The complex ion $[PtCl_2(en)_2]^{2+}$ exhibits both geometrical and optical isomerism. This is due to its square planar geometry where the coordination number of Pt is 4, and 'en' (ethylene diamine) is a bidentate ligand. Here are the key points regarding the isomerism:
- Geometrical Isomerism: In a square planar complex, geometrical isomerism arises due to the different possible spatial arrangements of the ligands. For $[PtCl_2(en)_2]^{2+}$, the arrangement of the chloride ions and the two bidentate ethylene diamine ligands can lead to cis and trans isomers.
- Optical Isomerism: This type of isomerism occurs when a complex is non-superimposable on its mirror image. In this complex, the presence of bidentate ethylene diamine ligands in a specific arrangement can cause the complex to have a chiral center, allowing for optical isomerism where enantiomers (mirror-image isomers) are possible.
Thus, $[PtCl_2(en)_2]^{2+}$ can exist in forms that display both geometrical and optical isomerism. Therefore, the correct answer is geometrical and optical isomerism.