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

Options

A. `8`
B. `6`
C. `1`
D. `4`

Answer

1

Explanation

In diamond, every `C` is tetrahedrally bonded to `4` other `C` atoms. It unit cell is cubic where `C` atoms are located at the corners , face centres and occupying the alternate tetrahedral voids:
Contribution form corners=`8xx(1)/(8)=1`
Contribution from face centres `=6xx(1)/(2)=3`
Contribution form tetrahedral voids=`8xx(1)/(2)=4`
Thus, total `C` atoms per unit of diamond is `4`. Note that total number of tetrahedral voids is `8`and only half of them are captured.