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(A) To determine the complex with the highest $CFSE$ (Crystal Field Stabilization Energy),we evaluate the nature of the ligand and the metal ion confi

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$t_{2g}^6 e_g^0$

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(A) To determine the complex with the highest $CFSE$ (Crystal Field Stabilization Energy),we evaluate the nature of the ligand and the metal ion configuration:$1$. $[Co(en)_3]^{3+}$: $Co^{3+}$ is a $d^6$ system. $en$ (ethylenediamine) is a Strong Field Ligand $(SFL)$,causing pairing of electrons. The configuration is $t_{2g}^6 e_g^0$. This complex has a high $CFSE$ due to the strong field splitting.$2$. $[CoF_6]^{3-}$: $Co^{3+}$ is a $d^6$ system. $F^-$ is a Weak Field Ligand $(WFL)$,resulting in a high-spin configuration $t_{2g}^4 e_g^2$.$3$. $[Mn(H_2O)_6]^{2+}$: $Mn^{2+}$ is a $d^5$ system. $H_2O$ is a $WFL$,resulting in a high-spin configuration $t_{2g}^3 e_g^2$.$4$. $[Zn(H_2O)_6]^{2+}$: $Zn^{2+}$ is a $d^{10}$ system with configuration $t_{2g}^6 e_g^4$. It has zero $CFSE$ because the $d-$orbitals are completely filled.Comparing these,$[Co(en)_3]^{3+}$ has the highest $CFSE$ due to the strong field ligand $en$ and the $d^6$ low-spin configuration $t_{2g}^6 e_g^0$.

The $d-$orbital electronic configuration of the complex among $[Co(en)_3]^{3+}$,$[CoF_6]^{3-}$,$[Mn(H_2O)_6]^{2+}$ and $[Zn(H_2O)_6]^{2+}$ that has the highest $CFSE$ is $:$

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