In a compound `XY_(2) O_(4)` , oxide ions are arranged in CCP and cations X are present in octahedral voids. Cations Y are equally distributed between octahedral and tetrahedral voids. The fraction of the octahedral voids occupied is :-

Options

A. `1//2`
B. `1//4`
C. `1//8`
D. `1//6`

Answer

1

Explanation

Unit cell of ccp is fcc, therfore number of oxide ions =`4`.
Number of tetrahedral voids=`2xx4=8`
Number of octahedral voids `= 4`
Accoding to the formula, number of cations `X` present per unit cell `=1`
Number of cations `Y` present per unit cell `=2`
sInce cations `Y` are equally distributed between octahedral and tetrahedral voids one cation is `Y` is in octahedral void whilst other cation `Y`is in tetrahedral void.
Therefore total number of octahedral voids captured is =`1+1=2`. Note that cation `X` is also present in octahedrial void hence fraction of the octahedral voids occupied is `2//4=1//2`