Final answer:
Yes, a transition metal complex can have six unpaired electrons if the metal has a d4 to d7 electronic configuration and forms a high-spin complex with weak-field ligands, as seen in [CoF6]3-.
Step-by-step explanation:
It is true that a complex of a metal in the transition series can have six unpaired electrons. This happens when the metal ion has a d4 to d7 electronic configuration in a high-spin complex.
For example, in a high-spin [CoF6]³⁻ complex, Cobalt (Co) is in the +3 oxidation state (Co3+) and has a d6 electronic configuration. Since fluoride is a weak-field ligand and does not cause significant splitting of the d-orbitals, all six d-electrons will remain unpaired, matching a high-spin scenario.
However, with strong-field ligands, the energy difference between the two sets of d-orbitals can be high enough to favor pairing of the electrons in the lower energy set, resulting in fewer unpaired electrons and a low-spin complex.