level can be divided into sublevels with energies determined by the formula [4]:

p = (2 l –1) / L ²,                                                                                               (2)

where l is the sublevel number ( l = 1 (s), l = 2 (p), l = 3 (d), l = 4 (f)), and L is the total number of sublevels.

The number of orbitals in the sublevels of the 1st, 2nd, 3rd, and 4th levels are in the ratio of 1; 1:3; 1:3:5; and 1:3:5:7, respectively. For the sublevels of the 5th, 6th, 7th, and 8th levels, the ratio is reversed: 7:5:3:1; 5:3:1; 3:1; and 1.

The proportions of sublevels at each level are as follows:

for the 1st level – 1;

for the 2nd level – 0.25, 0.75;

for the 3rd level – 0.111, 0.333, 0.555;

for the 4th level – 0.0625, 0.1875, 0.3125, 0.4375;

for the 5th level – 0.0625, 0.1875, 0.3125, 0.4375;

for the 6th level – 0.111, 0.333, 0.555;

for the 7th level – 0.25, 0.75;

for the 8th level – 1.

Thus, the total number of blocks (1s, 2s, 2p, 3s, 3p, 3d, 4s, …, 8s) is 20.

Nanotechnologies in construction      2026; 18 (4):

Нанотехнологии в строительстве     537–544

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES

Nanob

Table 1

Period Number	Quantum Numbers	Orbital Quantum Number	Atom orbitals
(n+1)	n	1
1	1	0	1s} I period
2	2	0	2s '	- II period
3	2	1	2p 3s ~
		и		~ Ill period
4	3	1	3p- 4s
		и		IV period
5	3 4 r	2 1	3d 4p 5s "
	Э	и		_ V period
6	4 5 6	2 1 0	4d 5P' 6s"
7	4 5 6 “7	3 2 1	4f 5d 6p 7s П	VI period
		и		VII period
	5	3	5f
О	6	2	6d
о	7 8	1 0	7p 8s	[ VIII period

Table 2

Principle quantum number n	Orbital quantum number l	Atom orbitals
1	0	1 s
2	0, 1	2 s , 2 p
3	0, 1, 2	3 s , 3 p , 3 d
4	0, 1, 2, 3	4 s , 4 p , 4 d , 4 f

Nanotechnologies in construction

Нанотехнологии в строительстве

2026; 18 (4): 537–544

Nanob

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES

Fig. 2. Energy of the block at level 1

Nanotechnologies in construction      2026; 18 (4):

Нанотехнологии в строительстве     537–544

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES

Nanob

The energies of the sublevels according to formula (2) will be as follows:

• •    for the 1^st level, all the energy is at 1s sublevel: e_1s= –13.6 eV ;

• •    for the 2^nd level, the distribution of energy between 2s and 2p sublevels will be as follows:

e2p = [–13.6–(–3.4)]×0.25 = (–13.6+3.4)×0.25 = –10.2×0.25 = –2.55 eV      e2p = –2.55 eV, e2sp = [–13.6–(–3.4)]×0.75 = (–13.6+3.4)×0.75= –10.2×0.75 = –7.65 eV       e2sp = –7.65 eV;

• •    for the 3^rd level, the distribution of energy between 3s, 3p, and 3d sublevels will be as follows:

e3d= [–3.4–(–1.51)]×0.111 = –1.89×0.111 = –0.21 eV                          e3d= –0.21 eV e3p= [–3.4–(–1.51)]×0.333 = –1.89×0.333 = –0.63 eV                       e3p= –0.63 eV e3sp= [–3.4–(–1.51)]×0.555 = –1.89×0.555 = –1.049 eV                        e3sp= –1.049 eV;

• •    for the 4^th level, the distribution of energy between 4f, 4d, 4p, and 4s sublevels will be as follows: e_4f= [–1.51–(–0.85)]×0.0625 = –0.66×0.0625 = –0.04 eV                     e_4f= –0.04 eV,

  e_4d= [–1.51–(–0.85)]×0.1875 = –0.66×0.1875 = –0.124 eV                    e_4d= –0.124 eV,

  e_4p= [–1.51–(–0.85)]×0.3125 = –0.66×0.3125 = –0.206 eV                    e_4p= –0.206 eV,

  e4^ps = [–1.51–(–0.85)]×0.4375 = –0.66×0.4375 = –0.29 eV                    e_4s^p= –0.29 eV;

• •    for the 5^th level, the distribution of energy between 5f, 5d, 5p, and 5s sublevels will be as follows: e_5f= [–0.85–(–0.54)]×0.0625 = –0.31×0.0625 = –0.02 eV                     e_5f= –0.02 eV,

  e_5d= [–0.85–(–0.54)]×0.1875 = –0.31×0.1875 = –0.06 eV                     e_5d= –0.06 eV,

  e_5p= [–0.85–(–0.54)×0.3125 = –0.31×0.3125 = –0.097 eV                    e_5p= –0.097 eV,

  e_5s^p = [–0.85–(–0.54)×0.4375 = –0.31×0.4375 = –0.1356 eV                   e_5s^p= –0.1356 eV;

