The atomic radius of the sphere. Effective atomic radius. Chemical bond properties
The effective radius of an atom or ion is understood as the radius of the sphere of its action, and the atom (ion) is considered to be an incompressible ball. Using the planetary model of the atom, it is represented as a nucleus around which electrons revolve in orbits. The sequence of elements in the Periodic system of Mendeleev corresponds to the sequence of filling the electron shells. The effective radius of an ion depends on the occupancy of the electron shells, but it is not equal to the radius of the outer orbit. To determine the effective radius, the atoms (ions) in the crystal structure are represented as contacting rigid balls, so that the distance between their centers is equal to the sum of the radii. Atomic and ionic radii were determined experimentally from X-ray measurements of interatomic distances and calculated theoretically on the basis of quantum mechanical concepts.
The sizes of ionic radii obey the following laws:
1. Within one vertical row of the periodic system, the radii of ions with the same charge increase with increasing atomic number, since the number of electron shells increases, and hence the size of the atom.
2. For the same element, the ionic radius increases with increasing negative charge and decreases with increasing positive charge. The radius of the anion is greater than the radius of the cation, since the anion has an excess of electrons, while the cation has a deficiency. For example, for Fe, Fe 2+, Fe 3+, the effective radius is 0.126, 0.080 and 0.067 nm, respectively, for Si 4-, Si, Si 4+, the effective radius is 0.198, 0.118 and 0.040 nm.
3. The sizes of atoms and ions follow the periodicity of the Mendeleev system; exceptions are elements from No. 57 (lanthanum) to No. 71 (lutetium), where the atomic radii do not increase, but decrease uniformly (the so-called lanthanide contraction), and elements from No. 89 (actinium) and beyond (the so-called actinoid contraction).
The atomic radius of a chemical element depends on the coordination number. An increase in the coordination number is always accompanied by an increase in interatomic distances. In this case, the relative difference between the values of atomic radii corresponding to two different coordination numbers does not depend on the type of chemical bond (provided that the type of bond in structures with compared coordination numbers is the same). A change in atomic radii with a change in the coordination number significantly affects the magnitude of volumetric changes during polymorphic transformations. For example, when iron is cooled, its transformation from a face-centered cubic modification to a body-centered cubic modification occurring at 906 ° C should be accompanied by an increase in volume by 9%, in fact, an increase in volume is 0.8%. This is due to the fact that due to a change in the coordination number from 12 to 8, the atomic radius of iron decreases by 3%. That is, the change in atomic radii during polymorphic transformations largely compensates for the volumetric changes that would have to occur if the atomic radius did not change in this case. The atomic radii of elements can only be compared with the same coordination number.
Atomic (ionic) radii also depend on the type of chemical bond.
In crystals with a metallic bond, the atomic radius is defined as half the interatomic distance between the nearest atoms. In the case of solid solutions, metallic atomic radii vary in a complex way.
Under the covalent radii of elements with a covalent bond is understood half of the interatomic distance between the nearest atoms connected by a single covalent bond. A feature of covalent radii is their constancy in different covalent structures with the same coordination numbers. So, distances in single C-C bonds in diamond and saturated hydrocarbons are the same and equal to 0.154 nm.
Ionic radii in substances with an ionic bond cannot be defined as half the sum of the distances between the nearest ions. As a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions differs from spherical. There are several approaches to estimating the value of ionic radii. Based on these approaches, the ionic radii of the elements are estimated, and then the ionic radii of other elements are determined from the experimentally determined interatomic distances.
Van der Waals radii determine the effective sizes of noble gas atoms. In addition, van der Waals atomic radii are considered to be half of the internuclear distance between the nearest identical atoms that are not chemically bonded, i.e. belonging to different molecules (for example, in molecular crystals).
When using the values of atomic (ionic) radii in calculations and constructions, their values should be taken from tables built according to one system.
Particle size often determines the type of crystal structure, is important for understanding the flow of many chemical reactions. The size of atoms, ions, molecules is determined by valence electrons. The basis for understanding this issue - the patterns of changes in orbital radii - are set out in Sec. 2.4. The atom has no boundaries and its size is a conditional value. Nevertheless, it is possible to characterize the size of a free atom by the orbital radius. But of practical interest are usually atoms and ions in the composition of a substance (in a molecule, polymer, liquid or solid), and not free ones. Since the states of a free and bound atom differ significantly (and, above all, their energy), the sizes must also differ.
