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 valence of elements. But the composition and properties depend on the electronic structure of atoms simple substances and compounds, therefore periodicity is observed in many properties of simple substances and compounds: temperature and heat of melting and boiling, length and energy chemical bond, electrode potentials, standard enthalpies of formation and entropies 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 close to it and at a considerable distance. Therefore, the boundaries of atoms are vague and indefinite. At the same time, in quantum mechanics the probability of electron distribution around the nucleus and the position of the maximum electron density for each orbital are calculated.
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 reference book) decrease over periods, because An increase in the number of electrons in atoms (ions) is not accompanied by the appearance of new electronic layers. The electron shell of an atom or ion of each subsequent element in a 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 because the atom (ion) of each element differs from its superior one by the appearance of a new electronic layer.
The change in orbital atomic radii for five periods is shown in Fig. 13, from which it is clear that the dependence has a “sawtooth” shape characteristic of the periodic law.
Rice. 13. Dependence of orbital radius
from the atomic number of elements of the first – fifth periods.
But during periods, the decrease in the size of atoms and ions does not occur monotonically: small “bursts” and “dips” are observed in individual elements. In the “gaps” there are, as a rule, elements that have 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 thanks to the development of electronic computing technology. Previously used effective 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. Effective radii determined in covalent molecules are called covalent radii, in metal crystals – metal radii, in compounds with ionic bonds – ionic radii. Effective radii differ from orbital radii, but their change with 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 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 rcov 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 connections. 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
- Popkov V. A., Puzakov S. A. General chemistry: textbook. - M.: GEOTAR-Media, 2010. - 976 pp.: 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. - 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. Inside one vertical row periodic table 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, 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).
Atomic radius 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, metal atomic radii change in a complex way.
Under the covalent radii of elements with covalent bond understand 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. So, distances in single S-S relations 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.
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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Atomic radii atomic radii
characteristics that make it possible to approximately estimate interatomic (internuclear) distances in molecules and crystals. Atomic radii are on the order of 0.1 nm. Determined mainly from X-ray structural analysis data.
ATOMIC RADIUSATOMIC RADIUS, characteristics that allow one to approximately estimate interatomic (internuclear) distances in molecules and crystals.
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 in orbits (cm. ORBITALS) electrons rotate. 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 (cm. 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 crystals with metal bond (cm. METAL LINK) atomic radius is defined as half the interatomic distance between nearest atoms. In the case of solid solutions (cm. SOLID SOLUTIONS) metallic atomic radii vary in complex ways.
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 (cm. IONIC BOND) 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.
Encyclopedic Dictionary. 2009 .
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