Question

A solid AB crystallises as a body-centred cubic lattice with the unit cell edge length equal to 384 pm. Calculate

1. the distance between the oppositely charged ions in the lattice, and
2. the radius of A⁺ ion if that of B⁻ is 180 pm.

Answer 1

a. In a body-centred cubic system

2r₊ + 2r₋ = body diagonal = `a sqrt 3`

∴ `r_+ + r_- = (a sqrt 3)/2`

= `(384 sqrt 3)/2` pm

= `(384 xx 1.732)/2` pm

= 332.5 pm

Hence, the distance between oppositely charged ions = 332.5 pm

b. ∵ r = 180 pm

r₊ = 332.5 − 180

r₊ = 152.5 pm