Question

An element A crystallises in a fcc structure. $200$ g of this element has $4.12\times {10}^{24}$ atoms. The density of A is $7.2$ g cm${}^{-3}$. Calculate the edge length of the unit cell.

• A. $26.97\times {10}^{-24}$ cm
• B. $299.9$ pm
• C. $5\times {10}^{-12}$ cm
• D. $2.99$ cm

Answer 1

Answer: (B)

$299.9$ pm

A fcc unit cell has $4$ atoms.

$200$ g corresponds to $4.12\times {10}^{24}$ atoms.

Hence, $4$ atoms corresponds to $\frac{200\times 4}{4.12\times {10}^{24}}$ g.

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$

Substituting values in the above expression, we get

$7.2=\frac{200\times 4}{4.12\times {10}^{24}\times a^3}$

Hence, $a=299.9\times {10}^{-10}$ cm $=299.9$ pm

Hence, the edge length of the unit cell is $299.9$ pm.