Q.Using crystal field theory, determine the electronic configuration and the number of unpaired electrons in $[\text{Co}(\text{NH}_3)_6]^{3+}$ ($\text{Co}^{3+}$ is $d^6$; $\text{NH}_3$ is a strong-field ligand for $\text{Co}^{3+}$), and state whether the complex is paramagnetic or diamagnetic.

[!TLDR] Strong-field $\text{NH}_3$ forces all six electrons to pair within $t_{2g}$ before any occupy $e_g$. [!ANSWER] …

$\text{Co}^{3+}$ is again $d^6$, but $\text{NH}_3$ is a strong-field ligand (Section 5.3), producing a $\Delta_o$ larger than the pairing energy $P$ — so it is now energetically cheaper for electrons to pair up within the lower $t_{2g}$ set than to occupy the higher $e_g$ set at all. All six electrons are therefore placed into the three $t_{2g}$ orbitals, pairing up as needed: two electrons in each of the three orbitals, giving $t_{2g}^6$, while the $e_g$ set remains completely empty, $e_g^0$. Every $t_{2g}$ orbital now holds a fu …

Since $\text{NH}_3$ is a strong-field ligand for $\text{Co}^{3+}$ ($\Delta_o > P$), fill all six d-electrons into the three lower $t_{2g}$ orbitals (p …

Applying Hund's rule (maximum unpaired electrons) unconditionally, without checking whether the ligand field is strong enough to override it — Hund's rule only decides the filling order WITHIN a single, already-known configuration; w …