Chemistry - Solid State Question with Solution | TestHub

The density of a unit cell is given by the formula:

$\rho =\frac{Z\times M}{N_A\times V}$

Rearranging for the volume of the unit cell $V$:

$V=\frac{Z\times M}{\rho \times N_A}$

For a body-centered cubic (bcc) structure, the number of atoms per unit cell is $Z=2$.

Given values are:
$M=92{\text{ g mol}}^{-1}$
$\rho \times N_A=5.0\times 10^{24}{\text{ g cm}}^{-3}{\text{ mol}}^{-1}$

Substituting these values into the formula:

$V=\frac{2\times 92}{5.0\times 10^{24}}$

$V=\frac{184}{5.0\times 10^{24}}$

$V=36.8\times 10^{-24}{\text{ cm}}^3$

$V=3.68\times 10^{-23}{\text{ cm}}^3$

Answer: $3.68\times 10^{-23}{\mathrm{cm}}^3$