Periodic table with electronic configurations of atoms. Electronic configurations of atoms of elements of small periods
The filling of orbitals in a non-excited atom is carried out in such a way that the energy of the atom is minimal (the principle of minimum energy). First, the orbitals of the first energy level are filled, then the second, and the orbital of the s-sublevel is filled first and only then the orbitals of the p-sublevel. In 1925, the Swiss physicist W. Pauli established the fundamental quantum mechanical principle of natural science (the Pauli principle, also called the exclusion principle or the exclusion principle). According to the Pauli principle:
The electronic configuration of an atom is expressed by a formula in which the filled orbitals are indicated by a combination of a number equal to the principal quantum number and a letter corresponding to the orbital quantum number. The superscript indicates the number of electrons in these orbitals.an atom cannot have two electrons that have the same set of all four quantum numbers.
Hydrogen and helium
The electronic configuration of the hydrogen atom is 1s 1, and the helium atom is 1s 2. A hydrogen atom has one unpaired electron, and a helium atom has two paired electrons. Paired electrons have same values all quantum numbers except spin. A hydrogen atom can give up its electron and turn into a positively charged ion - the H + cation (proton), which has no electrons (electronic configuration 1s 0). A hydrogen atom can add one electron and become a negatively charged H - ion (hydride ion) with the electron configuration 1s 2.Lithium
The three electrons in a lithium atom are distributed as follows: 1s 2 1s 1. Only electrons from the outer energy level, called valence electrons, participate in the formation of a chemical bond. In a lithium atom, the valence electron is the 2s sublevel electron, and the two electrons of the 1s sublevel are internal electrons. The lithium atom quite easily loses its valence electron, transforming into the Li + ion, which has the 1s 2 2s 0 configuration. Note that the hydride ion, helium atom, and lithium cation have same number electrons. Such particles are called isoelectronic. They have similar electronic configurations but different nuclear charges. The helium atom is very chemically inert, which is associated with special stability electronic configuration 1s 2 . Orbitals that are not filled with electrons are called vacant. In the lithium atom, three orbitals of the 2p sublevel are vacant.Beryllium
The electronic configuration of the beryllium atom is 1s 2 2s 2. When an atom is excited, electrons from a lower energy sublevel move to vacant orbitals of a higher energy sublevel. The process of excitation of a beryllium atom can be conveyed by the following diagram:1s 2 2s 2 (ground state) + hν→ 1s 2 2s 1 2p 1 (excited state).
A comparison of the ground and excited states of the beryllium atom shows that they differ in the number of unpaired electrons. In the ground state of the beryllium atom there are no unpaired electrons; in the excited state there are two. Despite the fact that when an atom is excited, in principle, any electrons from lower energy orbitals can move to higher orbitals, for consideration chemical processes Only transitions between energy sublevels with similar energies are significant.
This is explained as follows. When a chemical bond is formed, energy is always released, i.e., the combination of two atoms goes into an energetically more favorable state. The process of excitation requires energy expenditure. When pairing electrons within the same energy level, the excitation costs are compensated by the formation of a chemical bond. When pairing electrons within different levels the excitation costs are so great that they cannot be compensated by the formation of a chemical bond. In the absence of a partner, whenever possible chemical reaction an excited atom releases a quantum of energy and returns to the ground state - this process is called relaxation.
Bor
Electronic configurations of atoms of elements of the 3rd period Periodic table elements will be to a certain extent similar to those given above (the subscript indicates the atomic number):
11 Na 3s 1
12 Mg 3s 2
13 Al 3s 2 3p 1
14 Si 2s 2 2p2
15P 2s 2 3p 3
However, the analogy is not complete, since the third energy level is split into three sublevels and all of the listed elements have vacant d-orbitals to which electrons can transfer upon excitation, increasing multiplicity. This is especially important for elements such as phosphorus, sulfur and chlorine.
The maximum number of unpaired electrons in a phosphorus atom can reach five:
This explains the possibility of the existence of compounds in which the valency of phosphorus is 5. The nitrogen atom, which has the same configuration of valence electrons in the ground state as the phosphorus atom, cannot form five covalent bonds.
