Question

Zinc selenide $(ZnSe)$ 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

Answer: 6

The relationship between density, edge length, number of atoms and the unit cell is:
$d=\frac{M\times Z}{a^3\times N_0}$
$a=?$
$Z=4M$
$=144gd$
$=5.267g/c{m}^3{N}_0$
$=6.023\times 10^{23}5.267$
$=\frac{144\times 4}{a^3\times 6.023\times 10^{23}}{a}^3$
$=18.16\times 10^{-23}c{m}^{3}a$
$=5.66\times 10^{-8}cma=5.66\mathring{A}$