Question

If the radius of an atom of an element which forms a body centered cubic unit cell is 173.2 pm , the volume of unit cell in $c{m}^3$ is:

• A. $3.12\times {10}^{-23}$
• B. $6.4\times {10}^{-23}$
• C. $3.2\times {10}^{-24}$
• D. $2.13\times {10}^{-23}$

Answer 1

The correct option is B $6.4\times {10}^{-23}$

Body centred cubic unit cell:
Atoms present at each corner and at the body centre of the unit cell.
diagonal of cube:
$d^2=a^2+a^2+a^2=3a^2$
$(4r{)}^2=3a^2$
$a=\frac{4r}{\sqrt{3}}\left(i\right)$
Volume of cube $=a^3$
$V=6.4\times {10}^{-23}c{m}^3$