Question

An ionic compound is made up of A cations and B anions. If A cations are present at the alternate corners and B anion is present on the body of the diagonal, what is the formula of the ionic compound?

Answer 1

Formula of ionic compound is AB${}_2$.
A cations are present at the alternate corners. There are 8 corners out of which 4 have A cation. Each corner contributes one eighth to the unit cell. Hence, total number of A cations present per unit cell $=\frac{1}{8}\times 4=0.5$.
B anion is present on the body of the diagonal. It fully contributes to the unit cell.
Hence, total number of B cations present per unit cell is 1
The ratio of number of A cations to number of B cations is
$0.5:1$ or $1:2$