`CsCl` crystallizes in body centred cubic lattice .If `'a'` is its edge length then which of the following expression is correct?

Options

A. `r_(Cs^(+))+r_(Cl^(-))=3a`
B. `r_(Cs^(+))+r_(Cl^(-))=(3a)/2`
C. `r_(Cs^(+))+r_(Cl^(-))=sqrt(3)/2 a`
D. `r_(Cs^(+))+r_(Cl^(-))=sqrt(3)a`

Answer

C

Explanation

In CsCl, the `Cl^(-)` ion lie at the corners of simple cube and `Cs^(+)` ion at the body centre. Along the body diagonal both `Cs^(+)` and `Cl^(-)` ions touch each other.
Therefore, `1//2` of body diagonal `r_(Cs^(+))+r_(Cl^(-))=sqrt(3)/2a`