A similar situation arises when comparing the valence capabilities of oxygen and sulfur, fluorine and chlorine. The pairing of electrons in a sulfur atom results in the appearance of six unpaired electrons:
3s 2 3p 4 (ground state) → 3s 1 3p 3 3d 2 (excited state).
This corresponds to the six-valence state, which is unattainable for oxygen. The maximum valency of nitrogen (4) and oxygen (3) requires a more detailed explanation, which will be given later.
The maximum valency of chlorine is 7, which corresponds to the configuration of the excited state of the atom 3s 1 3p 3 d 3.
The presence of vacant 3d orbitals in all elements of the third period is explained by the fact that, starting from the 3rd energy level, partial overlap of sublevels of different levels occurs when filled with electrons. Thus, the 3d sublevel begins to fill only after the 4s sublevel is filled. The energy reserve of electrons in atomic orbitals of different sublevels and, consequently, the order of their filling increases in the following order:
Orbitals for which the sum of the first two quantum numbers (n + l) is smaller are filled earlier; if these sums are equal, the orbitals with the lower principal quantum number are filled first.
This pattern was formulated by V. M. Klechkovsky in 1951.
Elements in whose atoms the s-sublevel is filled with electrons are called s-elements. These include the first two elements of each period: hydrogen. However, already in the next d-element - chromium - there is some “deviation” in the arrangement of electrons in energy levels in the ground state: instead of the expected four unpaired electrons on the 3d sublevel, the chromium atom has five unpaired electrons in the 3d sublevel and one unpaired electron in the s sublevel: 24 Cr 4s 1 3d 5 .
The phenomenon of the transition of one s-electron to the d-sublevel is often called “leakthrough” of an electron. This can be explained by the fact that the orbitals of the d-sublevel filled by electrons become closer to the nucleus due to increased electrostatic attraction between electrons and the nucleus. As a result, the state 4s 1 3d 5 becomes energetically more favorable than 4s 2 3d 4. Thus, the half-filled d-sublevel (d 5) has increased stability compared to other possible electron distribution options. The electronic configuration corresponding to the existence of the maximum possible number of paired electrons, achievable in previous d-elements only as a result of excitation, is characteristic of the ground state of the chromium atom. The electronic configuration d 5 is also characteristic of the manganese atom: 4s 2 3d 5. For the following d-elements, each energy cell of the d-sublevel is filled with a second electron: 26 Fe 4s 2 3d 6 ; 27 Co 4s 2 3d 7 ; 28 Ni 4s 2 3d 8 .
In the copper atom, the state of a completely filled d-sublevel (d 10) becomes achievable due to the transition of one electron from the 4s sub-level to the 3d sublevel: 29 Cu 4s 1 3d 10. The last element of the first row of d-elements has the electronic configuration 30 Zn 4s 23 d 10.
The general trend, manifested in the stability of the d 5 and d 10 configurations, is also observed in elements of lower periods. Molybdenum has an electronic configuration similar to chromium: 42 Mo 5s 1 4d 5, and silver to copper: 47 Ag5s 0 d 10. Moreover, the d 10 configuration is already achieved in palladium due to the transition of both electrons from the 5s orbital to the 4d orbital: 46Pd 5s 0 d 10. There are other deviations from the monotonic filling of d- and f-orbitals.
Problem 1. Write electron configurations the following elements: N, Si, F e, Kr, Te, W.
Solution. The energy of atomic orbitals increases in the following order:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d .
Each s-shell (one orbital) can contain no more than two electrons, the p-shell (three orbitals) - no more than six, the d-shell (five orbitals) - no more than 10, and the f-shell (seven orbitals) - no more than 14.
In the ground state of an atom, electrons occupy orbitals with the lowest energy. The number of electrons is equal to the charge of the nucleus (the atom as a whole is neutral) and the atomic number of the element. For example, a nitrogen atom has 7 electrons, two of which are in the 1s orbital, two in the 2s orbital, and the remaining three electrons in the 2p orbital. Electronic configuration of the nitrogen atom:
7 N: 1s 2 2s 2 2p 3. Electronic configurations of the remaining elements:
14 Si: 1s 2 2s 2 2p 6 3s 2 3p 2 ,
26 F e : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6,
36 K r: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 3p 6 ,
52 Te : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 3p 6 5s 2 4d 10 5p 4,
74 Te : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 3p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 4 .
Problem 2. Which inert gas and which element ions have the same electronic configuration as the particle resulting from the removal of all valence electrons from a calcium atom?
