Old wording. Successes of modern natural science
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4.1. Periodic law D.I. Mendeleev
The periodic law is the greatest achievement of chemical science, the basis of all modern chemistry. With his discovery, chemistry ceased to be a descriptive science; scientific foresight became possible in it.
Periodic law open D. I. Mendeleev in 1869, the scientist formulated this law as follows: "The properties of simple bodies, as well as the forms and properties of the compounds of elements, are in a periodic dependence on the magnitude of the atomic weights of the elements."
A more detailed study of the structure of matter showed that the periodicity of the properties of elements is due not to atomic mass, but to the electronic structure of atoms.
The nuclear charge is a characteristic that determines the electronic structure of atoms, and hence the properties of elements. Therefore, in the modern formulation, the Periodic Law sounds like this: the properties of simple substances, as well as the forms and properties of compounds of elements, are in a periodic dependence on the serial number (on the charge of the nucleus of their atoms).
The expression of the Periodic Law is the periodic system of elements.
4.2. Periodic system of D. I. Mendeleev
The periodic system of elements of D. I. Mendeleev consists of seven periods, which are horizontal sequences of elements arranged in ascending order of the charge of their atomic nucleus. Periods 1, 2, 3, 4, 5, 6 contain 2, 8, 8, 18, 18, 32 elements, respectively. The seventh period is not completed. Periods 1, 2 and 3 are called small the rest - large.
Each period (except the first) begins with alkali metal atoms (Li, Na, K, Rb, Cs, Fr) and ends with a noble gas (Ne, Ar, Kr, Xe, Rn) preceded by a typical non-metal. In periods from left to right, metallic properties gradually weaken and non-metallic properties increase, since with an increase in the positive charge of the nuclei of atoms, the number of electrons in the outer level increases.
In the first period, besides helium, there is only one element - hydrogen. It is conditionally placed in the IA or VIIA subgroup, since it shows similarities with both alkali metals and halogens. The similarity of hydrogen with alkali metals is manifested in the fact that hydrogen, like alkali metals, is a reducing agent and, donating one electron, forms a singly charged cation. Hydrogen has more in common with halogens: hydrogen, like halogens, is a non-metal, its molecule is diatomic, it can exhibit oxidizing properties, forming salt-like hydrides with active metals, for example, NaH, CaH 2.
In the fourth period, Ca is followed by 10 transition elements (decade Sc - Zn), followed by the remaining 6 basic elements of the period (Ga - Kr). The fifth period is similarly constructed. concept transition element usually used to refer to any element with valence d- or f-electrons.
The sixth and seventh periods have double insertions of elements. The element Ba is followed by an intercalated decade of d-elements (La - Hg), and after the first transitional element La there are 14 f-elements - lanthanides(Se - Lu). After Hg are the remaining 6 main p-elements of the sixth period (Tl - Rn).
In the seventh (incomplete) period, Ac is followed by 14 f-elements- actinides(Th - Lr). Recently, La and Ac have been classified as lanthanides and actinides, respectively. The lanthanides and actinides are placed separately at the bottom of the table.
Thus, each element in the periodic system occupies a strictly defined position, which is marked ordinal or atomic, number.
In the periodic system, eight groups (I - VIII) are located vertically, which in turn are divided into subgroups - main, or subgroups A and side, or subgroup B. Subgroup VIIIB is special, it contains triads elements that make up the families of iron (Fe, Co, Ni) and platinum metals (Ru, Rh, Pd, Os, Ir, Pt).
The similarity of elements within each subgroup is the most noticeable and important pattern in the periodic system. In the main subgroups, from top to bottom, metallic properties increase and non-metallic properties weaken. In this case, there is an increase in the stability of compounds of elements in the lowest oxidation state for this subgroup. In side subgroups, on the contrary, from top to bottom, the metallic properties weaken and the stability of compounds with the highest oxidation state increases.
4.3. Periodic system and electronic configurations of atoms
Since the nuclei of reacting atoms do not change during chemical reactions, the chemical properties of atoms depend on the structure of their electron shells.
The filling of electron layers and electron shells of atoms occurs in accordance with the Pauli principle and Hund's rule.
Pauli principle (Pauli prohibition)
Two electrons in an atom cannot have four identical quantum numbers (each atomic orbital can contain no more than two electrons).
The Pauli principle determines the maximum number of electrons that have a given principal quantum number n(i.e. located on a given electron layer): N n = 2n 2 . On the first electronic layer (energy level) there can be no more than 2 electrons, on the second - 8, on the third - 18, etc.
In the hydrogen atom, for example, there is one electron, which is in the first energy level in the 1s state. The spin of this electron can be directed arbitrarily (m s = +1/2 or m s = –1/2). It should be emphasized once again that the first energy level consists of one sublevel - 1s, the second energy level - of two sublevels - 2s and 2p, the third - of three sublevels - 3s, 3p, 3d, etc. The sublevel, in turn, contains orbitals, the number of which is determined by the side quantum number l and equal to (2 l + 1). Each orbital is conventionally denoted by a cell, the electron located on it - by an arrow, the direction of which indicates the orientation of the spin of this electron. This means that the state of an electron in a hydrogen atom can be represented as 1s 1 or depicted as a quantum cell, Fig. 4.1:
Rice. 4.1. Symbol for an electron in a hydrogen atom in 1s orbitals
For both electrons of a helium atom n = 1, l = 0, m l= 0, m s = +1/2 and –1/2. Therefore, the electronic formula for helium is 1s 2 . The electron shell of helium is complete and very stable. Helium is a noble gas.
According to the Pauli principle, no two electrons with parallel spins can be in the same orbital. The third electron in the lithium atom occupies the 2s orbital. The electronic configuration of Li: 1s 2 2s 1, and for beryllium 1s 2 2s 2. Since the 2s orbital is filled, the fifth electron at the boron atom occupies the 2p orbital. At n= 2 side (orbital) quantum number l takes the values 0 and 1. When l = 0 (2s state) m l= 0, while l = 1 (2p is the state) m l can be equal to +1; 0; -one. The 2p state corresponds to three energy cells, fig. 4.2.
