The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively _____

In FCC: The atoms at the face diagonals touch each. If a is the edge length of cube and r is the radius of the atom.

So, $$\begin{gathered} \sqrt{2}\mathrm{a}=4\mathrm{r} \\ \Rightarrow \mathrm{a}=2\sqrt{2}\mathrm{r} \end{gathered}$$

In bcc: The atoms at the body diagonal touch each other.

So, $$\begin{gathered} \sqrt{3}\mathrm{a}=4\mathrm{r} \\ \Rightarrow \mathrm{a}=\frac{4}{\sqrt{3}}\mathrm{r} \end{gathered}$$

In simple cubic: The atoms at the corners touch each other.

So, a = 2r