Question

Ga (atomic mass $70u$) crystallizes in a hexagonal close packed structure. The total number of voids in $0.581g$ of Ga is $\times {10}^{21}$ (Round off to the nearest integer). $[\text{Given}=N_A=6.023\times {10}^{23}]$
(JEE Main 2021)

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 $=\frac{0.581}{70}\times 3\times 6.023\times {10}^{23}$ $=14.99\times {10}^{21}$ $=15\times {10}^{21}$