Rice. 4.2. The location of the electrons of the boron atom in orbitals
For a nitrogen atom (electronic configuration 1s 2 2s 2 2p 3 two electrons at the first level, five - at the second) the following two variants of the electronic structure are possible, fig. 4.3:
Rice. 4.3. Possible options for the arrangement of electrons of the nitrogen atom in orbitals
In the first scheme, Fig.4.3a, the total spin is 1/2 (+1/2 –1/2 +1/2), in the second (Fig.4.3b), the total spin is 3/2 (+1/2 + 1/2+1/2). The location of the spins is determined Hund's rule which reads: the energy levels are filled in such a way that the total spin is maximum.
In this way , of the two given schemes of the structure of the nitrogen atom, the first one corresponds to the stable state (with the lowest energy), where all p-electrons occupy different orbitals. The sublevel orbitals are filled in the following way: first, one electron with identical spins, and then the second electron with opposite spins.
Starting with sodium, the third energy level with n = 3 is filled. 4.4.
Rice. 4.4. Distribution of electrons in orbitals for atoms of elements of the third period in the ground state
In an atom, each electron occupies a free orbital with the lowest energy corresponding to its greatest bond with the nucleus. In 1961 V.M. Klechkovsky formulated a general position according to which the energy of electron orbitals increases in the order of increasing sum of the principal and secondary quantum numbers ( n + l), and in the case of equality of these sums, the orbital with a lower value of the principal quantum number n has less energy.
The sequence of energy levels in ascending order of energy is roughly as follows:
1s< 2s < 2p < 3s < 3р < 4s ≈ 3d < 4p < 5s ≈ 4d < 5p < 6s ≈ 5d ≈ 4f < 6p.
Consider the distribution of electrons in the orbitals of atoms of elements of the fourth period (Fig. 4.5).
Rice. 4.5. Distribution of electrons over the orbitals of atoms of elements of the fourth period in the ground state
After potassium (electronic configuration 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1) and calcium (electronic configuration 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2), the inner 3d shell is filled with electrons (transition elements Sc - Zn) . It should be noted that there are two anomalies: for Cr and Cu atoms by 4 s-shell contains not two electrons, but one, i.e. the so-called “failure” of the outer 4s electron to the previous 3d shell occurs. The electronic structure of the chromium atom can be represented as follows (Fig. 4.6).
Rice. 4.6. Orbital distribution of electrons for a chromium atom
The physical reason for the "violation" of the order of filling is associated with the different penetrating power of the electron orbitals to the nucleus, the special stability of the electronic configurations d 5 and d 10, f 7 and f 14, corresponding to the filling of electronic orbitals with one or two electrons, as well as the screening effect of the internal electronic layers of the charge kernels.
The electronic configurations of Mn, Fe, Co, Ni, Cu, and Zn atoms are represented by the following formulas:
25 Mn 1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 4s 2 ,
26 Fe 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 ,
27 Co 1s 2 2s 2 2p 6 3s 2 3p 6 3d 7 4s 2 ,
28 Ni 1s 2 2s 2 2p 6 3s 2 3p 6 3d 8 4s 2 ,
29 Cu 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 ,
30 Zn 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 .
After zinc, starting from element 31 - gallium up to element 36 - krypton, the filling of the fourth layer (4p - shells) continues. The electronic configurations of these elements are as follows:
31 Ga 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 1 ,
32 Ge 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 2 ,
33 As 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 3 ,
34 Se 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 4 ,
35 Br 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 5 ,
36 Kr 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 .
It should be noted that if the Pauli exclusion is not violated, electrons in excited states can be located in other atomic orbitals.
4.4. Types of chemical elements
All elements of the periodic system are divided into four types:
1. At atoms s-elements the s-shells of the outer layer (n) are filled. The s elements are hydrogen, helium, and the first two elements of each period.
2. At atoms p-elements electrons fill p-shells of the outer level (np). The p-elements include the last 6 elements of each period (except the first).
3. Do d-elements the d-shell of the second level outside (n-1) d is filled with electrons. These are elements of intercalated decades of large periods located between s- and p- elements.
4. Do f-elements filled with electrons f-sublevel of the third outside level (n-2) f . The family of f-elements includes lanthanides and actinides.
From the consideration of the electronic structure of unexcited atoms, depending on the atomic number of the element, it follows:
The number of energy levels (electronic layers) of an atom of any element is equal to the number of the period in which the element is located. Hence, s-elements are in all periods, p-elements are in the second and subsequent periods, d-elements are in the fourth and subsequent periods, and f-elements are in the sixth and seventh periods.
The period number coincides with the principal quantum number of the outer electrons of the atom.
s- and p-elements form the main subgroups, d-elements form secondary subgroups, f-elements form families of lanthanides and actinides. Thus, the subgroup includes elements whose atoms usually have a similar structure not only of the outer, but also of the pre-outer layer (with the exception of elements in which there is a "dip" of the electron).
The group number usually indicates the number of electrons that can participate in the formation of chemical bonds. This is the physical meaning of the group number. For elements of secondary subgroups, the valence electrons are not only the outer, but also the penultimate shells. This is the main difference in the properties of the elements of the main and secondary subgroups.
Elements with valence d- or f-electrons are called transition elements.
The group number, as a rule, is equal to the highest positive oxidation state of the elements that they exhibit in compounds. An exception is fluorine - its oxidation state is -1; Of the Group VIII elements, only Os, Ru, and Xe have an oxidation state of +8.
4.5. Periodicity of properties of atoms of elements
Such characteristics of atoms as their radius, ionization energy, electron affinity, electronegativity, oxidation state, are associated with the electronic structure of the atom.
There are radii of metal atoms and covalent radii of non-metal atoms. The radii of metal atoms are calculated on the basis of interatomic distances, which are well known for most metals based on experimental data. In this case, the radius of a metal atom is equal to half the distance between the centers of two neighboring atoms. The covalent radii of non-metals in molecules and crystals of simple substances are calculated in a similar way. The larger the atomic radius, the easier it is for outer electrons to break away from the nucleus (and vice versa). Unlike atomic radii, ion radii are conventional values.