For bound atoms, one can also introduce quantities characterizing their size. Although the electron clouds of bound atoms can differ significantly from spherical ones, it is customary to characterize the sizes of atoms effective (apparent) radii .
The sizes of atoms of the same element essentially depend on the composition of which chemical compound What type of bond is the atom with. For example, for hydrogen, half of the interatomic distance in the H 2 molecule is 0.74/2 = 0.37 Å, and in metallic hydrogen, the value of the radius is 0.46 Å. Therefore, allocate covalent, ionic, metallic and van der Waals radii . As a rule, in the concepts of effective radii, interatomic distances (more precisely, internuclear distances) are considered to be the sum of the radii of two neighboring atoms, taking the atoms as incompressible balls. In the presence of reliable and accurate experimental data on interatomic distances (and such data have been available for a long time both for molecules and for crystals with an accuracy of thousandths of an angstrom), one problem remains to determine the radius of each atom - how to distribute the interatomic distance between two atoms . It is clear that this problem can be solved unambiguously only by introducing additional independent data or assumptions.
End of work -
This topic belongs to:
Chemical bond properties
On the site site read: "chemical bond properties" ..
If you need additional material on this topic, or you did not find what you were looking for, we recommend using the search in our database of works:
What will we do with the received material:
If this material turned out to be useful for you, you can save it to your page on social networks:
| tweet |
All topics in this section:
covalent radii
The most obvious situation is with covalent radii for atoms that form nonpolar diatomic molecules. In such cases, the covalent radius is exactly half the interatomic distance
Ionic radii
Because at n. y. it is difficult to observe molecules with ionic bonds and at the same time a large number of compounds that form ionic crystals are known, then when it comes to ionic radii,
metal radii
In itself, the determination of metal radii is not a problem - it is enough to measure the internuclear distance in the corresponding metal and divide it in half. In table. 20 are some meth
van der Waals radii
Van der Waals radii can be determined by measuring the distances between atoms in a crystal when there is no chemical bond between them. In other words, atoms belong to different molecules.
Questions for self-examination
1. What are orbital and effective radii? 2. What is the difference between the radius of a pellet and an atom or ion? 3. In what cases is the covalent radius equal to half the length
Effective charges of atoms
When a chemical bond is formed, the electron density is redistributed, and in the case polar bond atoms are electrically charged. These charges are called effective. They are hara
Effective charges in some ionic crystals
Substance CsF CsCl NaF NaCl LiF LiCl LiI DEO 3.3
Effective charges of atoms in oxides (according to N. S. Akhmetov)
Oxide Na2O MgO Al2O3 SiO2 P2O5 SO
Questions for self-examination
1. What is the effective charge of an atom? 2. Can the effective charge exceed (in modulus) the oxidation state of the atom? 3. What is the degree of ionicity of a bond? 4. K
Valence
In general, valency characterizes the ability of the atoms of an element to form compounds containing a certain composition (certain ratios of the number of different elements in the compound). Often in
Questions for self-examination
1. Define the concepts: degree of oxidation; covalence; coordination number; steric number. 2. Determine the covalence, oxidation state and CN for: H2S; H
Bond energy
The magnitude of energy is the most important characteristic of a bond, which determines the resistance of substances to heat, lighting, mechanical stress, and reactions with other substances[†]. Exist various methods uh
Binding energies of diatomic molecules in a gas (N. N. Pavlov)
Molecule H2 Li2 Na2 K2 F2 Cl2
Questions for self-examination
1. Predict the change in the C–N bond energy in the series H3CNH2, H2CNH, HCNH. 2. Predict the change in the binding energy in the series O2, S2, Se2
Chemical bond and Periodic system of elements
Let us consider the regularities of the structure and properties of some simple substances and the simplest compounds, determined by the electronic structure of their atoms. Noble gas atoms (group VIIIA) have completely
Change in interatomic distances for simple substances of the VIA group
Substance Distance between atoms, Å inside molecules between molecules difference S
Additional
3. General chemistry / ed. E. M. Sokolovskaya. M.: Publishing House of Moscow State University, 1989. 4. Ugay Ya. O. General Chemistry. M.: Higher. school, 1984. 5. He is the same. General and inorganic chemistry. M..
