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

[!TLDR] Weak-field $\text{F}^-$ does not force pairing; electrons spread out (Hund's rule) as far as possible. [!ANSWER] …

$\text{Co}^{3+}$ has a $d^6$ configuration. $\text{F}^-$ is a weak-field ligand (Section 5.3), meaning the crystal field splitting $\Delta_o$ it produces is smaller than the pairing energy $P$ — so it is energetically cheaper for electrons to occupy the higher $e_g$ set singly than to pair up within the lower $t_{2g}$ set. Filling the six electrons by Hund's rule (maximum unpaired first): the first three electrons occupy the three $t_{2g}$ orbitals singly, the next two occupy the two $e_g$ orbitals singly (all five d-orbitals now singly occupied, five unpaired electrons at this stage), and only the sixth electron is left with no empty orbital to enter, so it must pair up in one of the (lower-energy, therefore preferred) $t_{2g}$ orbitals. The final configuration is $t_{2g}^4$ (one orbital with 2 electrons paired, two orbitals with 1 electron each: $2+1+1=4$) $e_g^2$ (one elect …

Identify the metal's d-electron count and the ligand's field strength; fill the split orbitals by Hund's rule (maximum unpaired electrons first, give …

Filling the orbitals as if the field were automatically strong (pairing electrons in $t_{2g}$ before singly filling $e_g$) without first checking that $\text{F}^-$ is a weak-field ligand — the fill …