From left to right, in periods, the value of the atomic radii of metals decreases, and the atomic radii of non-metals change in a complex way, since it depends on the nature of the chemical bond. In the second period, for example, the atomic radii first decrease and then increase, especially sharply when passing to a noble gas atom.
In the main subgroups, the atomic radii increase from top to bottom, as the number of electron layers increases.
The radius of the cation is less than the radius of the corresponding atom, and with an increase in the positive charge of the cation, its radius decreases. Conversely, the radius of an anion is always greater than the radius of its corresponding atom. Particles (atoms and ions) that have the same number of electrons are called isoelectronic. In the series of isoelectronic ions, the radius decreases with decreasing negative and increasing positive ion radius. Such a decrease takes place, for example, in the series: O 2–, F –, Na +, Mg 2+, Al 3+.
Ionization energy is the energy required to detach an electron from an atom in the ground state. It is usually expressed in electronvolts (1 eV = 96.485 kJ/mol). In a period from left to right, the ionization energy increases with increasing nuclear charge. In the main subgroups, from top to bottom, it decreases, since the distance between the electron and the nucleus increases and the screening effect of the inner electron layers increases.
Table 4.1 shows the values of the ionization energies (energy of detachment of the first, second, etc. electrons) for some atoms.
In the second period, when passing from Li to Ne, the energy of detachment of the first electron increases (see Table 4.1). However, as can be seen from the table, the ionization energy increases unevenly: for boron and oxygen following beryllium and nitrogen, respectively, its slight decrease is observed, which is due to the peculiarities of the electronic structure of atoms.
The outer s-shell of beryllium is completely filled, therefore, in the next boron, an electron enters the p-orbital. This p-electron is less strongly bound to the nucleus than the s-electron, so the removal of p-electrons requires less energy.
Table 4.1.
Ionization energies I atoms of certain elements
Each p orbital of the nitrogen atom has one electron. At the oxygen atom, an electron enters the p-orbital, which is already occupied by one electron. Two electrons in the same orbital repel strongly, so it is easier to remove an electron from an oxygen atom than from a nitrogen atom.
Alkali metals have the lowest ionization energy, so they have pronounced metallic properties, the highest ionization energy is in inert gases.
electron affinity is the energy released when an electron is attached to a neutral atom. Electron affinity, like ionization energy, is usually expressed in electron volts. Halogens have the highest electron affinity, while alkali metals have the lowest. Table 4.2 shows the values of electron affinity for atoms of some elements.
Table 4.2.
Electron affinity of atoms of some elements
Electronegativity- the ability of an atom in a molecule or ion to attract the valence electrons of other atoms. Electronegativity (EO) as a quantitative measure is an approximate value. About 20 electronegativity scales have been proposed, the most recognized of which was the scale developed by L. Pauling. On fig. 4.7 shows the values of EO according to Pauling.
Rice. 4.7. Electronegativity of the elements (according to Pauling)
Fluorine is the most electronegative of all elements on the Pauling scale. Its EO is taken equal to 4. The least electronegative is cesium. Hydrogen occupies an intermediate position, since when interacting with some elements, it gives up an electron, and when interacting with others, it acquires.
4.6. Acid-base properties of compounds; Kossel scheme
To explain the nature of the change in the acid-base properties of the compounds of the elements, Kossel (Germany) proposed using a simple scheme based on the assumption that a purely ionic bond exists in the molecules and that the Coulomb interaction takes place between the ions. The Kossel scheme describes the acid-base properties of compounds containing E-H and E-O-H bonds, depending on the charge of the nucleus and the radius of the element that forms them.
The Kossel scheme for two metal hydroxides, for example, LiOH and KOH, is shown in fig. 4.8.
Rice. 4.8. Kossel scheme for LiOH and KOH
As can be seen from the presented scheme, the radius of the Li + ion is less than the radius of the K + ion and the OH - group is more strongly bonded to the lithium cation than to the potassium cation. As a result, KOH will be easier to dissociate in solution and the basic properties of potassium hydroxide will be more pronounced.
Similarly, one can analyze the Kossel scheme for the two bases CuOH and Cu(OH) 2 . Since the radius of the Cu 2+ ion is smaller and the charge is greater than that of the Cu + ion, the Cu 2+ ion will hold the OH - group more firmly. As a result, the Cu(OH) 2 base will be weaker than CuOH.
Thus, base strength increases as the cation radius increases and its positive charge decreases.
In the main subgroups, from top to bottom, the strength of the bases increases, since the radii of the element ions increase in this direction. In periods from left to right, there is a decrease in the radii of the ions of elements and an increase in their positive charge, therefore, in this direction, the strength of the bases decreases.
The Kossel scheme for two anoxic acids, for example, HCl and HI, is shown in fig. 4.9
Rice. 4.9. Kossel's scheme for HCl and HI
Since the radius of the chloride ion is smaller than that of the iodide ion, the H+ ion is more strongly bound to the anion in the hydrochloric acid molecule, which will be weaker than the hydroiodic acid. Thus, the strength of anoxic acids increases with increasing negative ion radius.
The strength of oxygen-containing acids changes in the opposite way. It increases with decreasing ion radius and increasing its positive charge. On fig. 4.10 shows the Kossel scheme for two acids HClO and HClO 4 .
Rice. 4.10. Kossel scheme for HClO and HClO 4
The C1 7+ ion is strongly bound to the oxygen ion, so the proton will be more easily split off in the HClO 4 molecule. At the same time, the bond of the C1 + ion with the O 2- ion is less strong, and in the HC1O molecule the proton will be more strongly retained by the O 2- anion. As a result, HClO 4 will be a stronger acid than HClO.
The advantage of the Kossel scheme is that, using a simple model, it makes it possible to explain the nature of the change in the acid-base properties of compounds in a series of similar substances. However, this scheme is purely qualitative. It only allows one to compare the properties of compounds and does not make it possible to determine the acid-base properties of an arbitrarily chosen one compound. The disadvantage of this model is that it is based only on electrostatic concepts, while in nature there is no pure (100%) ionic bond.
