A solid`A^(+)B^(-)` has a body centred cubic structure. The distance of closest approach between the two ions is `0.767Å`.The edge length of the unit cell is

Options

A. `sqrt3//sqrt2" pm"`
B. 142=2 pm
C. `sqrt2" pm"`
D. 81.63 pm

Answer

D

Explanation

For a b.c.c. arrangement of `A^(+)B^(-),2(r^(+)+r^(-))`=length of the body diagonal of the cube.
`r^(+)+r^(-)`=distance of closest of closest approach of ions
=18.0 pm
i.e., `2times76.7=asqrt3`where a=edge length
or `a=(2times76.7)/sqrt3=81.63" pm"`