# Sodium metal crystallises in body centred cubic lattice with cell edge 4.29

Sodium metal crystallises in body centred cubic lattice with cell edge 4.29Å. What is the radius of sodium atom?

Solution :
In a body centered cubic lattice, atoms touch along the body diagonal of the cube . Thus
$4r= \sqrt 3 a$
or $r= \large\frac{\sqrt{3}}{4} $$a \qquad= \bigg(\large\frac{\sqrt 3}{4} \bigg)$$(4.29 \dot{A})=1.86 \dot{A}$
answered May 3, 2017 by