JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Solid State

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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: 8

Solution

A face centred cubic lattice has eight corner atoms shared between eight cells and six face atoms shared between two cells, so it contributes

8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4

atoms to one unit cell. Such a lattice offers two tetrahedral voids for every lattice point, that is eight voids per cell, and half of them hold a carbon atom, adding

\frac{1}{2} \times 8 = 4

more. The unit cell of diamond holds

4 + 4 = 8

carbon atoms.

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Integer answer

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