Question

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

Answer 1

For face-centred cubic unit, $Z=4$

We know that, $V=\frac{Z\times M}{N_0\times d}$

$=\frac{4\times 108}{(6.023\times {10}^{23})\times 10.5}=6.83\times {10}^{-23}$$=68.3\times {10}^{-24}$

Let $a$ be the edge length of the unit cell.

So, $V=a^3$

or $a^3=68.3\times {10}^{-24}$

$a=(68.3\times {10}^{-24}{)}^{1/3}cm$

$=4.09\times {10}^{-8}cm$

$=409pm$