\( [MnCl_4]^{2-} \) - \( dsp^2 \)
Let's analyze the hybridization of the metal ion in each of these complexes:
- \( [Ni(H_2O)_6]^{2+} \): The complex consists of Ni²⁺ surrounded by six water molecules. In the case of Ni²⁺ (which has a d⁸ electron configuration), the central metal ion typically undergoes octahedral geometry, which corresponds to an \( sp^3d^2 \) hybridization. This hybridization is correct for this complex.
- \( [CoF_6]^{3-} \): The complex consists of Co³⁺ surrounded by six fluoride ions. The Co³⁺ ion, with a d⁶ electron configuration, also adopts octahedral geometry.
Therefore, the hybridization of Co³⁺ in this complex is \( sp^3d^2 \). This is correct. - \( [Cu(NH_3)_4]^{2+} \): The complex consists of Cu²⁺ surrounded by four ammonia molecules. The Cu²⁺ ion (with a d⁹ electron configuration) typically adopts a square planar geometry (not octahedral), which corresponds to \( dsp^2 \) hybridization. However, Cu²⁺ generally forms a tetrahedral geometry in the presence of NH₃, which should be \( sp^3 \). Hence, this match is incorrect.
- \( [MnCl_4]^{2-} \): The complex consists of Mn²⁺ surrounded by four chloride ions. The Mn²⁺ ion (with a d⁵ electron configuration) adopts a tetrahedral geometry, and the hybridization for a tetrahedral geometry is \( sp^3 \). Hence, the hybridization \( dsp^2 \) is incorrect.
Thus, the incorrect match is for \( [Cu(NH_3)_4]^{2+} \) and \( [MnCl_4]^{2-} \), but only (1) has the correct hybridization.
Therefore, the correct answer is Option (1).