4.7. Redox properties of elements and their compounds
A change in the redox properties of simple substances is easy to establish by considering the nature of the change in the electronegativity of the corresponding elements. In the main subgroups, from top to bottom, electronegativity decreases, which leads to a decrease in oxidizing and an increase in reducing properties in this direction. In periods from left to right, electronegativity increases. As a result, in this direction, the reducing properties of simple substances decrease, while the oxidizing properties increase. Thus, strong reducing agents are located in the lower left corner of the periodic table of elements (potassium, rubidium, cesium, barium), while strong oxidizing agents are located in its upper right corner (oxygen, fluorine, chlorine).
The redox properties of compounds of elements depend on their nature, the degree of oxidation of the elements, the position of the elements in the periodic system, and a number of other factors.
In the main subgroups, from top to bottom, the oxidizing properties of oxygen-containing acids, in which the atoms of the central element have the same oxidation state, decrease. Strong oxidizing agents are nitric and concentrated sulfuric acids. Oxidizing properties are the stronger, the greater the positive oxidation state of the element in the compound. Potassium permanganate and potassium dichromate show strong oxidizing properties.
In the main subgroups, the reducing properties of simple anions increase from top to bottom. Strong reducing agents are HI, H 2 S, iodides and sulfides.
The periodic law of Dmitry Ivanovich Mendeleev is one of the fundamental laws of nature, which links the dependence of the properties of chemical elements and simple substances with their atomic masses. At present, the law has been refined, and the dependence of properties is explained by the charge of the atomic nucleus.
The law was discovered by Russian scientists in 1869. Mendeleev presented it to the scientific community in a report to the congress of the Russian Chemical Society (the report was made by another scientist, since Mendeleev was forced to urgently leave on the instructions of the Free Economic Society of St. Petersburg). In the same year, the textbook "Fundamentals of Chemistry" was published, written by Dmitry Ivanovich for students. In it, the scientist described the properties of popular compounds, and also tried to give a logical systematization of chemical elements. It also presented for the first time a table with periodically arranged elements as a graphical interpretation of the periodic law. All subsequent years, Mendeleev improved his table, for example, he added a column of inert gases, which were discovered 25 years later.
The scientific community did not immediately accept the ideas of the great Russian chemist, even in Russia. But after the discovery of three new elements (gallium in 1875, scandium in 1879 and germanium in 1886), predicted and described by Mendeleev in his famous report, the periodic law was recognized.
- It is a universal law of nature.
- The table that graphically represents the law includes not only all known elements, but also those that are still being discovered.
- All new discoveries did not affect the relevance of the law and the table. The table is improved and changed, but its essence has remained unchanged.
- It made it possible to clarify the atomic weights and other characteristics of some elements, to predict the existence of new elements.
- Chemists have received reliable clues on how and where to look for new elements. In addition, the law allows, with a high degree of probability, to determine in advance the properties of yet undiscovered elements.
- He played a huge role in the development of inorganic chemistry in the 19th century.
Discovery history
There is a beautiful legend that Mendeleev saw his table in a dream, and woke up in the morning and wrote it down. Actually, it's just a myth. The scientist himself said many times that he devoted 20 years of his life to the creation and improvement of the periodic table of elements.
It all started with the fact that Dmitry Ivanovich decided to write a textbook on inorganic chemistry for students, in which he was going to systematize all the knowledge known at that time. And of course, he relied on the achievements and discoveries of his predecessors. For the first time, attention was paid to the relationship between atomic weights and the properties of elements by the German chemist Döbereiner, who tried to break the elements known to him into triads with similar properties and weights that obey a certain rule. In each triple, the middle element had a weight close to the arithmetic mean of the two extreme elements. The scientist was thus able to form five groups, for example, Li-Na-K; Cl–Br–I. But these were far from all known elements. In addition, the trio of elements obviously did not exhaust the list of elements with similar properties. Attempts to find a common pattern were later made by the Germans Gmelin and von Pettenkofer, the French J. Dumas and de Chancourtua, the British Newlands and Odling. The German scientist Meyer advanced the furthest, who in 1864 compiled a table very similar to the periodic table, but it contained only 28 elements, while 63 were already known.
Unlike his predecessors, Mendeleev succeeded in 
make a table that includes all known elements located in a certain system. At the same time, he left some cells blank, roughly calculating the atomic weights of some elements and describing their properties. In addition, the Russian scientist had the courage and foresight to declare that the law he discovered was a universal law of nature and called it a "periodic law." Saying "a", he went further and corrected the atomic weights of elements that did not fit into the table. Upon closer examination, it turned out that his corrections were correct, and the discovery of the hypothetical elements he described was the final confirmation of the truth of the new law: practice proved the validity of the theory.
Makhov B.F.
In connection with the development by the author of the “Vibrational Model of the Neutral Atom” with the inclusion of the “world ether”, in which the concepts of “permanent positive charge of the atomic nucleus” and “Coulomb field” become redundant, the question arises of a new formulation of the Periodic Law. Such a formulation is proposed in this article, where the problem of the mathematical expression of the Periodic Law is also considered. In the article, the author uses his own version of the "Symmetric Quantum Periodic System of Neutral Atoms (SC-PSA)", adequate to the Vibrational Model.
More and more away from us 1869 - the time of the first formulation of the Periodic Law by D.I. Mendeleev (PZM) and his development of the Periodic Table of Elements (PSE-M), in which the atomic weight of the element was taken as the main ordering criterion, a more or less understandable characteristic then available. But even Dmitry Ivanovich himself said that "we do not know the reasons for the periodicity." At that time, only 63 elements were known, and their properties (mostly chemical) were known little and not always accurately.
Nevertheless, the problem of systematization of elements has already declared itself and required a solution. Mendeleev's ingenious intuition allowed him to successfully (at the then level of knowledge) cope with the task. His formulation of the PZM (October 1971): "... the properties of the elements, and therefore the properties of the simple and complex bodies they form, are in a periodic dependence on their atomic weight."
Dmitry Ivanovich arranged all the elements in a row (Mendeleev's series) in order of increasing atomic weight, in which, however, he also allowed deviations for known pairs of elements (based on chemical properties), i.e. in fact, there is a dependence not only on atomic weight.
