Express the relation between atomic radius(r) and edge length(a) of a f.c.c unit cell.

In a face centred cube we have one atom each at the corners and one atom on each face. Let us consider the triangle ADC.

Then the face diagonal AC will be 4r( the diameter of the face centred atom and the radii of the 2 atoms in the corners).

According to Pythagoras theorem AC²= AD² + DC²

AD² = DC² = a² (edge length)

AC² = 4r

Therefore