The number of carbon atoms per unit cell of diamond is:

Diamond has fcc unit cell structure made up of atoms. This accounts for 8 × 1/8 + 6 × 1/2 = 1 + 3 = 4 C atoms. C atoms are also present in one half of the tetrahedral voids. There are 8 tetrahedral voids in fcc structure. This accounts for remaining 8 × 1/2 = 4 C atoms. Thus, total 4 + 4 = 8 C atoms are present per unit cell of diamond.