Question

An element (atomic mass = 100 g/mol) that has a bcc structure has a unit cell edge length of 400 pm. The density of the element is:
(Take $N_A=6\times {10}^{23}$)

• A. $10gc{m}^{-3}$
• B. $5.2gc{m}^{-3}$
• C. $7.2gc{m}^{-3}$
• D. $2.1gc{m}^{-3}$

Answer 1

The correct option is B $5.2gc{m}^{-3}$

Density $\rho$ is given by
$\rho =\frac{ZM}{a^3\times N_A}$
Since it has a BCC structure, $Z=2$
$\therefore \rho =\frac{2\times 100}{(400{)}^3\times 6\times {10}^{23}\times {10}^{-30}}$
$\Rightarrow \rho =\frac{2\times 100}{(4{)}^3\times 6\times {10}^{-1}}$
$\approx 5.2g/c{m}^{-3}$