For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = packing efficiency 100 )

Step-by-step solution

Total number of atoms in a unit cell No. of x = 6 × 1 2 = 3 atom (at face centres) No. of y = 8 × 1 8 = 1 atom (at all corners) So, the formula of compound is x 3 y Now If radius of x is r and radius of y is R then side length a = 2 R and face diagonal 2 a = 2 R + 2 r r = 2 − 1 R Now Packing fraction = volume   of   atoms   Volume   of   unit   cell = 1 × 4 3 πR 3 + 3 × 4 3 πr 3 a 3 Substituting a = 2   R and r = 0 . 414   R = 4 3 πR 3