One of the most important characteristics of the chemical elements involved in the formation of a chemical bond is the size of an atom (ion): with its increase, the strength of interatomic bonds decreases. The size of an atom (ion) is usually determined by the value of its radius or diameter. Since an atom (ion) does not have clear boundaries, the concept of "atomic (ionic) radius" implies that 90–98% of the electron density of an atom (ion) is contained in the sphere of this radius. Knowing the values of atomic (ionic) radii makes it possible to estimate internuclear distances in crystals (that is, the structure of these crystals), since for many problems the shortest distances between the nuclei of atoms (ions) can be considered the sum of their atomic (ionic) radii, although such additivity is approximate and is satisfied not in all cases.
Under atomic radius chemical element (about the ionic radius, see below), involved in the formation of a chemical bond, in the general case, agreed to understand half the equilibrium internuclear distance between the nearest atoms in the crystal lattice of the element. This concept, which is quite simple if we consider atoms (ions) as rigid spheres, actually turns out to be complex and often ambiguous. The atomic (ionic) radius of a chemical element is not a constant value, but varies depending on a number of factors, the most important of which are the type of chemical bond
and coordination number.
If the same atom (ion) in different crystals forms different types chemical bond, then it will have several radii - covalent in a crystal with a covalent bond; ionic in a crystal with an ionic bond; metallic in metal; van der Waals in a molecular crystal. The influence of the type of chemical bond can be seen in the following example. In diamond, all four chemical bonds are covalent and are formed sp 3-hybrids, so all four neighbors of a given atom are on the same and
the same distance from it d= 1.54 A˚) and the covalent radius of carbon in diamond will be
is equal to 0.77 A˚. In an arsenic crystal, the distance between atoms bound by covalent bonds ( d 1 = 2.52 A˚), much less than between atoms bound by van der Waals forces ( d 2 = 3.12 A˚), so As will have a covalent radius of 1.26 A˚ and van der Waals of 1.56 A˚ .
The atomic (ionic) radius also changes very sharply with a change in the coordination number (this can be observed during polymorphic transformations of elements). The smaller the coordination number, the lower the degree of space filling with atoms (ions) and the smaller the internuclear distances. An increase in the coordination number is always accompanied by an increase in internuclear distances.
It follows from the foregoing that the atomic (ionic) radii of different elements involved in the formation of a chemical bond can only be compared when they form crystals in which the same type of chemical bond is realized, and these elements in the formed crystals have the same coordination numbers .
Let us consider the main features of atomic and ionic radii in more detail.
Under covalent radii of elements It is customary to understand half of the equilibrium internuclear distance between the nearest atoms connected by a covalent bond.
A feature of covalent radii is their constancy in different "covalent structures" with the same coordination number Z j. In addition, covalent radii, as a rule, are additively bonded to each other, that is, the A–B distance is half the sum of the A–A and B–B distances in the presence of covalent bonds and the same coordination numbers in all three structures.
There are normal, tetrahedral, octahedral, quadratic and linear covalent radii.
The normal covalent radius of an atom corresponds to the case when an atom forms as many covalent bonds as it corresponds to its place in the periodic table: for carbon - 2, for nitrogen - 3, etc. This results in different meanings normal radii depending on the multiplicity (order) of the bond (single bond, double, triple). If the bond is formed when the hybrid electron clouds overlap, then they speak of tetrahedral
(Z k = 4, sp 3-hybrid orbitals), octahedral ( Z k = 6, d 2sp 3-hybrid orbitals), quadratic ( Z k = 4, dsp 2-hybrid orbitals), linear ( Z k = 2, sp-hybrid orbitals) covalent radii.
It is useful to know the following about covalent radii (the values \u200b\u200bof covalent radii for a number of elements are given in).
