Question

Silver crystallises in a face-centred cubic unit cell. The density of $Ag$ is $10.5gc{m}^{-3}$. Calculate the volume of unit cell (in $c{m}^3$).

• A. $68.3\times {10}^{-24}c{m}^3$
• B. $24.2\times {10}^{-24}c{m}^3$
• C. $14.8\times {10}^{-26}c{m}^3$
• D. $77.4\times {10}^{-28}c{m}^3$

Answer 1

The correct option is A $68.3\times {10}^{-24}c{m}^3$

Silver crystallises in face-centred cubic unit cell.
For face-centred cubic unit, $Z=4$.
$\text{Density,}\rho =\frac{Z\times M}{N_A\times V}$
where,
$Z$ is number of atoms in unit cell
$N_A$ is avagadro number
$M$ is molar mass of element
$V$ is volume of unit cell

$V=\frac{Z\times M}{N_A\times \rho }$
$V=\frac{4\times 108}{(6.023\times {10}^{23})\times 10.5}=6.83\times {10}^{-23}$
$V=68.3\times {10}^{-24}c{m}^3$