How can you determine the effective radius of an atom. Atomic radius: what is it and how to determine it

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 different points in the perinuclear 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 the crystal structures of simple substances with a coordination number of 12. For other values ​​of the co.n. the necessary correction is taken into account.

Values covalent radii (r cov) calculated as half the homoatomic bond length. If it is impossible to determine the length of a single homoatomic bond, the r cov value of the atom of element A is obtained by subtracting the covalent radius of the atom of element B from the length of the heteroatomic bond A-B. Covalent radii depend mainly on the size of the inner electron shell.

Radii of valence-unbonded atoms - van der Waals radii (r w) determine the effective sizes of atoms due to the repulsive forces of filled energy levels.

Electron energy values ​​determined by Slater's rules. allowed us 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	rcov	r w	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 changes in 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 principal quantum number increase. For d-elements, in the atoms of which the orbitals of the previous energy level are filled, this tendency does not have a distinct character during the transition from elements of the fifth period to elements of the sixth period.

In short periods, the radii of atoms generally decrease, since the increase in the charge of the nucleus during the transition to each subsequent element causes the attraction of external electrons with increasing force; the number of energy levels at the same time remains constant.

The change in 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 ionization energy. An atom can lose one or more electrons, becoming a positively charged ion - a cation. This ability is quantified by ionization energy.

List of used literature

1. Popkov V. A., Puzakov S. A. General chemistry: textbook. - M.: GEOTAR-Media, 2010. - 976 pp.: ISBN 978-5-9704-1570-2. [With. 27-28]
2. Volkov, A.I., Zharsky, I.M. Big chemical reference book / A.I. Volkov, I.M. Zharsky. - Mn.: Modern School, 2005. - 608 with ISBN 985-6751-04-7.

The effective radius of an atom or ion is understood as the radius of its sphere of action, and the atom (ion) is considered an incompressible ball. Using the planetary model of an atom, it is represented as a nucleus around which electrons orbit. The sequence of elements in Mendeleev's Periodic Table corresponds to the sequence of filling electron shells. The effective radius of the ion depends on the filling of the electron shells, but it is not equal to the radius of the outer orbit. To determine the effective radius, atoms (ions) in the crystal structure are represented as touching rigid balls, so that the distance between their centers is equal to the sum of the radii. Atomic and ionic radii are determined experimentally from X-ray measurements of interatomic distances and calculated theoretically based on quantum mechanical concepts.

The sizes of ionic radii obey the following laws:

1. Within one vertical row of the periodic table, the radii of ions with the same charge increase with increasing atomic number, since the number of electron shells, and therefore the size of the atom, increases.

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, and 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 radii of the atoms do not increase, but uniformly decrease (the so-called lanthanide contraction), and elements from No. 89 (actinium) onwards (the so-called actinide 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 in 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 the structures with the compared coordination numbers is the same). A change in atomic radii with a change in coordination number significantly affects the magnitude of volumetric changes during polymorphic transformations. For example, when cooling iron, its transformation from a modification with a face-centered cubic lattice to a modification with a body-centered cubic lattice, which takes place at 906 o C, should be accompanied by an increase in volume by 9%, in reality the 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, changes in atomic radii during polymorphic transformations largely compensate for those volumetric changes that should have occurred if the atomic radius had not changed. Atomic radii of elements can only be compared if they have the same coordination number.

Atomic (ionic) radii also depend on the type of chemical bond.

In metal bonded crystals, the atomic radius is defined as half the interatomic distance between adjacent atoms. In the case of solid solutions, metallic atomic radii change in a complex way.

The covalent radii of elements with a covalent bond are understood as half the interatomic distance between 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. Thus, the 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 ionic bonds cannot be determined as half the sum of the distances between nearby 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 ionic radii. Based on these approaches, the ionic radii of elements are estimated, and then the ionic radii of other elements are determined from 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 the internuclear distance between the nearest identical atoms that are not connected to each other by a chemical bond, i.e. belonging to different molecules (for example, in molecular crystals).

When using atomic (ionic) radii in calculations and constructions, their values ​​should be taken from tables constructed according to one system.

Atomic ions; have the meaning of the radii of the spheres representing these atoms or ions in molecules or crystals. Atomic radii make it possible to approximately estimate internuclear (interatomic) distances in molecules and crystals.

The electron density of an isolated atom decreases rapidly as the distance to the nucleus increases, so the radius of an atom could be defined as the radius of the sphere in which the bulk (for example, 99%) of the electron density is concentrated. However, to estimate internuclear distances, it turned out to be more convenient to interpret atomic radii differently. This led to the emergence of different definitions and systems of atomic radii.

