Chemistry - Solid State Question with Solution | TestHub

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

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

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

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

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

Given values:
$d=8.92{\text{ g cm}}^{-3}$
$N_A=6.022\times 10^{23}{\text{ mol}}^{-1}$
$a=3.608\times 10^{-8}\text{ cm}$

Substituting the values into the formula:

$M=\frac{8.92\times 6.022\times 10^{23}\times (3.608\times 10^{-8}{)}^3}{4}$

$M=\frac{8.92\times 6.022\times 10^{23}\times 46.97\times 10^{-24}}{4}$

$M=\frac{252.3}{4}$

$M\approx 63.07\text{ g/mol}$

Rounding to the nearest integer, the atomic mass of the element is $63\text{ g/mol}$.

Answer: $63$ g/mol