Sodium crystallises in body centred cubic lattice. The edge length of its unit cell is $0.424 \mathrm{nm}$. The density of the metal is

We know that the formula for density $=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{a}}^3\times {\mathrm{N}}_0}$

Here, $Z=2$ (because bcc presence)

$\mathrm{M}=$ molar mass of $\mathrm{Na}=23$

$a=$ edge length of unit cell $=0.424 \mathrm{nm}=0.424 \times {10}^{-8} \mathrm{cm}$

Hence, the Density $=\frac{2\times 23}{{\left(0.424\times {10}^{-8}\right)}^3\times 6.02\times {10}^{23}}=1002 \mathrm{g}/{\mathrm{cm}}^3=1.002\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$

So, the correct option is C) $1.002\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$.