CsCl crystallises in body-centred cubic lattice. If 'a' is its edge length then which of the following expressions is correct-

Options

A. `r_(Cs^(+))+r_(Cl^(-))=sqrt3a`
B. `r_(Cs^(+))+r_(Cl^(-))=3a`
C. `r_(Cs^(+))+r_(Cl^(-))=(3a)/2`
D. `r_(Cs^(+))+r_(Cl^(-))=sqrt3/2a`

Answer

D

Explanation

CsCl crystallises in body-centred cubic lattice. Here, oppositely charged ions are in contact to be placed in body diagonal.
`therefore` Length of body diagonal = `sqrt(a^(2)+2a^(2))=sqrt3a`.
Therefore, `2r_(Cs^(+))+2r_(Cl^(-))=sqrt3a`.
or, `r_(Cs^(+))+r_(Cl^(-))=sqrt3/2a`.