An element crystallises in a structure having a f.c.c unit cell of an edge $200 \mathrm{pm}$. Calculate the density of element, if $20 \mathrm{gm}$ the element contains $2.4\times {10}^{23}$ atoms.

Mathematically, the formula of density can be represented using the formula

$\mathrm{d}=\frac{\mathrm{z}\times \mathrm{w}}{\mathrm{N}\times {\mathrm{a}}^3}$

In FCC unit cell, the number of atoms per unit cell, $\mathrm{z}=4$

And we know that $\mathrm{N}=2.4\times {10}^{23}$ atoms

Substituting these values in the equation and solving we get,

$\mathrm{d}=\frac{4\times 200}{24\times {10}^{23}\times 8\times {10}^{-24}}$

$=\frac{1000}{24}$

$\mathrm{d}=41.67 \mathrm{gm} {\mathrm{cm}}^{-3}$