• •    for the 6^th level, the distribution of energy between 6d, 6p, and 6s sublevels will be as follows:

e6d= [–0.54–(–0.38)]×0.1111 = –0.16×0.1111 = –0.018 eV                      e6d= –0.018 eV, e6p= [–0.54–(–0.38)]×0.3333 = –0.16×0.3333 = –0.051 eV                    e6p= –0.051 eV, e6sp= [–0.54–(–0.38)]×0.5555 = –0.16×0.5555 = –0.089 eV                    e6sp= –0.089 eV;

• •    for the 7^th level, the distribution of energy between the 7p and 7s sublevels will be as follows:

e7p= [–0.38–(–0.28)]×0.25 = –0.1×0.25 = –0.025 eV                        e7p= –0.025 eV, e7sp= [–0.38–(–0.28)]×0.75 = –0.1×0.75 = –0.075 eV                         e7sp= –0.075 eV,

• •    for the 8^th level, all the energy will be at the 8s sublevel:

e_8s= [–0.28–(–0.21)]×1 = –0.07×1 = –0.07 eV                              e_8s= –0.07 eV.

The sublevel boundaries (in Figures 1, 2, and 3) are represented in thin lines and are as follows:

E2p= –13.6–(–7.65) = –5.95

E3sp= –3.4–(–1.049) = –2.35

E3p= –2.35–(–0.63) = –1.72

E4sp= –1.51–(–0.29) = –1.22

E4p= –1.22–(–0.206) = –1.014

E4pd= –1.014–(–0.124) = –0.89

E5s= –0.85–(–0.1356) = –0.7144

E5p= –0.7144–(–0.097) = –0.6174

E5pd= –0.6174–(–0.06) = –0.5574

E6s= –0.54–(–0.089) = –0.45

E6p= –0.45–(–0.053) = –0.398

E7sp= –0.38–(–0.075) = –0.305.

As can be seen from the calculations presented above, the sequence of energy values of the formed blocks: 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f, 6s, 6p, 6d, 7s, 7p, 8s coincides with the experimentally determined sequence (Table 3).

Figure 4 presents a block-type distribution table of chemical elements [3].

Table [3, 4] offers a number of advantages:

• •    It is visually well-structured;

• •    Each level begins with an alkali metal and ends with a noble gas;

• •    Elements are arranged sequentially according to their atomic numbers;

• •    Element blocks (1s, 2s, 2p, 3s, 3p, …, 7p, 8s) follow one another in sequence [1].

Nanotechnologies in construction      2026; 18 (4):

Нанотехнологии в строительстве     537–544

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES

Nanob

Table 3. Block numbers (N), blocks, block energy, atomic mass of the block, and number of elements in the block

N	1	2	3	4	5	6	7	8	9	10
nl	1s	2s	2p	3s	3p	4s	3d	4p	5s	4d
eV	–13.6	–7.65	–2.55	–1.05	–0.63	–0.29	–0.21	–0.21	–0.14	–0.12
Ar. atomic mass unit	2.5	8.0	15.33	23.6	32.2	39.6	55.3	76.1	86.55	99.8
Z (elements number)	1;2	3;4	5–10	11;12	13–18	19;20	21–30	31–36	37;38	39–48
N	11	12	13	14	15	16	17	18	19	20
nl	5p	5s	4f	5d	6p	7s	5f	6d	7p	8s
eV	–0.1	–0.09	–0.04	–0.06	–0.05	–0.08	–0.02	–0.018	–0.025	–0.07
Ar. atomic mass unit	123.5	135.1	153.8	188	210	224.5	246	273	292	–
Z (elements number)	49–54	55;56	57–70	71–80	81–86	87;88	89–102	103–112	113–118	119;120

Thus, the Periodic Law of Chemical Elements Distribution can be formulated as follows:

“ The periodic and cyclic variation in the properties of chemical elements is dependent on the distribution of sublevel energies l (l = s, p, d, f) across the energy levels n (n = 1, 2, 3, …, 8). ”

The energies of the level boundaries ( E_n ) are determined by the formula:

E_n = –13.6/ n ².

The distribution of sublevel energies (pl) across all levels n is determined by the formula:

pnl = (2l – 1) / L², where: l = 1 (s), l = 2 (p), l = 3 (d), l = 4 (f); and Ln is the total number of sublevels at level n.

It follows from the presented material that a system of two equations is central to the Periodic Law. According to these equations, the block energy increases, cyclically transitioning from negative values to values approaching zero in the 8s block. It is our view that the existence of chemical elements in nature concludes with block 8s.

Therefore, the total number of elements existing in nature is evidently 120.

Nanotechnologies in construction      2026; 18 (4):

Нанотехнологии в строительстве     537–544

Nanob

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES

Nanotechnologies in construction Нанотехнологии в строительстве

2026; 18 (4): 537–544

THE RESULTS OF THE SPECIALISTS’ AND SCIENTISTS’ RESEARCHES