The covalent radius of an X atom is defined as half the length of a simple chemical bond X—X. Thus, for halogens, covalent radii are calculated from the equilibrium internuclear distance in the X 2 molecule, for sulfur and selenium - in S 8 and Se 8 molecules, for carbon - in a diamond crystal. The exception is the hydrogen atom, for which the covalent atomic radius is taken to be 30 pm, while half the internuclear distance in the H 2 molecule is 37 pm. For compounds with a covalent bond, as a rule, the additivity principle is satisfied (the length of the X-Y bond is approximately equal to the sum of the atomic radii of the X and Y atoms), which makes it possible to predict the bond lengths in polyatomic molecules.

Ionic radii are defined as values ​​whose sum for a pair of ions (for example, X + and Y -) is equal to the shortest internuclear distance in the corresponding ionic crystals. There are several systems of ionic radii; systems differ in numerical values ​​for individual ions depending on which radius and which ion is taken as the basis when calculating the radii of other ions. For example, according to Pauling, this is the radius of the O 2- ion, taken equal to 140 pm; according to Shannon - the radius of the same ion, taken equal to 121 pm. Despite these differences, different systems for calculating internuclear distances in ionic crystals lead to approximately the same results.

Metallic radii are defined as half the shortest distance between atoms in a metal's crystal lattice. For metal structures that differ in the type of packing, these radii are different. The closeness of the atomic radii of various metals often indicates the possibility of the formation of solid solutions by these metals. The additivity of radii allows one to predict the parameters of crystal lattices of intermetallic compounds.

Van der Waals radii are defined as quantities whose sum is equal to the distance to which two chemically unrelated atoms of different molecules or different groups of atoms of the same molecule can approach each other. On average, van der Waals radii are approximately 80 pm larger than covalent radii. Van der Waals radii are used to interpret and predict the stability of molecular conformations and the structural ordering of molecules in crystals.

Lit.: Housecroft K., Constable E. Modern course in general chemistry. M., 2002. T. 1.

EFFECTIVE ATOMIC RADIUS - see Radius is atomic.

Geological Dictionary: in 2 volumes. - M.: Nedra. Edited by K. N. Paffengoltz et al.. 1978 .

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Particle sizes often determine the type of crystal structure and are important for understanding the occurrence of many chemical reactions. The size of atoms, ions, and molecules is determined by valence electrons. The basis for understanding this issue - the patterns of changes in orbital radii - are presented in subsection. 2.4. An atom has no boundaries and its size is a relative value. Nevertheless, it is possible to characterize the size of a free atom by its 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 bonded atoms, you can also enter quantities characterizing their size. Although electron clouds of bound atoms can differ significantly from spherical ones, the sizes of atoms are usually characterized by effective (apparent) radii .

The sizes of atoms of the same element significantly depend on the composition of which chemical compound and what type of bond the atom has. 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 radius value is 0.46 Å. Therefore, they highlight 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 the sum of the radii of two neighboring atoms, taking the atoms to be incompressible spheres. In the presence of reliable and accurate experimental data on interatomic distances (and such data have been available for a long time for both molecules and 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.

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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
Since under n. u. It is difficult to observe molecules with ionic bonds and at the same time a large number of compounds are known that form ionic crystals, then when it comes to ionic radii,

Metal radii
Determining metal radii in itself is not a problem - it is enough to measure the internuclear distance in the corresponding metal and divide in half. In table 20 are some meth

Vander 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, the atoms belong to different molecules

Self-test questions
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 atomic charges
When a chemical bond is formed, a redistribution of electron density occurs, and in the case of a polar bond, the atoms become 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

Self-test questions
1. What is the effective charge of an atom? 2. Can the effective charge exceed (in absolute value) the oxidation state of an atom? 3. What is the degree of ionicity of a bond? 4. K

Valence
In general, valence characterizes the ability of the atoms of an element to form compounds containing a certain composition (certain ratios of the amounts of different elements in the compound). Often in

Self-test questions
1. Define the concepts: degree of oxidation; covalency; coordination number; steric number. 2. Determine covalency, oxidation state and CN for: H2S; H

Communication energy
The amount of energy is the most important characteristic of a bond, determining the resistance of substances to heat, lighting, mechanical stress, and reactions with other substances[†]. There are various methods

Binding energies of diatomic molecules in a gas (N. N. Pavlov)
Molecule H2 Li2 Na2 K2 F2 Cl2

Self-test questions
1. Predict the change in the energy of the C–N bond in the series Н3СNН2, Н2СНН, НННН. 2. Predict the change in binding energy in the series O2, S2, Se2

Chemical Bonding and the Periodic Table 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. The noble gas atoms (group VIIIA) are completely

Changes in interatomic distances for simple substances of group VIA
Substance Distance between atoms, Å inside molecules between molecules difference S

Additional
3. General chemistry / ed. E. M. Sokolovskaya. M.: Moscow State University Publishing House, 1989. 4. Ugai Ya. O. General chemistry. M.: Higher. school, 1984. 5. Same. General and inorganic chemistry. M..