Statement I: The geometrical isomers of the complex \([M(NH_3)_4Cl_2]\)are optically inactive

Statement II: Both geometrical isomers of the complex \([M(NH_3)_4Cl_2]\)possess axis of symmetry.

Both Statement I and statement II are correct and statement II is the correct explanation of statement I

The correct answer is indeed Option 1: 1. Both Statement I and Statement II are correct, and Statement II is the correct explanation of Statement I.

Statement I: The geometrical isomers of the complex \([M(NH_3)_4Cl_2]\) are optically inactive.

Statement II: Both geometrical isomers of the complex \([M(NH_3)_4Cl_2]\) possess an axis of symmetry.

Both statements are correct:

Statement I is true. Geometrical isomers are stereoisomers that have different spatial arrangements of ligands but have the same connectivity between atoms. For a complex to exhibit optical activity, it must be chiral, meaning it must lack any internal symmetry elements. Geometrical isomers of the type \([M(NH_3)_4Cl_2]\) do not possess chiral centers and are optically inactive.

Statement II is the correct explanation for Statement I. Both geometrical isomers of the complex \([M(NH_3)_4Cl_2]\) possess a plane of symmetry, which is perpendicular to the coordination plane containing the central metal ion and four ammonia ligands. This plane of symmetry divides the molecule into two identical halves, leading to the absence of chirality and optical inactivity.