JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Coordination Compounds

Every pair of ligands in an $\mathrm{M}{\mathrm{L}}_5$ defines one $\mathrm{L}\text{-}\mathrm{M}\text{-}\mathrm{L}$ angle, so each geometry has $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$ such angles. In the square pyramidal nickel complex the apical ligand makes $90^{\circ }$ with each of the four basal ligands ($4$ angles), neighbouring basal ligands are $90^{\circ }$ apart ($4$ angles), and the two pairs of opposite basal ligands are $180^{\circ }$ apart ($2$ angles): eight $90^{\circ }$ angles and two $180^{\circ }$ angles. In the trigonal bipyramidal iron complex the three equatorial ligands are $120^{\circ }$ apart ($3$ angles), each axial ligand makes $90^{\circ }$ with each equatorial one ($6$ angles), and the two axial ligands are $180^{\circ }$ apart ($1$ angle). Counting every $90^{\circ }$, $120^{\circ }$ and $180^{\circ }$ angle across both complexes gives $10+10=20$.