Question

Diamond has a three dimensional structure of $C$ atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where $50\%$ of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is____________

Answer 1

Effective atoms of carbon in fcc unit cell $=8\times \frac{1}{8}+6\times \frac{1}{2}=4$
Total number of tetrahedral void in fcc unit cell = 8
$50\%$ of the tetrahedral voids are also occupied by carbon atoms so number of atoms occupied in $1$ unit cell $=4\times 1=4$

$\therefore \text{Total carbon atoms in a unit cell}=4+4=8$