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

Rearranging the formula to solve for molar mass $M$:

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

Substituting the given values:

$M=\frac{20.4\times 6.022\times 10^{23}\times 5.6\times 10^{-23}}{4}$

$M=\frac{20.4\times 6.022\times 5.6}{4}$

$M=171.98\approx 172{\text{g mol}}^{-1}$

Answer: $172{\text{g mol}}^{-1}$