Question

If three elements $P,Q$ and $R$ crystallize in a cubic type lattice with $P$ atoms at the corners, $Q$ atoms at the cube center and $R$ atoms at the edges, then write the formula of the compound.

Answer 1

P atoms are at corners. There are 8 corners and contribution of each corner is $\frac{1}{8}$. Therefore, total P atom is $8\times \frac{1}{8}=1$.

Q is at the centre of the cube. Therefore, total Q atom is 1.

R are present at the edges. There are 12 edges and contribution of each edge is $\frac{1}{4}$. Total R atoms are $\frac{1}{4}\times 12=3$. Formula is $PQ{R}_3$.