Question

The values of the crystal field stabilization energies for a high spin \(d^6\) metal ion in octahedral and tetrahedral fields, respectively, are :

• A. \(-0.4\Delta_0\) and \(-0.27\Delta_t\)
• B. \(-1.6\Delta_0\) and \(-0.4\Delta_t\)
• C. \(-0.4\Delta_0\) and \(-0.6\Delta_t\)
• D. \(-2.4\Delta_0\) and \(-0.27\Delta_t\)

Hint:

High spin octahedral d6 is \(t_{2g}^4 e_g^2\) and high spin tetrahedral d6 is \(e^3 t_2^3\). Use \(-0.4\Delta_0\) per \(t_{2g}\) and \(+0.6\Delta_0\) per \(e_g\) electron; \(-0.6\Delta_t\) per e and \(+0.4\Delta_t\) per \(t_2\) electron.

Answer 1

The Correct Option is C

Octahedral, high spin \(d^6\): configuration \(t_{2g}^4 e_g^2\).
CFSE \(= 4(-0.4\Delta_0) + 2(+0.6\Delta_0) = -1.6\Delta_0 + 1.2\Delta_0 = -0.4\Delta_0\).
Tetrahedral, \(d^6\) (always high spin): \(e^3 t_2^3\).
CFSE \(= 3(-0.6\Delta_t) + 3(+0.4\Delta_t) = -1.8\Delta_t + 1.2\Delta_t = -0.6\Delta_t\).
So the values are \(-0.4\Delta_0\) and \(-0.6\Delta_t\).
Answer: (3) \(-0.4\Delta_0\) and \(-0.6\Delta_t\)