Solution. The electron shell of the calcium atom has the structure 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2. When two valence electrons are removed, a Ca 2+ ion is formed with the configuration 1s 2 2s 2 2p 6 3s 2 3p 6. The atom has the same electronic configuration Ar and ions S 2-, Cl -, K +, Sc 3+, etc.
Problem 3. Can the electrons of the Al 3+ ion be in the following orbitals: a) 2p; b) 1p; c) 3d?
Solution. The electronic configuration of the aluminum atom is: 1s 2 2s 2 2p 6 3s 2 3p 1. The Al 3+ ion is formed by the removal of three valence electrons from an aluminum atom and has the electronic configuration 1s 2 2s 2 2p 6 .
a) electrons are already in the 2p orbital;
b) in accordance with the restrictions imposed on the quantum number l (l = 0, 1,…n -1), with n = 1 only the value l = 0 is possible, therefore, the 1p orbital does not exist;
c) electrons can be in the 3d orbital if the ion is in an excited state.
Task 4. Write the electronic configuration of the neon atom in the first excited state.
Solution. The electronic configuration of the neon atom in the ground state is 1s 2 2s 2 2p 6. The first excited state is obtained by the transition of one electron from the highest occupied orbital (2p) to the lowest unoccupied orbital (3s). The electronic configuration of the neon atom in the first excited state is 1s 2 2s 2 2p 5 3s 1.
Problem 5. What is the composition of the nuclei of the isotopes 12 C and 13 C, 14 N and 15 N?
Solution. The number of protons in the nucleus is equal to the atomic number of the element and is the same for all isotopes of a given element. The number of neutrons is equal to the mass number (indicated at the top left of the element number) minus the number of protons. Different isotopes of the same element have different numbers neutrons.
Composition of the indicated kernels:
12 C: 6p + 6n; 13 C: 6p + 7n; 14 N: 7p + 7n; 15 N: 7p + 8n.
Initially the elements in periodic table chemical elements D.I. Mendeleev were arranged according to their atomic masses and chemical properties, but in fact it turned out that decisive role It is not the mass of the atom that plays a role, but the charge of the nucleus and, accordingly, the number of electrons in a neutral atom.
The most stable state of an electron in an atom chemical element corresponds to the minimum of its energy, and any other state is called excited, in which the electron can spontaneously move to a level with a lower energy.
Let's consider how electrons in an atom are distributed among orbitals, i.e. electronic configuration of a multielectron atom in the ground state. To construct the electronic configuration, the following principles are used for filling orbitals with electrons:
- Pauli principle (prohibition) - in an atom there cannot be two electrons with the same set of all 4 quantum numbers;
- the principle of least energy (Klechkovsky's rules) - the orbitals are filled with electrons in order of increasing energy of the orbitals (Fig. 1).
Rice. 1. Energy distribution of orbitals of a hydrogen-like atom; n is the principal quantum number.
The energy of the orbital depends on the sum (n + l). The orbitals are filled with electrons in order of increasing sum (n + l) for these orbitals. Thus, for the 3d and 4s sublevels, the sums (n + l) will be equal to 5 and 4, respectively, as a result of which the 4s orbital will be filled first. If the sum (n + l) is the same for two orbitals, then the orbital with the smaller n value is filled first. So, for 3d and 4p orbitals, the sum (n + l) will be equal to 5 for each orbital, but the 3d orbital is filled first. According to these rules, the order of filling the orbitals will be as follows:
1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<5d<4f<6p<7s<6d<5f<7p
An element's family is determined by the last orbital to be filled by electrons, according to energy. However, it is impossible to write electronic formulas in accordance with the energy series.
41 Nb 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 3 5s 2 correct notation of electronic configuration
41 Nb 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 3 incorrect electronic configuration entry
For the first five d - elements, the valence (i.e., electrons responsible for the formation of a chemical bond) is the sum of the electrons on d and s, the last ones filled with electrons. For p-elements, the valence is the sum of the electrons located in the s and p sublevels. For s elements, the valence electrons are the electrons located in the s sublevel of the outer energy level.
