Sodium metal crystallises in a body centred cubic lattice with unit...

Edge length of the unit cell $( a ) = 4x{10}^{- 8}cm$

Radius of sodium atom $( r ) = ?$

Since, sodium crystallises in body centered cubic arrangement.

The radius of the atom and the edge length of the cubic unit cell are related as follows,

For bcc structure, $4r = \sqrt{3}a ⇒ r = \dfrac{\sqrt{3}}{4}a$

$r = \dfrac{1 . 732 \times 4 \times {10}^{- 8}}{4}r = 1 . 732 \times {10}^{- 8}cmr = 17 . 3Å$.