1. Covalent radii, unlike ionic ones, cannot be interpreted as the radii of atoms that have a spherical shape. Covalent radii are used only to calculate the internuclear distances between atoms united by covalent bonds, and do not say anything about the distances between atoms of the same type that are not covalently bonded.
2. The value of the covalent radius is determined by the multiplicity of the covalent bond. A triple bond is shorter than a double bond, which in turn is shorter than a single bond, so the covalent radius of a triple bond is smaller than the covalent radius of a double bond, which is smaller
single. It should be borne in mind that the order of the multiplicity of the relationship does not have to be an integer. It can also be fractional if the bond is resonant (benzene molecule, Mg2 Sn compound, see below). In this case, the covalent radius has an intermediate value between the values corresponding to integer orders of the bond multiplicity.
3. If the bond is of a mixed covalent-ionic nature, but with a high degree of the covalent component of the bond, then the concept of the covalent radius can be introduced, but the influence of the ionic component of the bond on its value cannot be neglected. In some cases, this effect can lead to a significant decrease in the covalent radius, sometimes down to 0.1 A˚. Unfortunately, attempts to predict the magnitude of this effect in various
cases have not yet been successful.
4. The value of the covalent radius depends on the type of hybrid orbitals that take part in the formation of a covalent bond.
Ionic radii, of course, cannot be defined as half the sum of the distances between the nuclei of the nearest ions, since, as a rule, the sizes of cations and anions differ sharply. In addition, the symmetry of the ions may differ somewhat from spherical. Nevertheless, for real ionic crystals under ionic radius It is customary to understand the radius of the ball, which approximates the ion.
Ionic radii are used for approximate estimates of internuclear distances in ionic crystals. It is assumed that the distance between the nearest cation and anion is equal to the sum of their ionic radii. The typical error in determining internuclear distances in terms of ionic radii in such crystals is ≈0.01 A˚.
There are several systems of ionic radii that differ in the values of the ionic radii of individual ions, but lead to approximately the same internuclear distances. The first work on the determination of ionic radii was carried out by V. M. Goldshmit in the 1920s. In it, the author used, on the one hand, the internuclear distances in ionic crystals measured by X-ray structural analysis, and, on the other hand, the values of the ionic radii F– and O2– determined by
refractometry method. Most other systems also rely on the internuclear distances in crystals determined by diffraction methods and on some "reference" values of the ionic radius of a particular ion. In the most widely known system
Pauling, this reference value is the ionic radius of the O2− peroxide ion, equal to
1.40A˚. This value for O2– agrees well with theoretical calculations. In the system of G. B. Bokiya and N. V. Belov, which is considered one of the most reliable, the ionic radius O2– is taken equal to 1.36 A˚.
In the 1970s and 1980s, attempts were made to directly determine the radii of ions by measuring the electron density using X-ray structural analysis, provided that the minimum of the electron density on the line connecting the nuclei is taken as the boundary of the ions. It turned out that this direct method leads to overestimated values of the ionic radii of cations and to underestimated values of the ionic radii of anions. In addition, it turned out that the values of ionic radii determined by a direct method cannot be transferred from one compound to another, and the deviations from additivity are too large. Therefore, such ionic radii are not used to predict internuclear distances.
It is useful to know the following about ionic radii (in the tables below, the values \u200b\u200bof ionic radii according to Bokiy and Belov are given).
1. The ionic radius for ions of the same element varies depending on its charge, and for the same ion it depends on the coordination number. Depending on the coordination number, tetrahedral and octahedral ionic radii are distinguished.
2. Inside one vertical row, more precisely, inside one group, periodic
system, the radii of ions with the same charge increase with an increase in the atomic number of the element, since the number of shells occupied by electrons increases, and hence the size of the ion.
|
Radius, A˚ |
3. For positively charged ions of atoms from the same period, the ionic radii rapidly decrease with increasing charge. The rapid decrease is explained by the action of two main factors in one direction: the strong attraction of “own” electrons by the cation, the charge of which increases with increasing atomic number; an increase in the strength of interaction between the cation and the anions surrounding it with an increase in the charge of the cation.