- Hund's rule - at one value of l, electrons fill the orbitals in such a way that the total spin is maximum (Fig. 2)
Rice. 2. Change in energy in the 1s -, 2s – 2p – orbitals of atoms of the 2nd period of the Periodic Table.
Examples of constructing electronic configurations of atoms
Examples of constructing electronic configurations of atoms are given in Table 1.
Table 1. Examples of constructing electronic configurations of atoms
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Electronic configuration |
Applicable rules |
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Pauli principle, Kleczkowski rules |
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Hund's rule |
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1s 2 2s 2 2p 6 4s 1 |
Klechkovsky's rules |
Beryllium Electronic configuration - 2s2. Electronic diagram of the outer quantum layer:
Bor Electronic configuration - 2s22р1. The boron atom can go into an excited state. Electronic diagram of the outer quantum layer:
An unexcited carbon atom can form two covalent bonds due to electron pairing and one through the donor-acceptor mechanism. An example of such a compound is carbon monoxide (II), which has the formula CO and is called carbon monoxide. Its structure will be discussed in more detail in section 2.1.2. An excited carbon atom is unique: all orbitals of its outer quantum layer are filled with unpaired electrons, i.e. It has the same number of valence orbitals and valence electrons. Its ideal partner is the hydrogen atom, which has one electron in its only orbital. This explains their ability to form hydrocarbons. Having four unpaired electrons, the carbon atom forms four chemical bonds: CH4, CF4, CO2. In molecules of organic compounds, the carbon atom is always in an excited state:
The nitrogen atom cannot be excited because there is no free orbital in its outer quantum layer. It forms three covalent bonds due to electron pairing:
Having two unpaired electrons in the outer layer, the oxygen atom forms two covalent bonds:
Neon
Electronic configuration - 2s22р6. Lewis symbol: Electron diagram of the outer quantum layer:
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The neon atom has a complete external energy level and does not form chemical bonds with any atoms. This is the second noble gas. THIRD PERIOD Atoms of all elements of the third period have three quantum layers. The electronic configuration of the two internal energy levels can be depicted as . The outer electronic layer contains nine orbitals, which are populated by electrons, obeying general laws. So, for a sodium atom the electronic configuration is: 3s1, for calcium - 3s2 (in an excited state - 3s13р1), for aluminum - 3s23р1 (in an excited state - 3s13р2). Unlike elements of the second period, atoms of elements of groups V – VII of the third period can exist both in the ground and in excited states. Phosphorus Phosphorus is a group 5 element. Its electronic configuration is 3s23р3. Like nitrogen, it has three unpaired electrons in its outermost energy level and forms three covalent bonds. An example is phosphine, which has the formula PH3 (compare with ammonia). But phosphorus, unlike nitrogen, contains free d-orbitals in the outer quantum layer and can go into an excited state - 3s13р3d1:
This gives it the opportunity to form five covalent bonds in compounds such as P2O5 and H3PO4.
However, it can be excited by transferring an electron first from R- on d-orbital (first excited state), and then with s- on d-orbital (second excited state):
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In the first excited state, the sulfur atom forms four chemical bonds in compounds such as SO2 and H2SO3. The second excited state of the sulfur atom can be depicted using an electron diagram:
This sulfur atom forms six chemical bonds in the compounds SO3 and H2SO4.
1.3.3. Electronic configurations of atoms of large elements periods THE FOURTH PERIODThe period begins with potassium (19K) electron configuration: 1s22s22p63s23p64s1 or 4s1 and calcium (20Ca): 1s22s22p63s23p64s2 or 4s2. Thus, in accordance with the Klechkovsky rule, after the p-orbitals of Ar, the outer 4s sublevel is filled, which has lower energy, because The 4s orbital penetrates closer to the nucleus; The 3d sublevel remains empty (3d0). Starting from scandium, the orbitals of the 3d sublevel are populated in 10 elements. They're called d-elements.
In accordance with the principle of sequential filling of orbitals, the chromium atom should have an electronic configuration of 4s23d4, but it exhibits an electron “leap”, which consists in the transition of a 4s electron to a 3d orbital that is close in energy (Fig. 11).
