1. Find CFSE for high-spin $d^6$ in an octahedral field

For octahedral splitting:

• Each electron in $t_{2g}$ contributes $-0.4\Delta_o$
• Each electron in $e_g$ contributes $+0.6\Delta_o$

For a high-spin $d^6$ ion in octahedral geometry, the electron configuration is: $t_{2g}^4 e_g^2$

So, $\text{CFSE} = 4(-0.4\Delta_o) + 2(+0.6\Delta_o)$ $= -1.6\Delta_o + 1.2\Delta_o$ $= -0.4\Delta_o$

2. Find CFSE for high-spin $d^6$ in a tetrahedral field

For tetrahedral splitting:

• Lower set: $e$ orbitals, each electron contributes $-0.6\Delta_t$
• Upper set: $t_2$ orbitals, each electron contributes $+0.4\Delta_t$

For a high-spin $d^6$ ion in tetrahedral geometry, the electron configuration is: $e^3 t_2^3$

So, $\text{CFSE} = 3(-0.6\Delta_t) + 3(+0.4\Delta_t)$ $= -1.8\Delta_t + 1.2\Delta_t$ $= -0.6\Delta_t$

3. Match with the options

The values are: $-0.4\Delta_o \quad \text{and} \quad -0.6\Delta_t$

This matches Option C.

4. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

They agree.