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Chemistry Question on coordination compounds

Among the following complexes, the one which shows zero crystal field stabilisation energy (CFSE) is

A

[Mn(H2O)6]3+[Mn(H_2 O)_6]^{3+}

B

[Fe(H2O)6]3+[Fe(H_2O)_6]^{3+}

C

[Co(H2O)6]2+[Co (H_2O)_6]^{2+}

D

Co(H2O)6]3+Co (H_2O)_6]^{3+}

Answer

[Fe(H2O)6]3+[Fe(H_2O)_6]^{3+}

Explanation

Solution

The CFSE for octahedral complex is given by
CFSE = [−0.4t2ge−+0.6ege−][-0.4t_{2g}e^- + 0.6e_ge^-]
For Mn3+,[3d4]→t2g3eg1Mn^{3+},[3d^4] \rightarrow t^3_{2g}e^1_g
∴      CFSE=[(−0.4×3)+(0.6×1)]=−0.6\therefore\, \, \, \, \, \, CFSE = [(-0.4 \times 3) + (0.6 \times 1)] = - 0.6
ForFe3+,[3d5]→t2g3eg2For Fe^{3+},[3d^5] \rightarrow t^3_{2g} e^2_g
      \, \, \, \, \, \, CFSE =[−(0.4×3)+(0.6×2)]=0 [-(0.4 \times 3) + (0.6 \times 2)] = 0
For Co2+,[3d7]→t2g5eg2Co^{2+}, [3d^7]\rightarrow t_{2g}^5 e^2_g
      \, \, \, \, \, \, CFSE =[(−0.4×5)+(2×0.6)]=0 [(-0.4 \times 5) + (2 \times 0.6)] = 0
= -0.8
For Co3+,[3d6]→t2g4eg2Co^{3+},[3d^6]\rightarrow t^4_{2g}e^2_g
CFSE = [(−0.4×4)+(2×0.6)][(-0.4 \times 4) + (2 \times 0.6)]
= -0.4