Chemistry - Solid State Question with Solution | TestHub

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

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

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

Given values are:
$d=1\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$
$M=23\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$
$N_A=6.022\times 10^{23}\mathrm{mo}{\mathrm{l}}^{-1}$

Rearranging the formula to find the volume $V$ of the unit cell:

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

Substituting the given values:

$V=\frac{2\times 23}{6.022\times 10^{23}\times 1}$

$V=\frac{46}{6.022\times 10^{23}}$

$V\approx 7.638\times 10^{-23}\mathrm{c}{\mathrm{m}}^3$

Rounding to one decimal place, the volume is $7.6\times 10^{-23}\mathrm{c}{\mathrm{m}}^3$.

Answer: $7.6\times 10^{-23}{\mathrm{cm}}^3$