Based on Crystal Field Theory,show the energy level splitting and determine the $d$-electron configuration and magnetic moment for the central metal atom/ion in the following complexes: $[CoF_6]^{3-}$,$[Co(H_2O)_6]^{2+}$,$[Co(CN)_6]^{3-}$.

(N/A) $1$. $[CoF_6]^{3-}$: $Co^{3+}$ is $3d^6$. $F^-$ is a weak field ligand. Splitting: $t_{2g}^4 e_g^2$. Number of unpaired electrons $(n)$ = $4$. Magnetic moment $\mu = \sqrt{n(n+2)} = \sqrt{4(6)} = \sqrt{24} \approx 4.90 \ BM$.
$2$. $[Co(H_2O)_6]^{2+}$: $Co^{2+}$ is $3d^7$. $H_2O$ is a weak field ligand. Splitting: $t_{2g}^5 e_g^2$. Number of unpaired electrons $(n)$ = $3$. Magnetic moment $\mu = \sqrt{3(5)} = \sqrt{15} \approx 3.87 \ BM$.
$3$. $[Co(CN)_6]^{3-}$: $Co^{3+}$ is $3d^6$. $CN^-$ is a strong field ligand. Splitting: $t_{2g}^6 e_g^0$. Number of unpaired electrons $(n)$ = $0$. Magnetic moment $\mu = 0 \ BM$ (Diamagnetic).