|
Radius, A˚ |
4. For negatively charged ions of atoms from the same period, the ionic radii increase with increasing negative charge. The two factors discussed in the previous paragraph in this case act in opposite directions, and the first factor prevails (an increase in the negative charge of the anion is accompanied by an increase in its ionic radius), therefore, an increase in ionic radii with an increase in the negative charge occurs much more slowly than a decrease in the previous case.
|
Radius, A˚ |
5. For the same element, that is, with the same initial electronic configuration, the radius of the cation is less than that of the anion. This is due to a decrease in the attraction of external "additional" electrons to the anion nucleus and an increase in the screening effect due to internal electrons (the cation has a lack of electrons, while the anion has an excess).
|
Radius, A˚ |
6. The sizes of ions with the same charge follow the periodicity of the periodic table. However, the value of the ionic radius is not proportional to the charge of the nucleus Z, which is due to the strong attraction of electrons by the nucleus. In addition, the lanthanides and actinides, in whose series the radii of atoms and ions with the same charge do not increase, but decrease with increasing atomic number (the so-called lanthanide contraction and actinide contraction), are an exception to the periodic dependence.11
11 Lanthanide contraction and actinide contraction are due to the fact that in lanthanides and actinides, electrons added with an increase in atomic number fill internal d And f-shells with a principal quantum number less than the principal quantum number of a given period. At the same time, according to quantum mechanical calculations in d and especially in f states, the electron is much closer to the nucleus than in s And p states of a given period with a large quantum number, therefore d And f-electrons are located in the inner regions of the atom, although the filling of these states with electrons (we are talking about electronic levels in the energy space) occurs differently.
metal radii are considered equal to half the shortest distance between the nuclei of atoms in the crystallizing structure of a metal element. They depend on the coordination number. If we take the metallic radius of any element at Z k \u003d 12 per unit, then with Z k = 8, 6 and 4 the metallic radii of the same element will be 0.98 respectively; 0.96; 0.88. Metallic radii have the property of additivity. Knowing their values makes it possible to approximately predict the parameters of the crystal lattices of intermetallic compounds.
The atomic radii of metals are characterized by the following features (data on the values of the atomic radii of metals can be found in).
1. The metallic atomic radii of transition metals are generally smaller than the metallic atomic radii of non-transition metals, reflecting the greater bond strength in transition metals. This feature is due to the fact that the metals of transition groups and the metals closest to them in the periodic system have electronic d-shells, and electrons in d-states can take part in the formation of a chemical bond. Strengthening of the bond may be associated partly with the appearance of a covalent component of the bond and partly with the van der Waals interaction of ionic cores. In crystals of iron and tungsten, for example, electrons in d-states make a significant contribution to the binding energy.
2. Within one vertical group, as we move from top to bottom, the atomic radii of metals increase, which is due to a sequential increase in the number of electrons (the number of shells occupied by electrons increases).
3. Within one period, more precisely, starting from the alkali metal to the middle of the transition metal group, in the direction from left to right, the atomic metal radii decrease. In the same sequence, the electric charge of the atomic nucleus increases and the number of electrons in the valence shell increases. With an increase in the number of binding electrons per atom, the metallic bond is strengthened, and at the same time, due to an increase in the charge of the nucleus, the attraction of core (internal) electrons by the nucleus increases, so the value of the metallic atomic radius decreases.
4. Transition metals of groups VII and VIII from the same period in the first approximation have almost the same metal radii. Apparently, when it comes to elements that have 5 and more d-electrons, an increase in the nuclear charge and the associated effects of attraction of core electrons, leading to a decrease in the atomic metallic radius, are compensated by the effects due to the increasing number of electrons in the atom (ion) that do not participate in the formation of a metallic bond, and leading to an increase in the metallic radius (increasing the number of states occupied by electrons).
