\([Cu(en)_2]^{2+}\) is more stable than \([Cu(NH_3)_4]^{2+}\) because

Ligand is didentate and forms a chelate complex

The correct answer is option 4. Ligand is didentate and forms a chelate complex.

The greater stability of \([Cu(en)_2]^{2+}\) compared to \([Cu(NH_3)_4]^{2+}\) is primarily due to the chelate effect caused by ethylenediamine (\(en\)). Therefore, the correct answer is Ligand is didentate and forms a chelate complex.

1. Heteroleptic Complex:

A heteroleptic complex is one that contains different types of ligands. Both \([Cu(en)_2]^{2+}\) and \([Cu(NH_3)_4]^{2+}\) are heteroleptic complexes, so this factor doesn't differentiate between them.

2. Alkyl Group in Ethylenediamine:

The presence of an alkyl group in ethylenediamine does not directly contribute to the stability of the complex.

3. Copper in +2 Oxidation State:

Both complexes involve copper in the +2 oxidation state, so this factor does not explain the difference in stability between the two complexes.

4. Chelate Complex Formation:

Ethylenediamine (\(en\)) is a bidentate ligand, meaning it can form two coordination bonds with the metal ion. In \([Cu(en)_2]^{2+}\), each ethylenediamine ligand forms two bonds with copper, creating a chelate complex.

The chelate effect refers to the enhanced stability observed in complexes with chelating ligands compared to similar complexes with non-chelating ligands.
In contrast, \([Cu(NH_3)_4]^{2+}\) involves ammonia ligands, which are not bidentate and do not form a chelate complex to the same extent.

The chelate effect leads to increased stability because the formation of a chelate ring helps to reduce the entropy of the system and increases the thermodynamic stability of the complex. Therefore, option 4 is the correct explanation for the greater stability of \([Cu(en)_2]^{2+}\).