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It has been experimentally established that atomic states in which the p-, d-, f-orbitals are half filled (p3, d5, f7), completely (p6, d10, f14) or free (p0, d0, f0) have increased stability. Therefore, if an atom lacks one electron before half-completion or completion of a sublevel, its “leap” from a previously filled orbital (in this case, 4s) is observed.
With the exception of Cr and Cu, all elements from Ca to Zn have the same number of electrons in their outer shell - two. This explains the relatively small change in properties in the series of transition metals. However, for the listed elements, both the 4s electrons of the outer and the 3d electrons of the pre-external sublevel are valence electrons (with the exception of the zinc atom, in which the third energy level is completely completed).
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The 4d and 4f orbitals remained free, although the fourth period was completed.
FIFTH PERIOD
The sequence of filling the orbitals is the same as in the previous period: first the 5s orbital is filled ( 37Rb 5s1), then 4d and 5p ( 54Xe 5s24d105p6). The 5s and 4d orbitals are even closer in energy, so most 4d elements (Mo, Tc, Ru, Rh, Pd, Ag) experience an electron transition from the 5s to the 4d sublevel.
SIXTH AND SEVENTH PERIODS
Unlike the previous one, the sixth period includes 32 elements. Cesium and barium are 6s elements. The next energetically favorable states are 6p, 4f and 5d. Contrary to Klechkovsky's rule, in lanthanum it is not the 4f but the 5d orbital that is filled ( 57La 6s25d1), however, for the elements following it, the 4f-sublevel is filled ( 58Ce 6s24f2), on which there are fourteen possible electronic states. Atoms from cerium (Ce) to lutetium (Lu) are called lanthanides - these are f-elements. In the series of lanthanides, sometimes an electron “leak” occurs, just as in the series of d-elements. When the 4f-sublevel is completed, the 5d-sublevel (nine elements) continues to be filled and the sixth period, like any other except the first, is completed by six p-elements.
The first two s elements in the seventh period are francium and radium, followed by one 6d element, actinium ( 89Ac 7s26d1). Actinium is followed by fourteen 5f elements - actinides. The actinides should be followed by nine 6d elements and six p elements should complete the period. The seventh period is incomplete.
The considered pattern of the formation of periods of a system by elements and the filling of atomic orbitals with electrons shows the periodic dependence of the electronic structures of atoms on the charge of the nucleus.
Period is a set of elements arranged in order of increasing charges of atomic nuclei and characterized by the same value of the principal quantum number of outer electrons. At the beginning of the period are filled ns -, and at the end - n.p. -orbitals (except for the first period). These elements form eight main (A) subgroups of the periodic system of D.I. Mendeleev.
Main subgroup is a set of chemical elements arranged vertically and having the same number of electrons at the outer energy level.
Within the period, with an increase in the charge of the nucleus and an increasing force of attraction of external electrons to it from left to right, the radii of atoms decrease, which in turn causes a weakening of metallic properties and an increase in non-metallic properties. Behind atomic radius take the theoretically calculated distance from the nucleus to the maximum electron density of the outer quantum layer. In groups, from top to bottom, the number of energy levels increases, and, consequently, the atomic radius. At the same time, the metallic properties are enhanced. Important properties of atoms that change periodically depending on the charges of the atomic nuclei also include ionization energy and electron affinity, which will be discussed in section 2.2.
Electronic configuration- a formula for the arrangement of electrons in different electron shells of an atom of a chemical element or molecule.
Electronic configuration is usually written for atoms in their ground state. To determine the electronic configuration of an element, the following rules exist:
- Filling principle. According to the filling principle, electrons in the ground state of an atom fill orbitals in a sequence of increasing orbital energy levels. The lowest energy orbitals are always filled first.
- Pauli's exclusion principle. According to this principle, any orbital can contain no more than two electrons, and then only if they have opposite spins (unequal spin numbers).
- Hund's rule. According to this rule, the filling of the orbitals of one subshell begins with single electrons with parallel (equal sign) spins, and only after single electrons occupy all the orbitals can the final filling of the orbitals with pairs of electrons with opposite spins occur.
