The edge length of a face-centred cubic unit cell is `508 p m`. If the radius of the cation is `110 p m` the radius of the anion is

Options

A. `249 p m`
B. `220 p m`
C. `608 p m`
D. `176 p m`

Answer

2

Explanation

`sqrt(2)a=660sqrt(2)p m`
so `a=660 p m`
Now if tetrahedral void is occupied by cations than
`(sqrt(3))/(4)a=(r_(+)+r_(-))`
`r_(-)((sqrt(3)xx600)/(4)-110)=110[(3)/(2)sqrt(3)-1]=1.598xx110. ` So, `(r_(+))/(r_(-))=(1)/(1.598)=(1)/(1.6)=(10)/(16)=0.625`
but `(r_(+))/(r_(-))gt0.414` so it must not be occupying tetrahedral void then
`a=2(r_(+)+r_(-))" "implies" "330=r_(+)+r_(-)`
`r_(-)=220p m`
`{(r_(+))/(r_(-))=0.5` it can occupy octahedral void `}`