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Atomic Radii

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As the radius of an isolated atom is difficult to define and more difficult to measure, internuclear distances in compounds or gaseous molecules are determined and the radius of the individual atoms calculated therefrom. The radius therefore depends upon

  1. bond order,
  2. the degree of the covalent or ionic nature of the bond,
  3. metallic character,
  4. oxidation state and size of the neighboring atoms,
  5. crystal or molecular structure etc.

Just as the size of an orbital cannot be specified exactly, neither can the size of an atom. We must make some arbitrary choices to obtain values for atomic radii. These values can be obtained by measuring the distances between atoms in chemical compounds.

Definition

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By considering the inter-atomic distances in the structures of elements it is easy to construct a system of the atomic radii of the elements $r_{at}$. This quantity is equal to half the shortest inter-atomic distance. In the structures of elements the atoms are bound by a metallic or covalent bond; therefore, the set of atomic radii can be subdivided into $r_{m}$ and $r_{c}$ according to the type of bond.

Trend

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Some interesting periodic trends are seen immediately on looking at the value of the radii. For the main group elements, atomic radii generally increase going down a group in the periodic table and decrease going across a period. These trends reflect two important effects :

  • From the top to the bottom of a group in the periodic table, the atomic radii increase because electrons occupy orbitals that are successively larger as the value of n, the principal quantum number, increases.
  • The atomic radii decrease from left to right across a period. The n value of the outermost orbitals stays the same,so we might expect the radii of the occupied orbitals to remain approximately constant. However, in crossing a period, as each successive electron is added, the nuclear charge also increases by the addition of one proton. The result is an increased attraction between the nucleus and electrons that is somewhat stronger than the increasing repulsion between electrons, causing atomic radii to decrease.

Periodic Table Elements

The periodic trend in the atomic radii of transition metal atoms across a period is somewhat different from that for main group elements. Going from left to right in a given period, the radii initially decrease. However, the size of the elements in the middle of a transition series change very little and a small increase in size occurs at the end of the series.

What is Atomic Radius?

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As mentioned earlier, atomic radii are sometimes estimated from measurements of the atom-to-atom distance in a crystal of the element. Radius of an element depends on different parameters. According to them there are different types of radius. Some of them are described here.

Orbital Radii:
Orbital radius is determined by the principal quantum number. It is the maximum in the radial probability distribution curve of the outermost orbital. For the cations obtained by stripping the atom of its outermost quantum shell electrons, the orbital radius decreases by a factor of 1.5 to 5 when compared with the atomic radius. For the anions formed by the gain of electrons in the outermost orbitals, the radii do not change appreciably.

Bragg-Slater Radii:
Bragg (1920) proposed a set of radii for elements whose sum gave the observed internuclear distances in a few hundred crystals, both ionic as well as covalent, within 6 pm. Slater (1964) gave an empirical rule that ionic radii of cations are about 85 pm less and those of the anions are 85 pm more than the corresponding atomic radii.

Covalent Radii:
Covalent radius r of an atom is half of the distance between the nuclei of two like atoms forming a covalent bond. The atomic radii are additive and give the covalent bond radii provided that the bonds formed are single bonds and the electronegativity of the bonded atoms does not differ much.

Van der Waals Radii:
When molecules having no inter molecular attraction in terms of chemical forces,weak dispersion forces operate. The inter nuclear distances in such cases are related to the Van der Waals radii. If the two atoms are identical and only weak dispersion forces exist between them, the half of the inter nuclear distance is termed as the Van der Waals radius.

Atomic and Ionic Radii

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From the wave mechanics, the radius of the isolated ion or atom will be infinite. As the electrons are transparent to X-rays, the position of the electrons around the nucleus cannot be determined experimentally in an ionic compound or ionic lattice.

Certain assumptions must be made, therefore, to have a useful concept of the ionic radii. these include i)existence of the ions, ii)correct apportioning of the inter nuclear distances between the ions and iii)constancy of the ionic radii. In simple words, atomic radius is the radius of an atom whereas ionic radius is the radius of an ion.