In the separation of Cu²⁺ and Cd²⁺ in second group qualitative analysis of cations, tetrammine copper (II) sulphate and tetrammine cadmium (II) sulphate react with KCN to form the corresponding cyano complexes. Which one of the following pairs of the complexes and their relative stability enable the separation of Cu²⁺ and Cd²⁺?

K₃[Cu(CN)₄] more stable and K₂[Cd(CN)₄] less stable

When tetrammine copper (II) sulphate \([Cu(NH_3)_4]SO_4\) reacts with KCN, it forms the cyano complex \([Cu(CN)_4]^{3-}\). The coordination number of copper in this complex is 4.

On the other hand, when tetrammine cadmium (II) sulphate \([Cd(NH_3)_4]SO_4\) reacts with \(KCN\), it forms the cyano complex \([Cd(CN)_4]^{2-}\). The coordination number of cadmium in this complex is 4 as well.

The relative stabilities of these complexes play a crucial role in the separation of \(Cu^{2+}\) and \(Cd^{2+}\) ions. In this context, \([Cu(CN)_4]^{3-}\) is more stable than \([Cd(CN)_4]^{2-}\). As a result, when KCN is added to the mixture of \(Cu^{2+}\) and \(Cd^{2+}\) ions, \([Cu(CN)_4]^{3-}\) will form preferentially due to its higher stability, while \([Cd(CN)_4]^{2-}\) will form to a lesser extent due to its lower stability.

Therefore, the correct answer is Option \((1)\): \(K_3[Cu(CN)_4]\) more stable and \(K_2[Cd(CN)_4]\) less stable.