The only difference of atomic radius and atomic radii is that the radii is the plural of atomic radius.The general picture of an atom in our mind is that of the sphere. If it is regarded as correct, then it is defined as:

The distance from the centre of the nucleus to the outermost shell containing the electrons.

It is not possible to measure the exact value of the atomic radius of an atom of an element.It is because atom is very much smaller in size.However, we can express the different forms of the atom.

## Why not possible to find exact Atomic Radii

A. It is not possible to isolate a single atom in order to determine its radius.

B. It is not possible to measure the exact distance of the atom.It does not have well-defined shape or boundary and probability of electron is level zero even at a large distance from the nucleus.

C.The atomic radius is likely to change due to environmental effect.
and many more reasons

Depending upon the nature of bonding of atoms these are:

In homoatomic molecules (containing the same type of atoms), covalent radii is defined as:

The one-half distance between the centres of two bonded atoms joins each other by a single covalent bond. The distance can be measured by the X-ray diffraction and spectroscopic method.Thus,

Covalent Radius(Rcovalent)=  Inter nuclear distance in the bonded atoms/(divided)2

Remember

A.In Heteroatomic atoms, covalent radius shifted towards the higher electronegative element.

B.If the two atoms linked to each other by a double bond or triple Bond, then the half of the Inter nuclear distance does not represent the covalent radii.

Van der Waal radii are the half the distance between two similar atoms belongs to the neighbouring molecule of the same substance in the solid state.

Actually, the van der Waal forces are weak forces. Their magnitude(power)  of attraction is smaller in gaseous as well as in the liquid state of the substance. Therefore radius is determined in the solid state when the magnitude of the force is expected to a maximum. The value of van der Waal radius is more than that of the covalent radius.For example, the van der Waal force of chlorine is 180 pm while covalent radius is 99 pm(picometer)

Half the distance between the centre of nuclei of two adjacent atoms in a metallic crystal. Since the metallic bond is weaker than covalent bond the internuclear molecular distance or atomic radii between the two atoms in metallic bond is more than the covalent bond.

Remember

Metallic bond is more than covalent bond