Question

A unit cell consists of a cube in which there are anions (Y) at each corner and cations (X) at the centre of alternate faces of the unit cell. What is the simplest formula of the compound ?

Answer 1

Effective no. of $Y\Rightarrow Z_Y=8\times \frac{1}{8}=1$ (Body corners contributes $\frac{1}{8}$ to the unit cell)

Effective no. of $X\Rightarrow Z_X=\frac{1}{2}\times \frac{1}{2}\times 6=\frac{3}{2}$ (Face centres contributes $\frac{1}{2}$ to the unit cell)

Formula of compound $=Y{X}_{\frac{3}{2}}=Y_2{X}_3$