Final answer:
The complex [Co(en)₃]Cl₃ does not have any unpaired electrons, but it exhibits cis-trans isomerism and has an optical isomer.
Step-by-step explanation:
The complex [Co(en)₃]Cl₃ does not have any unpaired electrons. The oxidation state of cobalt (Co) in this complex is +3, which means there are 7 d-electrons. When complexing with en (ethylenediamine), it acts as a strong-field ligand, causing the complex to be low spin. In the low spin configuration, all the d-electrons are paired, resulting in zero unpaired electrons.
This complex does not have any geometric isomers but it has an optical isomer. The [Co(en)₃]Cl₃ complex exhibits cis-trans isomerism. The cis form of the complex exists as a pair of optical isomers, which means that it has a nonsuperimposable mirror image.