Question

$Ga$ (atomic mass $70\text{u}$) crystallizes in a hexagonal close packed structure. The total number of voids in $0.581\text{g}$ of $Ga$ is $x\times {10}^{21}$. The value of $x$ is
(Round off $x$ to the nearest integer).
$[\text{Given}=N_A=6.023\times {10}^{23}]$

Answer 1

$Ga$ crystallizes in a hexagonal close packing. No. of $Ga$ atoms per unit cell $=\frac{1}{6}\times 12+\frac{1}{2}\times 2+1\times 3=6$
No. of tetrahedral voids $=2\times 6=12$
No. of octahedral voids $=6$
Total voids per unit cell $=18$
Total voids per atom of $Ga$ $=\frac{18}{6}=3$
$\therefore$ Total no. of voids in given sample $=\frac{0.581}{70}\times 3\times 6.023\times {10}^{23}$ $=14.99\times {10}^{21}$ $=15\times {10}^{21}$