A metal crystallises in a face centred cubic lattice with edge length of $450 \mathrm{pm}$. Molar mass of metal is $50 \mathrm{g}{ \mathrm{mol}}^{-1}$. Then the density of metal is:

It is provided in the question that metal has FCC structure meaning$Z=4$, with molar mass of $50 \mathrm{g}{ \mathrm{mol}}^{-1}$ and the length of the edge of the unit cell is $450 \mathrm{pm}$.

We know that the formula for density can be expressed as:  $\mathrm{d}=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{a}}^3\times {\mathrm{N}}_{\mathrm{A}}}$

Substituting the given values we get:

$d=\frac{4\times 50}{{\left(450\times {10}^{-10}\right)}^3\times 6.023\times {10}^{23}}$

$d=3.64 \mathrm{g} {\mathrm{cm}}^{-3}$
Hence, the required answer is option B) $3.64 \mathrm{g}/\mathrm{cc}$.