The d-orbital electronic configuration of the complex among [Co(en)3]3+, [CoF6]3-, [Mn(H2O)6]2+ and [Zn(H2O)6]2+ that…

🧠 CFSE Maximum for Each Complex

Compute CFSE (per electron, ignoring pairing) for each:

🗺️ Evaluate Each

| Complex | Metal/d-config | Ligand strength | Spin | Configuration | CFSE (×Δₒ) | |---|---|---|---|---|---| | $[\mathrm{Co(en)_3}]^{3+}$ | Co(III) d⁶ | strong (en) | LS | $t_{2g}^6 e_g^0$ | $-2.4$ ✓ | | $[\mathrm{CoF_6}]^{3-}$ | Co(III) d⁶ | weak (F⁻) | HS | $t_{2g}^4 e_g^2$ | $-0.4$ | | $[\mathrm{Mn(H_2O)_6}]^{2+}$ | Mn(II) d⁵ | weak (H₂O) | HS | $t_{2g}^3 e_g^2$ | $0$ | | $[\mathrm{Zn(H_2O)_6}]^{2+}$ | Zn(II) d¹⁰ | irrelevant | filled | $t_{2g}^6 e_g^4$ | $0$ |

Highest CFSE = $[\mathrm{Co(en)_3}]^{3+}$ with $t_{2g}^6 e_g^0$ → CFSE = $-2.4\Delta_o$.

⚡ CFSE Maximum Configurations (Octahedral)

| Config | CFSE (×Δₒ) | |---|---| | $t_{2g}^6 e_g^0$ (LS d⁶) | $-2.4$ ← max | | $t_{2g}^5 e_g^0$ (LS d⁵) | $-2.0$ | | $t_{2g}^4 e_g^0$ (LS d⁴) | $-1.6$ | | $t_{2g}^3 e_g^0$ (d³) | $-1.2$ | | $t_{2g}^6 e_g^2$ | $-1.2$ | | $t_{2g}^3 e_g^2$ (d⁵ HS) | $0$ | | $t_{2g}^6 e_g^4$ (d¹⁰) | $0$ |

⚠️ d⁵ HS and d¹⁰ Both Have Zero CFSE

$t_{2g}^3 e_g^2$: $3(-0.4) + 2(+0.6) = -1.2 + 1.2 = 0$. Same for filled d¹⁰: $6(-0.4) + 4(+0.6) = -2.4 + 2.4 = 0$.

$\boxed{\text{Answer: (1) } t_{2g}^6 e_g^0}$