Question

The diameter of atoms forming a closed packed structure in the given figure is $4\times {10}^{-8}$ cm.

The maximum radius of the atom occupying the space in between is $\times {10}^{-8}$ cm.

Answer 1

When we talk about the maximum possible radius of an atom that can be accommodated in the empty space, we come up with a figure as follows.

Here, we can use Pythagoras theorem.
$(2R{)}^2+(2R{)}^2=(2R+2r{)}^{2}2\sqrt{2}R=2R+2r2R(\sqrt{2}-1=2r)$
When we substitute $\sqrt{2}=1.414andR=2\times {10}^{-8}cm$, we get:
$r=0.828\times {10}^{-8}cm$