To determine which complex can show fac- and mer- isomerism, we need to understand what these isomers are:
Facial (fac-) and Meridional (mer-) Isomerism:
- The fac-isomer (facial isomer) occurs when three identical ligands are adjacent to each other, forming one face of an octahedron.
- The mer-isomer (meridional isomer) occurs when three identical ligands are in a planar arrangement around the central atom.
Fac- and mer- isomerism typically occurs in octahedral complexes with a formula of the type $Ma_3b_3$, where a and b are different ligands.
Let's analyze each option:
- $[Co(NH_3)_3(NO_2)_3]$: This complex is of the type $Ma_3b_3$ (with a = NH_3 and b = NO_2), which allows for both fac- and mer- isomerism.
- $[Pt(NH_3)_2Cl_2]$: This complex is square planar or can be perceived as $Ma_2b_2$, leading to cis-trans isomerism, not fac-mer.
- $[Co(NH_3)_4a_2]^+$: This complex of type $Ma_4b_2$ forms cis-trans-type isomers but not fac-mer isomers.
- $[CoCl_2(en)_2]$: This complex forms enantiomers (optical isomers) or geometrical isomers but not fac-mer isomers.
Therefore, the correct answer is $[Co(NH_3)_3(NO_2)_3]$ as it is the only complex that can exhibit both fac- and mer- isomerism.