How can different no. of unpaired electrons lead to different colours of co-ordination compounds?

Question

To make the question clear I would like to take an example. $\ce{K_3[Fe(CN)6]}$ and $\ce{K3[FeF6]}$ shows different colors in solutions. It is given in my textbook that it is because of different number of unpaired electrons. But, how can the no. of unpaired electrons affect the frequency of light emitted?

The colors of co-ordination compounds are due to d-d transition of electrons. $\ce{CN^-}$ is a strong field ligand while $\ce{F^-}$ is a weak field ligand. Thus, there will be difference in the crystal field splitting energy in both of the given compounds. This, results in a different energy gap between the eg and t2g energy levels in them. Thus, when electrons undergo transition different frequencies corresponding to different energy gap is emitted.

I was hoping this as the answer. But, in my textbook the reason is attributed to only the difference in no. of unpaired electrons. Why is it so?

Answer 1

The crystal field splitting does definitely contribute.But it is not the only thing to contribute to the colour of the coordinate complex solution. The colour is equivalent to the spectra (emission or the absorption) of the solution, and hence by enumerating the factors contributing to the emission spectra of a solution, we can compare the colours of two different solutions.

It usually is an unpaired electron which shifts between the various available orbitals and paired electrons rarely do so, since the energy required to unpair acts as a barrier for its' transitions. Moreover, there might also be spin inversions (see Hyperfine structure) which might give additional lines in the spectra. Presence of unpaired electrons helps in producing additional energy levels in the electric and magnetic fields of the ligands (zeeman and stark effect), providing additional lines in the spectra. All these establish the uniqueness of the spectral distribution which the solution absorbs, and hence the colour.

The number of unpaired electrons also determines the resultant magnetic field of other species in the solution, which alters the energy levels of the solvating molecules.