Question

The efficiency of packing in the case of a metal crystal for face-centered cubic is

Answer 1

Answer: 74

Packing efficiency is the percentage of total space filled by the constituent particles in the unit cell. For a face centred cubic unit cell, there are four atoms per unit cell. The edge length, $a=2\sqrt{2}r$ .
In face centred cubic, packing efficiency $=\frac{volumeoccupiedbyparticlesinaunitcell\times 100}{volumeofaunitcell}$
$=\frac{\text{Volume occupied by 4 atoms in the unit cell}\times 100}{\text{Volume of the unit cell}}$
$=\frac{4\times \left(4/3\right)\pi r^3\times 100}{{\left(2\sqrt{2}r\right)}^3}=\frac{\left(16/3\right)\pi r{}^3\times 100}{16\sqrt{2}r{}^3}=74\text{\%}$