Assertion:  Bis(dimethylglyoxiamto)nickel(II) can show geometrical isomerism.

Reason:  Tetrahedral complexes with chiral structures exhibit optical isomerism

Assertion is incorrect, but the reason is correct.

The correct answer is option 4. Assertion is incorrect, but the reason is correct.

Let us break down the assertion and reason provided:

Assertion: Bis(dimethylglyoximate)nickel(II) can show geometrical isomerism.

This assertion suggests that the complex \([Ni(dmg)_2]\), where dmg stands for dimethylglyoximate, is capable of exhibiting geometrical isomerism. Geometrical isomerism occurs in coordination compounds when different spatial arrangements of ligands are possible around the central metal atom. This typically occurs in coordination complexes with certain coordination geometries, such as square planar or octahedral.

However, in the case of bis(dimethylglyoximate)nickel(II), the complex typically adopts a square planar geometry rather than a tetrahedral one. Square planar complexes with different ligands in adjacent positions can exhibit geometrical isomerism, but bis(dimethylglyoximate)nickel(II) is not tetrahedral.

Reason: Tetrahedral complexes with chiral structures exhibit optical isomerism.

This reason highlights another type of isomerism, optical isomerism, which occurs in chiral molecules or coordination complexes. Chirality arises when a molecule or complex lacks an internal plane of symmetry and cannot be superimposed onto its mirror image. Tetrahedral complexes with different ligands attached to the central metal atom can exhibit chirality and therefore optical isomerism.

The reason provided is correct because tetrahedral coordination complexes with chiral structures indeed have the potential to exhibit optical isomerism due to their non-superimposable mirror images.

In summary, while the reason is valid, the assertion is incorrect because bis(dimethylglyoximate)nickel(II) is typically square planar rather than tetrahedral, and geometrical isomerism in this complex arises from different ligands in adjacent positions.