Chemistry - Solid State Question with Solution | TestHub

For an fcc structure, the number of atoms per unit cell is $Z=4$.

The density $d$ of the crystal is given by the formula:

$d=\frac{Z\times M}{a^3\times N_A}$

Substituting the given values $M=197{\text{ g mol}}^{-1}$ and $a^3\times N_A=40{\text{ cm}}^3{\text{ mol}}^{-1}$:

$d=\frac{4\times 197}{40}$

$d=\frac{197}{10}$

$d=19.7{\text{ g cm}}^{-3}$

Answer: $19.7\mathrm{g}{\mathrm{cm}}^{-3}$