Question

An atom crystallizes in a fcc lattice having a radius of $\sqrt{2}\stackrel{\circ }{A}$. What is the volume (in $c{m}^3$) of one unit cell?

• A. $1.6\times {10}^{-22}c{m}^3$
• B. $2.8\times {10}^{-24}c{m}^3$
• C. $6.4\times {10}^{-23}c{m}^3$
• D. $5.6\times {10}^{-24}c{m}^3$

Answer 1

The correct option is C $6.4\times {10}^{-23}c{m}^3$

For a fcc lattice:
Along the face diagonal
$\sqrt{2}\times a=4\times r$
where
$a\text{is ledge length of unit cell}$
$r\text{is the radius of the atom}=\sqrt{2}\stackrel{\circ }{A}=\sqrt{2}\times {10}^{-8}cm$


$\therefore a=2\sqrt{2}r$

Volume (V) of a unit cell is given by:

$V=a^3=(2\sqrt{2}r{)}^{3}V=16\sqrt{2}{r}^3=16\times \sqrt{2}\times (\sqrt{2}\times {10}^{-8}{)}^{3}V=6.4\times {10}^{-23}c{m}^3$