Question

An element crystallizes in a structure having a fcc unit cell with edge length $200$ pm. Calculate its density (in g cm${}^{-3}$) if $200$ g of this element contain $24\times {10}^{23}$ atoms.

• A. $10.4$
• B. $2.6$
• C. $41.6$
• D. $83.2$

Answer 1

Answer: (C)

$41.6$

Weight of $24\times {10}^{23}$ atoms $=200$ g

$\therefore$ Weight of $4$ atoms $=\frac{200}{24\times {10}^{23}}\times 4$ g

The fcc structure contains $4$ atoms in a unit cell.

Density $=\frac{\text{Mass of unit cell}}{\text{Volume of unit cell}}$ $=\frac{200\times 4}{24\times {10}^{23}\times (200\times {10}^{-10}{)}^3}$ $=41.6$ g cm${}^{-3}$

Hence, the density of the unit cell is $41.6$ g cm${}^{-3}$.