5. The increase in radii (see paragraph 2) for transition elements, which occurs during the transition from the fourth to the fifth period, is not observed for transition elements at
transition from the fifth to the sixth period; the metallic atomic radii of the corresponding (vertical comparison) elements in these last two periods are almost the same. Apparently, this is due to the fact that the elements located between them are completed with a relatively deep f-shell, so the increase in the charge of the nucleus and the associated attraction effects turn out to be more significant than the effects associated with an increasing number of electrons (lanthanide contraction).
|
Element from 4 periods |
Radius, A˚ |
Element from period 5 |
Radius, A˚ |
Element from period 6 |
Radius, A˚ |
6. Usually, metallic radii are much larger than ionic radii, but they do not differ so significantly from the covalent radii of the same elements, although without exception they are all larger than covalent ones. The large difference in the values of the metallic atomic and ionic radii of the same elements is explained by the fact that the bond, which owes its origin to almost free conduction electrons, is not strong (hence the observed relatively large interatomic distances in the metal lattice). A significantly smaller difference in the values of the metallic and covalent radii of the same elements can be explained if we consider the metallic bond as some special "resonant" covalent bond.
Under van der Waals radius It is customary to understand half of the equilibrium internuclear distance between the nearest atoms connected by a van der Waals bond. Van der Waals radii determine the effective sizes of noble gas atoms. In addition, as follows from the definition, the van der Waals atomic radius can be considered to be half the internuclear distance between the nearest atoms of the same name, connected by a van der Waals bond and belonging to different molecules (for example, in molecular crystals). When atoms approach each other at a distance less than the sum of their van der Waals radii, a strong interatomic repulsion occurs. Therefore, van der Waals atomic radii characterize the minimum allowable contacts of atoms belonging to different molecules. Data on the values of van der Waals atomic radii for some atoms can be found in).
Knowing the van der Waals atomic radii makes it possible to determine the shape of molecules and their packing in molecular crystals. The van der Waals radii are much larger than all the radii of the same elements listed above, which is explained by the weakness of the van der Waals forces.
Periodic properties of elements
Periodicity is expressed in the structure of the electron shell of atoms, therefore, properties that depend on the state of electrons are in good agreement with the periodic law: atomic and ionic radii, ionization energy, electron affinity, electronegativity and valency of elements. But the composition and properties of simple substances and compounds depend on the electronic structure of atoms, therefore, periodicity is observed in many properties of simple substances and compounds: the temperature and heat of melting and boiling, the length and energy of a chemical bond, electrode potentials, standard enthalpies formation and entropy of substances, etc. The periodic law covers more than 20 properties of atoms, elements, simple substances and compounds.
According to quantum mechanics, an electron can be located at any point around the nucleus of an atom, both near it and at a considerable distance. Therefore, the boundaries of atoms are vague, indefinite. At the same time, quantum mechanics calculates the probability of distribution of electrons around the nucleus and the position of the maximum electron density for each orbital.
Orbital radius of an atom (ion)is the distance from the nucleus to the maximum electron density of the most distant outer orbital of this atom (ion).
Orbital radii (their values are given in the handbook) decrease in periods, because an increase in the number of electrons in atoms (ions) is not accompanied by the appearance of new electron layers. The electron shell of an atom or ion of each subsequent element in the period becomes denser compared to the previous one due to an increase in the charge of the nucleus and an increase in the attraction of electrons to the nucleus.
Orbital radii in groups increase as an atom (ion) of each element differs from the parent by the appearance of a new electronic layer.
Change of orbital atomic radii for five periods is shown in fig. 13, from which it can be seen that the dependence has a “sawtooth” form characteristic of the periodic law.
Rice. 13. Dependence of the orbital radius
from the atomic number of the elements of the first - fifth periods.
But in periods, the decrease in the size of atoms and ions does not occur monotonically: individual elements have small “bursts” and “dips”. In the "dips" there are, as a rule, elements whose electronic configuration corresponds to a state of increased stability: for example, in the third period it is magnesium (3s 2), in the fourth - manganese (4s 2 3d 5) and zinc (4s 2 3d 10) etc.
Note. Calculations of orbital radii have been carried out since the mid-seventies of the last century due to the development of electronic computers. Previously used effective the radii of atoms and ions, which are determined from experimental data on internuclear distances in molecules and crystals. It is assumed that the atoms are incompressible balls that touch their surfaces in compounds. The effective radii determined in covalent molecules are called covalent radii, in metal crystals - metal radii, in compounds with ionic bond - ionic radii. The effective radii differ from the orbital radii, but their change depending on the atomic number is also periodic.
