A compound is formed from elements X and Y.. The atoms of Y (anions) form ccp lattice. The atoms of X (cations) occupy half of the octahedral voids and half of tetrahedral voids. What is the formula of the compound ?

Options

A. `X_(3)Y_(2)`
B. `X_(2)Y_(3)`
C. `XY`
D. `X_(4)Y_(3)`

Answer

A

Explanation

Key Idea
(i) first find number of atoms of X (cations) which is equal to numberof octahedral voids = number of atoms present in the lattice and number of
tetrahedral voids ` = 2 xx` number of atoms present in the lattice
(ii) Now , calculate the ratio of elements X and Y and then , derive the formula.
Suppose, number of atoms of Y (anions) present in ccp at lattice points = N
Since, `(1)/(2) ` of the octahedral and `(1)/(2)` of tetrahedral voids are occupied by the atoms of X (cations) .
Therefore , total number of atoms of X (cations)
` = (1)/(2) N + (2N)/(2) = (3)/(2)N`
Ratio of `X : Y = (3)/(2) N : N = 3 : 2 `
Hence, formula of the compound of `X_(3) Y_(2)`