Chemistry - Solid State Question with Solution | TestHub

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

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

$m=\frac{Z\times M}{N_A}$

where $M$ is the molar mass and $N_A$ is Avogadro's number.

Rearranging the formula to solve for $M$:

$M=\frac{m\times N_A}{Z}$

Substituting the given values:

$M=\frac{1.8\times 10^{-22}\times 6.022\times 10^{23}}{4}$

$M=\frac{1.8\times 60.22}{4}$

$M=\frac{108.396}{4}$

$M=27.099{\text{ g mol}}^{-1}\approx 27.0{\text{ g mol}}^{-1}$

Answer: $27.0\mathrm{g}{\mathrm{mol}}^{-1}$