JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Solid State

In a cubic close packed structure the octahedral voids sit at the body centre and at the twelve edge centres of the unit cell. The body centre lies wholly inside the cell and each edge centre is shared by four cells, so the cell contains $1+12\times \frac{1}{4}=4$ octahedral voids. The same cell has lattice points at the eight corners and the six face centres, that is $8\times \frac{1}{8}+6\times \frac{1}{2}=4$ of them. The number of octahedral voids per lattice site is therefore $\frac{4}{4}=1$.