An ionic compound is made up of cations A and anions `B`. if cations `A` are at the alternate corners and anions are at the alternate faces of the cubic unit cell then empirical formula of the compound will be

Options

A. `AB_(2)`
B. `A_(2)B_(3)`
C. `AB_(3)`
D. `AB`

Answer

1

Explanation

There are `8` corners. As there are four `A` cations at the alternate corners and contribution of each `=1//8` the number of `A` cation per unit cell is
`= 4xx(1)/(8)=(1)/(2)`
There are `6` square faces of the cubic unit cell. but there can be only two `B` anions on alternate faces (top, bottom, and left ,right or front, rear).As contributon of each of them `=(1)/(2)`
The number of `B` anions per unit cell.
`=2xx(1)/(2)=1`
Hence simplest ratio of cations to anions. `(A:B)`
`=(1)/(2):1` or `1:2`.
thus the empirical formula of the ionic compound is `AB_(2)`. There are `4` body diagonals. Since atoms within the body of the unit cell are not shared by any other unit cell there are `8` more atoms giving a total of `9`atoms.