Which of the following complex ions has electrons that are symmetrically filled in both t 2 g and e g…

Metal ion having either ${\mathrm{d}}^5 \text{or} {\mathrm{d}}^{10}$ configuration can be filled symmetrically in both ${\mathrm{t}}_{2\mathrm{g}} \text{and} {\mathrm{e}}_{\mathrm{g}}$ orbitals. ${\mathrm{Co}}^{+2}$ has ${\mathrm{d}}^7$ configuration, ${\mathrm{Co}}^{+3}$ has ${\mathrm{d}}^6$ configuration. ${\mathrm{Mn}}^{+2}$ has ${\mathrm{d}}^5$ configuration but ${\mathrm{CN}}^{-}$ is strong field ligand and it will pair the electrons due to which electronic configuration is ${{\mathrm{t}}_{2\mathrm{g}}}^5{{\mathrm{e}}_{\mathrm{g}}}^0$.

As $\mathrm{F}$ is weak field ligand hence back pairing of electrons do not take place or in case of weak field ligand pairing energy of electrons (P )is greater than crystal field splitting energy in octahedral complex $\left({∆}_o\right)$ i.e.$P>{∆}_o$ , hence electrons will go in $e_g$ orbitals, instead of back paired in $t_{2g}$ orbitals.