Question

Zinc selenide $\left(\right.ZnSe\left.\right)$ crystallizes in a face-centred cubic unit cell and has a density of $5.267g/cc.$ Calculate the edge length of the unit cell.
Give the answer as the nearest integer.

Answer 1

The relationship between density, edge length, number of atoms and the unit cell is:
$d =\frac{ M \times Z }{ a ^{3} \times N _{0}} $
$a =? $
$Z =4\, M $
$=144 \,gd $
$=5.267 \,g / cm ^{3} N _{0}$
$=6.023 \times 10^{23} 5.267$
$=\frac{144 \times 4}{ a ^{3} \times 6.023 \times 10^{23}} a ^{3}$
$=18.16 \times 10^{-23}\, cm ^{3} a $
$=5.66 \times 10^{-8} \,cma =5.66\,\mathring{A} $