An important characteristic of an atom is its size, i.e., atomic radius. The size of an individual atom is not determined, since its outer boundary is blurred due to the probabilistic presence of electrons at various points in the circumnuclear space. Because of this, depending on the type of bond between atoms, metallic, covalent, van der Waals, ionic, and other atomic radii are distinguished.
"Metal" radii (r me) found by halving the shortest interatomic distances in crystal structures simple substances with a coordination number of 12. For other values of c.h. necessary correction is taken into account.
Values covalent radii (r cov) calculated as half the length of a homoatomic bond. If it is impossible to determine the length of a single homoatomic bond, the r cov value of an atom of element A is obtained by subtracting the covalent radius of an atom of element B from the length of the heteroatomic A-B connections. Covalent radii depend mainly on the size of the inner electron shell.
Radii of valence-unbound atoms - van der Waals radii (r w) determine the effective sizes of atoms due to the repulsive forces of the filled energy levels.
Electron energy values determined by Slater's rules. made it possible to estimate the relative value - the apparent size of the atom - r cmp (empirical radius).
The bond length is given in angstroms (1 Å = 0.1 nm = 100 pm).
| Element | r me | r cov | rw | r cmp |
| H | 0.46 | 0.37 | 1.20 | 0.25 |
| He | 1.22 | 0.32 | 1.40 | - |
| Li | 1.55 | 1.34 | 1.82 | 1.45 |
| Be | 1.13 | 0.90 | - | 1.05 |
| B | 0.91 | 0.82 | - | 0.85 |
| C | 0.77 | 0.77 | 1.70 | 0.70 |
| N | 0.71 | 0.75 | 1.55 | 0.65 |
| O | - | 0.73 | 1.52 | 0.60 |
| F | - | 0.71 | 1.47 | 0.50 |
| Ne | 1.60 | 0.69 | 1.54 | - |
| Na | 1.89 | 1.54 | 2.27 | 1.80 |
| mg | 1.60 | 1.30 | 1.73 | 1.50 |
| Al | 1.43 | 1.18 | - | 1.25 |
| Si | 1.34 | 1.11 | 2.10 | 1.10 |
| P | 1.30 | 1.06 | 1.80 | 1.00 |
| S | - | 1.02 | 1.80 | 1.00 |
| Cl | - | 0.9 | 1.75 | 1.00 |
| Ar | 1.92 | 0.97 | 1.88 | - |
| K | 2.36 | 1.96 | 2.75 | 2.20 |
| Ca | 1.97 | 1.74 | - | 1.80 |
| sc | 1.64 | 1.44 | - | 1.60 |
| Ti | 1.46 | 1.36 | - | 1.40 |
| V | 1.34 | 1.25 | - | 1.35 |
| Cr | 1.27 | 1.27 | - | 1.40 |
| Mn | 1.30 | 1.39 | - | 1.40 |
| Fe | 1.26 | 1.25 | - | 1.40 |
| co | 1.25 | 1.26 | - | 1.35 |
| Ni | 1.24 | 1.21 | 1.63 | 1.35 |
| Cu | 1.28 | 1.38 | 1.40 | 1.35 |
| Zn | 1.39 | 1.31 | 1.39 | 1.35 |
| Ga | 1.39 | 1.26 | 1.87 | 1.30 |
| Ge | 1.39 | 1.22 | - | 1.25 |
| As | 1.48 | 1.19 | 1.85 | 1.15 |
| Se | 1.60 | 1.16 | 1.90 | 1.15 |
| Br | - | 1.14 | 1.85 | 1.15 |
| kr | 1.98 | 1.10 | 2.02 | - |
| Rb | 2.48 | 2.11 | - | 2.35 |
| Sr | 2.15 | 1.92 | - | 2.00 |
| Y | 1.81 | 1.62 | - | 1.80 |
| Zr | 1.60 | 1.48 | - | 1.55 |
| Nb | 1.45 | 1.37 | - | 1.45 |
| Mo | 1.39 | 1.45 | - | 1.45 |
| Tc | 1.36 | 1.56 | - | 1.35 |
| Ru | 1.34 | 1.26 | - | 1.30 |
| Rh | 1.34 | 1.35 | - | 1.35 |
