On the basis of crystal field theory,explain why $Co(III)$ forms a paramagnetic octahedral complex with weak field ligands,whereas it forms a diamagnetic octahedral complex with strong field ligands.

(N/A) $Co^{3+}$ has a $d^{6}$ electronic configuration.
In the presence of a strong field ligand,the crystal field splitting energy $\Delta_{o}$ is greater than the pairing energy $P$ (i.e.,$\Delta_{o} > P$). This forces the electrons to pair up in the lower energy $t_{2g}$ orbitals,resulting in a $t_{2g}^{6} e_{g}^{0}$ configuration.
Since all electrons are paired in the $t_{2g}^{6} e_{g}^{0}$ configuration,the complex is diamagnetic.
In the presence of a weak field ligand,$\Delta_{o} < P$. The electrons occupy the higher energy $e_{g}$ orbitals before pairing occurs,resulting in a $t_{2g}^{4} e_{g}^{2}$ configuration.
In the $t_{2g}^{4} e_{g}^{2}$ configuration,there are four unpaired electrons,making the complex paramagnetic.