# Question #2205b

The unit cell of face centered cubic lattice (FCC) has been shown in above figure. It is obvious from the figure that $4 R$ is the length of the diagonal of every square face of the cell having length of each side $a$,the edge length of unit cube.
${a}^{2} + {a}^{2} = {\left(4 R\right)}^{2}$
$\implies 16 {R}^{2} = 2 {a}^{2}$
$\implies R = \frac{a}{2 \sqrt{2}}$