Chemistry - Solid State Question with Solution | TestHub

Let the number of atoms of element B forming the cubic close packed (ccp) lattice be $N$.

The number of tetrahedral voids generated in a ccp lattice is $2N$.

Since atoms of element A occupy $1/3$rd of the tetrahedral voids, the number of atoms of A is $\frac{1}{3}\times 2N=\frac{2N}{3}$.

The ratio of the number of atoms of A to that of B is $\frac{2N}{3}:N=2:3$.

Thus, the simplest formula of the compound is $A_2{B}_3$.

Comparing this with the given formula $A_x{B}_y$, we get $x=2$ and $y=3$.

Therefore, the value of $(x+y)$ is $2+3=5$.

Answer: $5$