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NEET CHEMISTRYMedium

A low spin complex of d6d^6-cation in an octahedral field will have the following energy: (Δ0\Delta_0 = Crystal field splitting energy in an octahedral field, PP = Electron pairing energy)

A

125Δ0+3P-\frac{12}{5}\Delta_0 + 3P

B

25Δ0+2P-\frac{2}{5}\Delta_0 + 2P

C

25Δ0+P-\frac{2}{5}\Delta_0 + P

D

125Δ0+P-\frac{12}{5}\Delta_0 + P

Step-by-Step Solution

In an octahedral crystal field, the dd orbitals split into lower energy t2gt_{2g} and higher energy ege_g orbitals. The energy of each electron in the t2gt_{2g} orbital is 0.4Δ0-0.4\Delta_0 (or 25Δ0-\frac{2}{5}\Delta_0) with respect to the barycentre. For a d6d^6 low spin complex, the strong field ligand forces all 6 electrons to pair up and occupy the lower energy t2gt_{2g} orbitals (configuration: t2g6eg0t_{2g}^6 e_g^0).

The Crystal Field Splitting Energy (CFSE) is calculated as: CFSE=6×(0.4Δ0)=2.4Δ0=125Δ0\text{CFSE} = 6 \times (-0.4\Delta_0) = -2.4\Delta_0 = -\frac{12}{5}\Delta_0.

Since all 6 electrons are completely paired in the 3 available t2gt_{2g} orbitals, there are 3 electron pairs. Thus, the total pairing energy is 3P3P. Therefore, the total energy of the complex is 125Δ0+3P-\frac{12}{5}\Delta_0 + 3P.

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