From the point of view of quantum mechanics, the electron configuration is a complete list of one-electron wave functions, from which the complete wave function of an atom can be compiled with a sufficient degree of accuracy (in the self-consistent field approximation).
Generally speaking, an atom, as a composite system, can be fully described only by a complete wave function. However, such a description is practically impossible for atoms more complex than the hydrogen atom, the simplest of all atoms of chemical elements. A convenient approximate description is the self-consistent field method. This method introduces the concept of the wave function of each electron. The wave function of the entire system is written as a properly symmetrized product of one-electron wave functions. When calculating the wave function of each electron, the field of all other electrons is taken into account as an external potential, which in turn depends on the wave functions of these remaining electrons.
As a result of applying the self-consistent field method, a complex system of nonlinear integrodifferential equations is obtained, which is still difficult to solve. However, the self-consistent field equations have rotational symmetry of the original problem (that is, they are spherically symmetric). This allows a complete classification of the single-electron wave functions that make up the complete atomic wave function.
To begin with, as in any centrally symmetric potential, the wave function in a self-consistent field can be characterized by the quantum number of the total angular momentum l (\displaystyle l) and the quantum number of the projection of angular momentum onto some axis m (\displaystyle m). Wave functions with different values m (\displaystyle m) correspond to the same energy level, i.e. they are degenerate. Also, states with different projections of the electron spin onto any axis correspond to the same energy level. Total for a given energy level 2 (2 l + 1) (\displaystyle 2(2l+1)) wave functions. Further, for a given value of angular momentum, the energy levels can be renumbered. By analogy with the hydrogen atom, it is customary to number the energy levels for a given l (\displaystyle l) beginning with n = l + 1 (\displaystyle n=l+1). The complete list of quantum numbers of single-electron wave functions from which the wave function of an atom can be composed is called the electron configuration. Since everything is degenerate in quantum number m (\displaystyle m) and along the spin, it is enough only to indicate the total number of electrons in the state with the data n (\displaystyle n), l (\displaystyle l).
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For historical reasons, in the electron configuration formula the quantum number l (\displaystyle l) written in Latin letters. State c is indicated by the letter s (\displaystyle s), p (\displaystyle p): l = 1 (\displaystyle l=1), d (\displaystyle d): l = 2 (\displaystyle l=2), f (\displaystyle f): l = 3 (\displaystyle l=3), g (\displaystyle g): l = 4 (\displaystyle l=4) and further alphabetically. To the left of the number l (\displaystyle l) write the number n (\displaystyle n), and above from the number l (\displaystyle l)- number of electrons in the data state n (\displaystyle n) And l (\displaystyle l). For example 2 s 2 (\displaystyle 2s^(2)) corresponds to two electrons in the state with n = 2 (\displaystyle n=2), l = 0 (\displaystyle l=0). Due to practical convenience (see Klechkovsky’s rule), in the complete formula for the electronic configuration the terms are written in order of increasing quantum number n (\displaystyle n), and then the quantum number l (\displaystyle l), For example 1 s 2 2 s 2 2 p 6 3 s 2 3 p 3 (\displaystyle 1s^(2)2s^(2)2p^(6)3s^(2)3p^(3)). Since this notation is somewhat redundant, sometimes the formula is shortened to 1 s 2 2 s 2 p 6 3 s 2 p 3 (\displaystyle 1s^(2)2s^(2)p^(6)3s^(2)p^(3)), i.e. they omit the number n (\displaystyle n) where it can be guessed from the rule of ordering terms.
Periodic law and atomic structure
All those involved in the structure of the atom in any of their research proceed from the tools that are provided to them by the periodic law, discovered by the chemist D. I. Mendeleev; Only in their understanding of this law do physicists and mathematicians use their own “language” to interpret the dependencies shown to them (although J. W. Gibbs’ rather ironic aphorism on this subject is known), but, at the same time, in isolation from chemists studying the substance , with all the perfection, advantages and versatility of their apparatus, neither physicists nor mathematicians, of course, can build their own research.
The interaction of representatives of these disciplines is also observed in the further development of the topic. The discovery of secondary periodicity by E. V. Biron (1915) provided another aspect in understanding issues related to the laws of the structure of electron shells. S. A. Shchukarev, student of E. V. Biron and
