The magnetic moment of an octahedral Co(II) complex is 4.0 BM . The el...
Electronic Configuration of the Octahedral Co(II) Complex
The electronic configuration of the octahedral Co(II) complex can be determined using the crystal field theory. In this theory, the ligands surrounding the central metal ion cause a splitting of the d orbitals into two sets of orbitals with different energies:
- t2g orbitals - lower in energy and occupied by 5 electrons
- eg orbitals - higher in energy and occupied by 2 electrons
The electronic configuration of the complex can be represented as:
Magnetic Moment of the Complex
The magnetic moment of the complex can be calculated using the formula:
where n is the number of unpaired electrons and BM is the Bohr magneton. For the given electronic configuration, the number of unpaired electrons is:
Substituting the values in the formula:
Therefore, the magnetic moment of the complex is 4.0 BM which is not consistent with the electronic configuration t2g5eg2. This can be explained by invoking the concept of spin-orbit coupling.
Spin-Orbit Coupling
Spin-orbit coupling is the interaction between the magnetic field generated by the motion of electrons (spin) and the magnetic field generated by the motion of electrons around the nucleus (orbit). This interaction causes a splitting of the energy levels of the d orbitals into two sets:
- t2g and eg' - lower in energy
- eg and t2g' - higher in energy
The electronic configuration of the complex can be rewritten as:
This configuration has one unpaired electron in the eg orbital, which gives a magnetic moment of:
The observed magnetic moment of 4.0 BM can be explained by assuming that the complex is in a high spin state, where the eg and t
2g' levels are close in energy and the electron can occupy both orbitals. In this state, the complex has two unpaired electrons in the eg orbital, which gives a magnetic moment of