Question

Total number of diamond unit cells in $1.2$ g of diamond sample is :

• A. $6.0\times {10}^{21}$
• B. $6.0\times {10}^{22}$
• C. $7.5\times {10}^{21}$
• D. $5.0\times {10}^{22}$

Answer 1

Answer: (C)

$7.5\times {10}^{21}$

In Diamond structure, there are carbon atoms at the FCC locations and 4 carbon atoms present in the alternate tetrahedral voids.
Therefore the total number of Carbon atoms per unit cell of Diamond is $4+4=8$
Moles of carbon in $1.2g$ of diamond = $\frac{1.2}{12}=0.1$
Number of atoms of carbon in $1.2g$ of diamond = $0.1\times 6\times {10}^{23}=6\times {10}^{22}$
Number of unit cells = $6\times {10}^{22}\times \frac{1}{8}=7.5\times {10}^{21}$