In a cubic close-packed structure of a mixed oxide one-eighth of tetrahedral voids are occupied by divalent ions `X^(2+)` while one half of the octahedral voids are occupied by trivalent ions `Y^(3+)`. What is the formula of the compound?

Explanation

Let the number of `O^(2-)` ions in the crystal = N
`:.` Number of tecrahedral voids = 2N
Number of octahedral voids = N
`:.` Number of `X^(2+)` ions `=(1)/(8) xx 2N =(N)/(4)`
Number of `Y^(3+)` ions `=(1)/(2) xx N =(N)/(2)`
`X^(2+) :Y^(3+) :O^(2-) =(N)/(4):(N)/(2):N`
`=1:2:4`
Hence, the formula of the compound is `XY_(2)O_(4)`.