Question

The d-electronic configuration of an octahedral Co(II) complex having a magnetic moment of 3.95 BM is:

• A. \( t_{2g}^6 e_g^1 \)
• B. \( t_{2g}^3 e_g^0 \)
• C. \( t_{2g}^5 e_g^2 \)
• D. \( e_g^4 t_{2g}^3 \)

Hint:

For d-block elements, determining the electronic configuration in an octahedral complex can be done by considering the splitting of the d-orbitals into \( t_{2g} \) and \( e_g \) orbitals. The magnetic moment is also a useful indicator to determine the number of unpaired electrons in the complex.

Answer 1

The Correct Option is C

For the given Co(II) complex, the electronic configuration of \( \text{Co}^{2+} \) is derived from the electron count of the neutral Co atom (\( \text{Co} = [Ar] 3d^7 4s^2 \)): \[ \text{Co}^{2+} = (Ar) 3d^7 4s^0 \] Since the magnetic moment is 3.95 BM, which suggests the presence of 3 unpaired electrons, the correct electronic configuration corresponds to \( t_{2g}^5 e_g^2 \), where the electrons are distributed in the \( t_{2g} \) and \( e_g \) orbitals in an octahedral field.
This configuration allows for 3 unpaired electrons, corresponding to a magnetic moment of approximately 3.95 BM, as calculated from: \[ \mu = \sqrt{n(n+2)} \quad \text{where} \quad n = \text{number of unpaired electrons} \] \[ \mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \, \text{BM} \] Thus, the correct electronic configuration is \( t_{2g}^5 e_g^2 \).