Atomic Radius

Atomic Radius

✓ Atomic radius is defined as half the distance between the nearest neighbours in a crystal of a pure element.

✓ Generally, it is expressed in terms of the cube edge element 'a'. It is denoted by 'r'.

Calculation of atomic radii

✓ Atomic radii can be calculated as follows in various crystal structures.

1. Simple Cubic (SC) structure

✓ The front view of a simple cubic structure is shown in Fig.0.16. There are eight atoms per unit cell situated at the eight corners.

✓ If 'a' is the side of the unit cell and 'r' can be the radius of atom, then from the geometry of Fig.0.16,

2. Body Centred Cubic (BCC) structure 

✓ We know that each BCC structure contains one atom at the body centre and shares one atom at each of its 8 corners.

✓ In this case, atoms touch each other along the diagonal of the cube as shown in Fig.0.17. 

Therefore, the diagonal of the cube in this case is 4 r.

From the geometry of the Fig.0.17,

3. Face Centred Cubic (FCC) structure

✓ In FCC lattice, there are eight corner atoms in the unit cell and one atom at the centre of each face.

✓ In this case, atoms are in contact along the face diagonal of the cube, as shown in Fig.0.18.

From the geometry of the Fig.0.18,

(AF)2 = AB2 + BF2

i.e., (4 r)2 = a2 + a2

or

(4 r)2 = 2a2 

or

4r = √2 a

4. Hexagonal Close Packed (HCP) structure

✓ The atoms touch each other along the edge of the hexagon. Thus from the Fig.0.13, the nearest neighbouring distance a = 2 r.