A metal has a body-centred cubic lattice and each lattice point is occupied by one atom. The atomic weight of the metal is $183.9$ a.m.u. If its density is $19.3\mathrm{gm}/\mathrm{cc}$. Calculate the edge length of the cube.

We know that the formula of density for a unit cell is mathematically given as:

$\text{ Density }=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{a}}^3\times {\mathrm{N}}_{\mathrm{A}}}$

Rearranging the formula and substituting the given values we get:

${\mathrm{a}}^3=\frac{\mathrm{Z}\times \mathrm{M}}{\mathrm{d}\times {\mathrm{N}}_{\mathrm{A}}}$

${\mathrm{a}}^3=\frac{2\times 183.9}{19.3\times 6\times {10}^{23}}$

${\mathrm{a}}^3=3.176\times {10}^{-23}$

Simplifying the value further we get:

$\mathrm{a}=3.16\times {10}^{-8}$

Hence, the required answer is $3.16{ \mathrm{A}}^0$.