Atomic Radius

2) Van der Waals Radius

It is one half the distance between the nuclei of two identical non-bonded isolated atoms or two adjacent identical atoms belonging to two neighboring molecules of an element in the solid-state. The magnitude of the Van der Waals radius is dependent on the packing of the atoms when the element is in the solid-state.

For example, the internuclear distance between two adjacent chlorine atoms of the two neighboring molecules in the solid-state is 360 pm. Therefore, the Van der Waals radius of the chlorine atom is 180 pm.

Know about Electron Gain Enthalpy?

3) Metallic Radius

A metal lattice or crystal consists of positive kernels or metal ions arranged in a definite pattern in a sea of mobile valence electrons. Each kernel is simultaneously attracted by a number of mobile electrons and each mobile electron is attracted by a number of metal ions.

Force of attraction between the mobile electrons and the positive kernels is called the metallic bond. It is one half the internuclear distance between the two adjacent metal ions in the metallic lattice. In a metallic lattice, the valence electrons are mobile, therefore, they are only weakly attracted by the metal ions or kernels.

In a covalent bond, a pair of electrons is strongly attracted by the nuclei of two atoms. Thus, a metallic radius is always longer than its covalent radius. For example, the metallic radius of sodium is 186 pm whereas its covalent radius as determined by its vapor which exists as Na₂ is 154 pm. The metallic radius of Potassium is 231 pm while its covalent radius is 203 pm.

Read about Metallic and Non-Metallic characters here.

Variation of Atomic Radii in the Periodic Table

Variation Within a Period

• The Covalent and Van der Waals radii decrease with an increase in the atomic number as we move from left to right in a period. The alkali metals at the extreme left of the periodic table have the largest size in a period. The halogens at the extreme right of the periodic table have the smallest size. The atomic size of nitrogen is the smallest. After nitrogen, atomic size increases for Oxygen and then decreases for fluorine. The size of atoms of inert gases is larger than those of the preceding halogens.
• As we move from left to right in a period, the nuclear charge increases by 1 unit in each succeeding element while the number of shells remains the same. This enhanced nuclear charge pulls the electrons of all the shells closer to the nucleus. This makes each individual shell smaller and smaller. This results in a decrease in the atomic radius as we move from left to right in a period.
• The atomic radius abruptly increases as we move from halogens to the inert gas. This is because inert gases have completely filled orbitals. Hence, the inter-electronic is maximum. We express the atomic size in terms of Van der Waals radius since they do not form covalent bonds. Van der Waals radius is larger than the covalent radius. Therefore, the atomic size of inert gas in a period is much higher than that of preceding halogen

Variation Within a Group

The atomic radii of elements increase with an increase in the atomic number from top to bottom in a group. As we move down the group, the principal quantum number increases. A new energy shell is added at each succeeding element. The valence electrons lie farther and farther away from the nucleus. As a result, the attraction of the nucleus for the electron decreases. Hence, the atomic radius increases.

A Solved Example for You

Q: Why is the Van der Waals Radius always greater than the Covalent Radius?

Ans: The Van der Waals forces of attraction are weak. Therefore, the internuclear distance in the case of atoms held by Van der Waal forces is much larger than those between covalently bonded atoms. Since a covalent bond is formed by the overlap of two half-filled atomic orbitals, a part of electron cloud becomes common. Therefore, covalent radii are always smaller than the van der Waal radius.