| Pd | 1.37 | 1.31 | 1.63 | 1.40 |
| Ag | 1.44 | 1.53 | 1.72 | 1.60 |
| CD | 1.56 | 1.48 | 1.58 | 1.55 |
| In | 1.66 | 1.44 | 1.93 | 1.55 |
| sn | 1.58 | 1.41 | 2.17 | 1.45 |
| Te | 1.70 | 1.35 | 2.06 | 1.40 |
| I | - | 1.33 | 1.98 | 1.40 |
| Xe | 2.18 | 1.30 | 2.16 | - |
| Cs | 2.68 | 2.25 | - | 2.60 |
| Ba | 2.21 | 1.98 | - | 2.15 |
| La | 1.87 | 1.69 | - | 1.95 |
| Ce | 1.83 | - | - | 1.85 |
| Pr | 1.82 | - | - | 1.85 |
| Nd | 1.82 | - | - | 1.85 |
| Pm | - | - | - | 1.85 |
| sm | 1.81 | - | - | 1.85 |
| Eu | 2.02 | - | - | 1.80 |
| Gd | 1.79 | - | - | 1.80 |
| Tb | 1.77 | - | - | 1.75 |
| Dy | 1.77 | - | - | 1.75 |
| Ho | 1.76 | - | - | 1.75 |
| Er | 1.75 | - | - | 1.75 |
| Tm | 1.74 | - | - | 1.75 |
| Yb | 1.93 | - | - | 1.75 |
| Lu | 1.74 | 1.60 | - | 1.75 |
| hf | 1.59 | 1.50 | - | 1.55 |
| Ta | 1.46 | 1.38 | - | 1.45 |
| W | 1.40 | 1.46 | - | 1.35 |
| Re | 1.37 | 1.59 | - | 1.35 |
| Os | 1.35 | 1.28 | - | 1.30 |
| Ir | 1.35 | 1.37 | - | 1.35 |
| Pt | 1.38 | 1.28 | 1.75 | 1.35 |
| Au | 1.44 | 1.44 | 1.66 | 1.35 |
| hg | 1.60 | 1.49 | 1.55 | 1.50 |
| Tl | 1.71 | 1.48 | 1.96 | 1.90 |
| Pb | 1.75 | 1.47 | 2.02 | 1.80 |
| Bi | 1.82 | 1.46 | - | 1.60 |
| Po | - | - | - | 1.90 |
| At | - | - | - | - |
| Rn | - | 1.45 | - | - |
| Fr | 2.80 | - | - | - |
| Ra | 2.35 | - | - | 2.15 |
| AC | 2.03 | - | - | 1.95 |
| Th | 180 | - | - | 1.80 |
| Pa | 1.62 | - | - | 1.80 |
| U | 1.53 | - | 1.86 | 1.75 |
| Np | 1.50 | - | - | 1.75 |
| Pu | 1.62 | - | - | 1.75 |
| Am | - | - | - | 1.75 |
The general trend of atomic radii is as follows. In groups, atomic radii increase, since with an increase in the number of energy levels, the sizes of atomic orbitals with a large value of the principal quantum number increase. For d-elements, in whose atoms the orbitals of the previous energy level are filled, this tendency does not have a distinct character during the transition from the elements of the fifth period to the elements of the sixth period.
In small periods, the radii of atoms generally decrease, since an increase in the charge of the nucleus during the transition to each next element causes the attraction of external electrons with increasing force; the number of energy levels at the same time remains constant.
The change in the atomic radius in periods for d-elements is more complex.
The value of the atomic radius is quite closely related to such an important characteristic of the atom as the ionization energy. An atom can lose one or more electrons, turning into a positively charged ion - a cation. This ability is quantified by the ionization energy.
List of used literature
- Popkov V. A., Puzakov S. A. General chemistry: textbook. - M.: GEOTAR-Media, 2010. - 976 p.: ISBN 978-5-9704-1570-2. [With. 27-28]
- Volkov, A.I., Zharsky, I.M. Big chemical reference book / A.I. Volkov, I.M. Zharsky. - Minsk: Modern school, 2005. - 608 with ISBN 985-6751-04-7.
