Question

A compound is formed by the elements $X$ and $Y$ which are in the cubic structure. Atoms $Y$ are present at centre as well as at face centres, whereas atoms $X$ are present at the edge centres as well as at body centre. What is the formula of the compound?

Answer 1

$i)$ $Y$ are present at face centres.

Total $6$ faces and contribution of atom on each face is $\frac{1}{2}$.

$\therefore$ $Y$ atoms per unit cell $=\frac{1}{2}\times 6=3$

$ii)$ $X$ are present in the edge centre.

Total edges are $12$ and contribution of atom present in the edge centre is $\frac{1}{4}\times 12=3$

$X$ are also present at the body centre. Contribution of atom in body centre is $1.$

$\therefore$ Total $X$ atoms per unit cell $=3+1=4$

Formula of compound is $X_4{Y}_3$.