Question

A compound $AB$ has zinc blende structure with '$A$' atoms at corners and face centre of the unit cell. If all the atoms present in one body diagonal are removed, the simplest formula of the compound becomes $A_x{B}_y$. The sum $(x+y)$ is:

Answer 1

A present in corners and face centre.
B present in alternate tetrahedral voids.
Along one body diagonal, two atoms of $A$ are present and one atom of $B$ is present. After removal of all the atoms along the body diagonal, number of $A$ per unit cell $=6\times \frac{1}{8}+6\times \frac{1}{2}=\frac{15}{4}$
Number of $B$ per unit cell $=4-1=3$
$x:y=\frac{15}{4}:3=5:4$
$x+y=5+4=9$