It became clear to scientists that when moving from one element in the PSE-M to the next, some characteristic of the element increases in steps by the same amount. This value is Z was called the serial number (mainly by chemists) or atomic number (by physicists). It turned out that the atomic weight itself in a certain way depends on Z. Therefore, as the main ordering criterion, the serial number Z was adopted, which, accordingly, was included in the 2nd formulation of the PZM instead of atomic weight.
Time passed, and new possibilities of systematization appeared. First of all, these are advances in the study of line optical spectra (LOS) of neutral atoms and characteristic X-ray radiation (XXR). It turned out that each element has a unique spectrum and a number of new elements were discovered from them. Quantum numbers, spectral terms, W. Pauli's exclusion principle, G. Moseley's law, etc. were proposed to describe the spectra. The study of atoms was crowned with the creation of the first models of the atom (MOA), after the death of D. I. Mendeleev.
Moseley's law, which related the frequency of the characteristic x-ray radiation to the serial number Z, made a particularly great contribution to science. He confirmed the correctness of the Mendeleev series and made it possible to indicate the numbers of the remaining undiscovered elements. But then, guided by good intentions, to give a serial number Z physical meaning, physicists at the level of knowledge of the beginning of the 19th century (the first models of the atom) came to a hasty conclusion that it cannot be anything else than a constant positive electric charge of the atomic nucleus (the number of elementary electric charges - eZ).
As a result, scientists came to the conclusion that a refined 2nd formulation of the PZM is needed, in which the constant positive electric charge of the atomic nucleus of an element was taken as the main systematization criterion.
But, unfortunately, at the beginning of the twentieth century, the first models of the atom were presented too mechanistically (planetary nuclear models), and the electrical neutrality of the atom as a whole was represented by the positive charge of the nucleus and the corresponding number of negative elementary particles - electrons, i.e. also at the level of primitive knowledge of that time about electricity. As a result, the concept of a constant Coulomb electric field was used, which attracts electrons rotating around the nucleus, etc. And God forbid the electron fall on the nucleus!
The discovery of the wave nature of the electron and many problems with the accepted model of the atom, they led to the transition to the "quantum mechanical model of the atom". Quantum mechanics (QM) has been hailed as the greatest achievement of the 20th century. But over time, the enthusiasm subsided. The reason is the shaky foundation on which the CME is built, based on the Schrödinger equation, which " describes motion of an electron. First of all, the approach itself is wrong - instead of considering the equilibrium quantum state of a neutral atom as a whole (at the macro level, in the language of synergetics), CMEs consider the motion of an electron (i.e., they work at an overly detailed micro level). Imagine that for the case of an ideal gas, instead of considering it at the macrolevel with time-constant parameters of the state of the gas (pressure, temperature, volume), they would suddenly begin to write the equations of motion for each of the billions of atoms and molecules of the gas, moaning loudly at the same time about the difficulty of the task and the insufficient power of modern computers. While at the macrolevel, the whole picture is easily and elegantly described using the equation for the connection of gas state parameters - the Clapeyron-Mendeleev equation. [FES, M, SE, 1984, p.288]
Something similar in complexity offers us the CME in the person of its founding fathers, especially for the case of atoms with large atomic numbers. However, Academician Lev Landau (1908-68), himself one of the pillars of the CME, already wrote: “An atom with more than one electron is a complex system of electrons interacting with each other. For such a system, one can, strictly speaking, consider only the states of the system as a whole. The same idea can be found in the works of the spectroscopy physicist Acad. Academy of Sciences of the BSSR Elyashevich M.A. (1908-95).
However, let us return to the consideration of the formulations of the Periodic Law. The modern (refined 2nd) formulation of the PZM is as follows:
"The properties of the elements are in a periodic relationship with the charge of their atomic nuclei." Nuclear charge eZ = atomic (serial) number of the element in the system, multiplied by the elementary electric charge (i.e. Z is numerically equal to the number of elementary electric charges).
Why is a new, 3rd formulation of the PZM needed?
1) From the 2nd formulation it is not very clear what properties are in question - if they are chemical, then they are not directly related to the elements (neutral atoms). When neutral atoms interact, their variable EMFs overlap, as a result, they exert a certain degree of excitation on each other. To describe a chemical bond, you need to know additionally - what is connected to what (composition and structure of the substance) and under what specific physical conditions (CFU), etc.
2) According to the “Vibrational Model” developed by the author, the nucleus of a neutral atom has neither a constant electric charge nor a constant Coulomb field created by it (instead, a pulsating nucleus, an alternating electromagnetic field - EMF, standing EMW, parametric resonance, high quality factor of oscillations, durability atom). See FI, 2008, No. 3, p.25
3) That is, there is no clear definition of either an argument or a function. As for the nature of the periodic dependence, there is also no certainty. The PZM is useless without simultaneously considering the table of the Periodic Table itself, which is why it is often not mentioned at all in textbooks in its current formulation (“vicious circle”). It is no coincidence that we still do not have a complete theory of the Periodic system and the most mathematical expression of the PZM.
4) Now you can use fundamentally new opportunities for a more correct formulation of the Periodic Law and the derivation of its mathematical expression, which give"Vibrational model of a neutral atom" (coupled vibrations of the nucleus and its environment) and "Symmetric quantum periodic system of neutral atoms (SC-PSA)", developed and published by the author.
5) According to the synergetic approach, the equilibrium quantum state of the atom as a whole (macroscopic approach) can be described by several time-independent parameters. The author has shown that they are a strictly individual (W. Pauli exclusion principle) set of 4 quantum numbers inherent in each atom, determined from its LOS (and not from the CME equations).
Such a set of quantum numbers uniquely determines the place of the element (its coordinates) in the SC-PSA developed by the author.
6) Such parameters must meet a number of requirements:
Respond to the physical nature of a neutral atom (according to the "Vibrational Model")
Be unambiguous
Be integer (which follows from the very essence of the radiation of the nucleus)
It is easy to measure (from the spectra of a neutral atom).
Thus, the meaning of quantum numbers known for each atom must be refined according to their physical nature.
