A compound is formed by elements of X, Y and Z . Atoms of Z (anions) fcc lattice. Atoms of X (cations) occupy all the octahedral voids. Atoms of Y (cations) occupy `(1)/(3)rd` of the tetrahedral voids. The formula of the compound is

Options

A. `X_(3)Y_(2)Z_(3)`
B. `X_(2)YZ`
C. `XY_(2)Z`
D. `X_(2)Y_(2)Z`

Answer

A

Explanation

Since, Z forms fcc lattice so per unit cell number of Z atoms = 4.
In fcc structure total number of octahedral
voids = 4 = number of X atoms.
In fcc structure, total number of tetrahedral voids = 8
Thus, number of Y atoms `=(1)/(3)xx8=(8)/(3)`
Thus, formula of compound is `Z_(4)X_(4)Y_(8//3)` or `X_(4)Y_(8//3)Z_(4)" or "XY_(2//3)Z" or "X_(3)Y_(2)Z_(3)`.