Diamond has a three dimensional structure ofC 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 ____

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answer is 8.

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Detailed Solution

Effective carbon atoms in the fcc unit cell = $8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$
There are 8 total tetrahedral voids in the fcc unit cell.
Carbon atoms occupy 50% of the tetrahedral voids, hence the total number of atoms in a unit cell is =4x1=4
One unit cell contains a total of = 4+4=8

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