Question

The length of the side of a unit cell for lithium is 351 pm, calculate its atomic radius. Lithium forms a body-centred cubic crystal.

• A. 303.9 pm
• B. 124.09 pm
• C. 151.9 pm
• D. 202.6 pm

Answer 1

The correct option is C 151.9 pm


From the figure, edge length $AB=a$, BC, face diagonal, $BC=\sqrt{2}a$
Body diagonal, $\left(AC\right)=\sqrt{(\sqrt{2}a{)}^2+a^2}=\sqrt{3}a$
$\Rightarrow 4r=\sqrt{3}a$
$\Rightarrow r=\frac{\sqrt{3}}{4}a$
$\Rightarrow r=\frac{\sqrt{3}}{4}\times 351=151.9\text{pm}$