JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Solid State

In the rock-salt arrangement the anions form a cubic close packed lattice and the cations fill every octahedral void, which places a cation and an anion in contact along each edge of the unit cell. Whether the ions actually touch along the edge is decided by the radius ratio $r_{+}/r_{-}=102/181\approx 0.56$; since this lies above the limiting value $0.414$ for octahedral coordination, the cation is large enough to hold the anions apart, so the cation and anion touch along the edge. The edge length is then twice the sum of the two radii, $a=2(r_{+}+r_{-})=2(102+181)=2(283)=566$ pm. The smaller value that follows from forcing anion-anion contact along the face diagonal applies only at the limiting ratio $0.414$ and is not appropriate here, so the edge length is $566$ pm.