7) Instead of E. Schrödinger's CME equation, the author proposes to use the quantum number connection equations (Makhov's equations) (the author found two such equations), which are the mathematical expression of the PZM, adequate to the new formulation. More on this in a forthcoming book.
8) In the light of the “Vibrational Model of the Neutral Atom” and the new idea of the variable EMF of the nucleus, for the new formulation of the Periodic Law, instead of the elementary electric charge, another physical quantity is needed, which, together with the ordinal number Z, characterizes the strength of the electromagnetic interaction (gradually changing with increasing Z) and uniquely determined from the spectrum of neutral atoms. And there is such a value - it is the fine structure constant (α) [FES-763], which is usually used in searches for the "upper boundary of the Periodic Table".
New wording of the PZM looks like that:
"The characteristics of neutral atoms are in a periodic dependence on the magnitude of the tension (aZ) alternating electromagnetic field (EMF) created by their nuclei. The author arrived at such a brief formulation on November 22, 2006, after a series of "lengthy" ones.
It can be seen from it that instead of the magnitude of the electric charge ( eZ), which includes an elementary electric charge, the intensity value is used ( aZ), which includes α - fine structure constant, which “in quantum electrodynamics is considered as a natural parameter characterizing the “strength” of electromagnetic interaction” [FES, p.763].
We have already spoken about the characteristics of neutral atoms (about quantum numbers, their physical nature, etc.), but the nature of the periodic dependence still needs to be clarified a little. Already now there are prerequisites for the derivation of the equations of connection of quantum numbers - this is (n+ l)- rules of academician V.M. Klechkovsky (1900-72) and (n- l)- dhn rule, prof. D.N. Trifonov, which were used by the author to construct the SC-PSA. Keeping in mind the variable EMF and the standing EMW propagating (to a specific depth for each atom), we can say that the sum of these quantum numbers represents the total energy of the standing EMW, and the difference is the depth of change in the oscillation parameter. That is, there are already bundles of quantum numbers that represent in the SC-PSA (n+ l)- period (they are all paired and form dyads), and (n- l)- groups of consecutive atoms - horizontal rows of SC-PSA (up to 4 in a period within Z ≤ 120), which are sequences f-, d-, p-, s- elements. That is, at one quantum energy level there can be several quantum states. Further consideration of the features of the two-unit standing EMW allows us to derive the equations for the connection of quantum numbers (Makhov's equations).
Example: Total standing EMW energy E n + l = E n + E l = const, where E n and E l - the average values of the energy of the electric and magnetic components of its parts.
To clarify the physical meaning of quantum numbers, we use the formula for the energy of a quantum emitter (in general form) E = Eo (2k + 1), hence → = 2k
Specifically, we have for E n + l= E o (2 + 1) → = n + l , that is the sum of quantum numbers (n+ l) is the ratio of the increment of the total energy of a standing EMW to its initial value, which gives a physical meaning to the above-mentioned first rule of academician V.M. Klechkovsky.
A standing EMW is a material carrier of parametric resonance (with a constant internal energy, energy is transferred from electrical to magnetic and vice versa with a huge frequency). In this case, the difference between the average values of the energy of the electric and magnetic components of the total energy of the EMW E n - l = E n - E l - the amount of parameter change is also quantized.
E n - l= E o (2 + 1) → = n - l , this attitude gives physical meaning to D.N. Trifonov’s rule and from here the rule becomes clear n - l ≥ 1, since otherwise there is no standing EMW (there should not be inherent in the traveling wave n = l, and associated energy loss). You can introduce the concept of "relative value of parameter change" : = = λ
The average values of the components of the total energy of the standing EMW are also quantized
E n=Eo(2 n + 1) → = 2n
E l=Eo(2 l + 1) → = 2l
hence the quantum numbers n and l acquire a new physical meaning as the quantum numbers of the components of the electric and magnetic energies of the total energy of a standing EMW (instead of the "principal quantum number" and "orbital quantum number").
The high and constant frequency of the standing EMW is expressed through periodic functions, in relation to our case - trigonometric. The duality of the standing EMW is in the parametric assignment of the function. A standing EMW as a harmonic wave can be described by sinusoidal equations of the form y = A sin (ω t + φ ),
then n t = n cosα and lt = l sin α (parametric definition of an ellipse).
here n and l - quantum numbers (dimensionless integer values), indicators of the maximum amplitude of the relative energy of the electric and magnetic components of the standing EMW, and n t and lt- current values of fluctuating quantities ( standing EMW components) at the moment, i.e. quantities are also dimensionless.*)
0 ≤ |n t| ≤n 0 ≤ |l t | ≤l
Let us clarify that there are exactly two dependencies- cosine and sinusoid At the interface "Nucleus-environment" at the initial moment of radiation, the first has a maximum amplitude - to = n (otherwise there is no radiation), and the amplitude is different - to = 0 (i.e. there is a phase shift). Starting to propagate from the core, one component of the standing EMW generates another and vice versa. The author would like to caution against jumping to the conclusion that to = 0, then the magnetic component of the total energy of the standing EMW is also equal to zero. This is not so, it is enough to recall the formula of a quantum harmonic emitter.
This is the equation of the ellipse + = 1 (in canonical form, common for the connection of harmonic oscillations) and is one of the equations for the connection of quantum numbers.
The physical meaning of this coupling equation becomes clearer if some transformations are made. To do this, we use the representation of the ellipse as hypotrochoids.
For our case ; .
This is the 1st quantum number relation equation (Makhov's equation).
Or clear enough 
.
It can be seen that the equation reflects the constancy of the total energy of a standing EMW. Thus, the above bundles of quantum numbers ( n+l) is the period number in SC-PSA, and ( n - l)- defines the sequence of location of the horizontal rows included in the period - found their place in the equation of communication, and the equation itself well reflects the structure of the SC-PSA.
We have obtained one more, 2nd connection equation for the remaining two quantum numbers (from the complete set in accordance with the W. Pauli exclusion principle) - m l andm s , but you can’t say about them in a nutshell, and with the physical meaning of the "spin" quantum number m s still needs to be figured out - see here.
