The correct option is B PF=43π[52r3++4r3−]16√2r3−
An edge diagonal runs from the middle of one edge - from the edge centre to the diagonally opposite edge centre.
Na+ ions occupy the edge centres and Cl− ions occupy the FCC lattice.
Removing atoms along an edge diagonal, means that two edge centres and one body centre get removed. So, out of 4, 2×14 (edge centres) and 1 (body centre) are not present anymore, giving us 4−32=52Na+ atoms.
Na+=5/2,Cl−=4
For FCC, 2√2a=4R and R=r− here.
Volume of unit cell = a3=16√2r3−
Occupied volume = 4πr3×52×r3+3+4πr3×4×r3−3=4π3×[5r3+2+4r3−]
Hence, packing fraction = Occupied volume / Total volume
= 4π3×[5r3+2+4r3−]16√2r3−