Beginning (serial number of the original element - Z M) of each M-dyad (a pair of SC-PSA periods) can be obtained from the identical transformation of the formula by V.M. Klechkovsky for the number Zl element at which the first time an element with data appears value lmax
Z M = Zl -1 = = ,
then atlmax = 0; 1; 2; 3; 4... we have Z M= 0; four; twenty; 56; 120..., i.e. these are the so-called tetrahedral numbers, which is indirectly related to some minimum initial quantum energy levels for the dyad (a tetrahedron among all spatial bodies has a minimum surface area with a fixed volume).
In more detail on this subject and the mentioned two equations of connection of quantum numbers, the author intends to report in the papers being prepared for publication.
The author does not claim this work, of course, to create a complete theory of the Periodic system of neutral atoms and its mathematical expression, but he considers it a necessary and important stage on this path, and to the best of his ability will contribute to further progress.
BIBLIOGRAPHY:
- Klechkovsky V.M. "The distribution of atomic electrons and the successive filling rule (n+ l)- group”, M., Atomizdat, 1968
- Klechkovsky V.M. “Development of some theoretical problems of the Periodic system of D.I. Mendeleev" (report at the symposium of the X Mendeleev Congress). M., Nauka, 1971, pp. 54-67.
- Trifonov D.N. "Structure and boundaries of the periodic system", Moscow, Atomizdat, 1976, 271 pages.
- Makhov B.F., book "Symmetric Quantum Periodic System of Elements" (SK-PSE), Moscow, 1997 - ISBN 5-86700-027-3
- Makhov B.F., Article "Symmetric quantum periodic system of elements (neutral atoms) - SC-PSA (or New Periodization of the Periodic System", in the journal RAE "Fundamental Research", 2007, No. 9, pp. 30-36 - ISSN 1812 -7339
- Makhov B.F., Report "The manifestation of pairing in the Periodic system of neutral atoms (SC-PSA)", in Proceedings of the V-Int. conference "Biniology, symmetrology and synergetics in natural sciences", Sept. 2007, Tyumen, Tsogu, Section "Physics and Chemistry", pp. 59-65 ISBN 978-5-88465-835-4
- Makhov B.F., Article "World broadcast" D.I. Mendeleev and his place in the Periodic system”, in the RANH journal “Fundamental Research”, 2008, no. 3, p. 25-28
- Makhov B.F., Article "The physical nature of metals in the light of the vibrational model of the atom", in the journal of the Russian Academy of Natural Sciences "Fundamental Research", 2008, No. 3, p. 29-37
- Landau L.D., Lifshits E.M. "Quantum mechanics. Non-relativistic theory”, Moscow: Nauka, 1974 (3rd ed.). pp. 293. and 1989 (4th ed.). page 302
- Makhov BF, book "On the model of the neutral atom and ways out of the crisis in atomic physics" (prepared for publication).
- Makhov B.F., the book "Three-dimensional SC-PSA" (prepared for publication).
- Bronstein I.N., Semendyaev K.A., Handbook of mathematics for engineers and students of higher educational institutions. Moscow: Nauka, Editor-in-Chief. FML, 1986 (13e, corr.), p.127
- Article "Fine structure constant", Physical Encyclopedic Dictionary - FES, p.763
Bibliographic link
Makhov B.F. PERIODIC LAW D.I. MENDELEEV - NEW FORMULATION AND MATHEMATICAL EXPRESSION OF THE LAW // Successes of modern natural science. - 2008. - No. 9. - P. 24-29;URL: http://natural-sciences.ru/ru/article/view?id=10547 (date of access: 12/17/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"
Periodic law D.I. Mendeleev and the Periodic Table of Chemical Elements is of great importance in the development of chemistry. Let's plunge into 1871, when professor of chemistry D.I. Mendeleev, through numerous trial and error, came to the conclusion that "... the properties of the elements, and therefore the properties of the simple and complex bodies they form, stand in a periodic dependence on their atomic weight." The periodicity of changes in the properties of elements arises due to the periodic repetition of the electronic configuration of the outer electronic layer with an increase in the charge of the nucleus.
Modern formulation of the periodic law is:
"the properties of chemical elements (i.e., the properties and form of the compounds they form) are in a periodic dependence on the charge of the nucleus of atoms of chemical elements."
While teaching chemistry, Mendeleev understood that remembering the individual properties of each element causes difficulties for students. He began to look for ways to create a system method to make it easier to remember the properties of elements. As a result, there was natural table, later it became known as periodical.
Our modern table is very similar to Mendeleev's. Let's consider it in more detail.
periodic table
The periodic table of Mendeleev consists of 8 groups and 7 periods.
The vertical columns of a table are called groups . The elements within each group have similar chemical and physical properties. This is explained by the fact that the elements of one group have similar electronic configurations of the outer layer, the number of electrons on which is equal to the group number. The group is then divided into main and secondary subgroups.
AT Main subgroups includes elements whose valence electrons are located on the outer ns- and np-sublevels. AT Side subgroups includes elements whose valence electrons are located on the outer ns-sublevel and the inner (n - 1) d-sublevel (or (n - 2) f-sublevel).
All elements in periodic table , depending on which sublevel (s-, p-, d- or f-) are valence electrons are classified into: s-elements (elements of the main subgroups I and II groups), p-elements (elements of the main subgroups III - VII groups), d- elements (elements of side subgroups), f- elements (lanthanides, actinides).
The highest valence of an element (with the exception of O, F, elements of the copper subgroup and the eighth group) is equal to the number of the group in which it is located.
For elements of the main and secondary subgroups, the formulas of higher oxides (and their hydrates) are the same. In the main subgroups, the composition of hydrogen compounds is the same for the elements in this group. Solid hydrides form elements of the main subgroups of groups I-III, and groups IV-VII form gaseous hydrogen compounds. Hydrogen compounds of the EN 4 type are more neutral compounds, EN 3 are bases, H 2 E and NE are acids.
The horizontal rows of the table are called periods. Elements in periods differ from each other, but they have in common that the last electrons are at the same energy level ( principal quantum numbern- equally ).
The first period differs from the others in that there are only 2 elements there: hydrogen H and helium He.
There are 8 elements (Li - Ne) in the second period. Lithium Li - an alkali metal begins the period, and closes its noble gas neon Ne.
In the third period, as well as in the second, there are 8 elements (Na - Ar). The alkali metal sodium Na begins the period, and the noble gas argon Ar closes it.
In the fourth period there are 18 elements (K - Kr) - Mendeleev designated it as the first large period. It also begins with the alkali metal Potassium and ends with the inert gas krypton Kr. The composition of large periods includes transition elements (Sc - Zn) - d- elements.
In the fifth period, similarly to the fourth, there are 18 elements (Rb - Xe) and its structure is similar to the fourth. It also begins with the alkali metal rubidium Rb, and ends with the inert gas xenon Xe. The composition of large periods includes transition elements (Y - Cd) - d- elements.
The sixth period consists of 32 elements (Cs - Rn). Except 10 d-elements (La, Hf - Hg) it contains a row of 14 f-elements (lanthanides) - Ce - Lu
The seventh period is not over. It starts with Francium Fr, it can be assumed that it will contain, like the sixth period, 32 elements that have already been found (up to the element with Z = 118).
Interactive periodic table
If you look at Mendeleev's periodic table and draw an imaginary line starting at boron and ending between polonium and astatine, then all metals will be to the left of the line, and non-metals to the right. Elements immediately adjacent to this line will have the properties of both metals and non-metals. They are called metalloids or semimetals. These are boron, silicon, germanium, arsenic, antimony, tellurium and polonium.
Periodic Law
Mendeleev gave the following formulation of the Periodic Law: "the properties of simple bodies, as well as the forms and properties of the compounds of elements, and therefore the properties of the simple and complex bodies formed by them, stand in a periodic dependence on their atomic weight."
There are four main periodic patterns:
Octet rule states that all elements tend to gain or lose an electron in order to have the eight-electron configuration of the nearest noble gas. Because Since the outer s and p orbitals of the noble gases are completely filled, they are the most stable elements.
Ionization energy is the amount of energy required to detach an electron from an atom. According to the octet rule, moving from left to right across the periodic table requires more energy to detach an electron. Therefore, the elements on the left side of the table tend to lose an electron, and those on the right side - to gain it. Inert gases have the highest ionization energy. The ionization energy decreases as you move down the group, because electrons at low energy levels have the ability to repel electrons from higher energy levels. This phenomenon is called shielding effect. Due to this effect, the outer electrons are less strongly bound to the nucleus. Moving along the period, the ionization energy gradually increases from left to right.
electron affinity is the change in energy upon acquisition of an additional electron by an atom of a substance in a gaseous state. When moving down the group, the electron affinity becomes less negative due to the screening effect.
Electronegativity- a measure of how strongly it tends to attract the electrons of another atom bound to it. Electronegativity increases as you move periodic table left to right and bottom to top. It must be remembered that noble gases do not have electronegativity. Thus, the most electronegative element is fluorine.
Based on these concepts, let's consider how the properties of atoms and their compounds change in periodic table.
So, in a periodic dependence are such properties of an atom that are associated with its electronic configuration: atomic radius, ionization energy, electronegativity.
Consider the change in the properties of atoms and their compounds depending on the position in periodic table of chemical elements.
The non-metallicity of the atom increases when moving in the periodic table left to right and bottom to top. Concerning the basic properties of oxides decrease, and acid properties increase in the same order - from left to right and from bottom to top. At the same time, the acidic properties of oxides are the stronger, the greater the degree of oxidation of the element forming it
By period from left to right basic properties hydroxides weaken, in the main subgroups from top to bottom, the strength of the bases increases. At the same time, if a metal can form several hydroxides, then with an increase in the degree of oxidation of the metal, basic properties hydroxides weaken.
By period from left to right the strength of oxygen-containing acids increases. When moving from top to bottom within the same group, the strength of oxygen-containing acids decreases. In this case, the strength of the acid increases with an increase in the degree of oxidation of the acid-forming element.
By period from left to right the strength of anoxic acids increases. When moving from top to bottom within the same group, the strength of anoxic acids increases.
Categories ,First option Periodic table of elements was published by Dmitri Ivanovich Mendeleev in 1869 and was called "The Experience of a System of Elements".
DI. Mendeleev arranged the 63 elements known at that time in ascending order of their atomic masses and obtained a natural series of chemical elements, in which he discovered a periodic recurrence of chemical properties. This series of chemical elements is now known as the Periodic Law (D.I. Mendeleev's formulation):
The properties of simple bodies, as well as the forms and properties of compounds of elements, are in a periodic dependence on the magnitude of the atomic weights of the elements.
The current wording of the law reads as follows:
The properties of chemical elements, simple substances, as well as the composition and properties of compounds are in a periodic dependence on the values of the charges of the nuclei of atoms.
Graphic image periodic law is the periodic table.
The cell of each element indicates its most important characteristics.
Periodic table contains groups and periods.
Group- a column of the periodic system, in which chemical elements are located that have chemical similarity due to identical electronic configurations of the valence layer.
Periodic system of D.I. Mendeleev contains eight groups of elements. Each group consists of two subgroups: main (a) and secondary (b). The main subgroup contains s- and p- elements, in the side - d- elements.
Group names:
I-a Alkali metals.
II-a Alkaline earth metals.
V-a Pnictogens.
VI-a Chalcogens.
VII-a Halogens.
VIII-a Noble (inert) gases.
Period is a sequence of elements written as a string, arranged in order of increasing charges of their nuclei. The period number corresponds to the number of electronic levels in the atom.
The period starts with an alkali metal (or hydrogen) and ends with a noble gas.
|
Parameter |
Down the group |
By period to the right |
|
Core charge |
is increasing |
is increasing |
|
Number of valence electrons |
Does not change |
is increasing |
|
Number of energy levels |
is increasing |
Does not change |
|
Atom radius |
is increasing |
Decreases |
|
Electronegativity |
Decreases |
is increasing |
|
Metal properties |
Are increasing |
Decrease |
|
Oxidation state in higher oxide |
Does not change |
is increasing |
|
The degree of oxidation in hydrogen compounds (for elements of groups IV-VII) |
Does not change |
is increasing |
Modern periodic table of chemical elements of Mendeleev.
