Match the following Complex ions with their respective hybridisation and choose the correct option.

(d)-(i), (c)-(ii), (b)-(iii), (a)-(iv)

The correct matching of the complex ions with their respective hybridizations is as follows:

(a) [Ni(CN)₄]^2- (iv) dsp²

(b) [Fe(CN)₆]^4- (iii) d²sp³

(c) [FeF₆]^4- (ii) sp³d²

(d) [Ni(CO)₄] (i) sp³

(a) [Ni(CN)₄]^2- (iv) dsp² :

In the complex ion [Ni(CN)₄]^2-, the central nickel ion (Ni) is coordinated with four cyanide ions (CN^-) as ligands. Each cyanide ion donates one electron pair to form a coordinate bond with the metal ion.

Nickel (Ni) has the electron configuration [Ar] 3d⁸ 4s². In the complex [Ni(CN)₄]^2-, the nickel ion loses two electrons to achieve a +2 oxidation state. Hence, the electron configuration becomes [Ar] 3d⁸. In dsp² hybridization, the d orbitals (3d) and the s orbital (4s) undergo hybridization to form five hybrid orbitals: four sp³ hybrid orbitals and one unhybridized d orbital. The hybrid orbitals are arranged in a square planar geometry around the central nickel ion.

In the case of [Ni(CN)₄]^2-, the four cyanide ligands occupy the four sp³ hybrid orbitals of nickel, forming four sigma (σ) bonds. The remaining unhybridized d orbital of nickel can accept a pair of electrons from the cyanide ligands, forming dπ-pπ bonds, which contribute to the overall stability of the complex.

Therefore, the correct hybridization of the central nickel ion in [Ni(CN)₄]^2- is dsp².

(b) [Fe(CN)₆]^4- (iii) d²sp³:

In this complex ion, the central metal ion is iron (Fe) coordinated to six cyanide ligands (CN^-). The coordination number of iron in this case is 6. The electronic configuration of iron is [Ar]3d6, and when it forms six bonds, it promotes one electron from the 3d orbital to the 4s orbital, giving it the electronic configuration [Ar]3d⁵ 4s¹.

In d²sp³ hybridization, the 4s, one 4p, and three 3d orbitals of iron hybridize to form five d²sp³ hybrid orbitals. Each of these orbitals forms a sigma bond with one of the cyanide ligands, resulting in an octahedral geometry for the complex ion.

(c) [FeF₆]^4- (ii) sp³d²:

In the complex ion [FeF₆]^4-, the central iron ion (Fe) is coordinated with six fluoride ions (F^-) as ligands. Each fluoride ion donates one electron pair to form a coordinate bond with the metal ion.

Iron (Fe) has the electron configuration [Ar] 3d⁶ 4s². In the complex [FeF₆]^4-, the iron ion loses two electrons to achieve a +2 oxidation state. Hence, the electron configuration becomes [Ar] 3d⁶.

In order to form six bonds, the electron configuration of iron can be represented as [Ar] 3d⁶ 4s⁰. To accommodate the formation of six bonds, iron promotes one electron from the 4s orbital to one of the empty 3d orbitals. This results in the electron configuration [Ar] 3d⁵.

In sp³d² hybridization, five hybrid orbitals are formed by hybridizing three 3d orbitals, one 4s orbital, and one 4p orbital. These five hybrid orbitals arrange themselves in an octahedral geometry around the central iron ion. Each hybrid orbital overlaps with the fluorine ligand's orbital to form five sigma (σ) bonds.

Therefore, the correct hybridization of the central iron ion in [FeF₆]^4-is sp³d².

(d) [Ni(CO)₄] (i) sp³:

In this complex ion, the central metal ion is nickel (Ni) coordinated with four carbon monoxide ligands (CO). The coordination number of nickel, in this case, is 4. The electronic configuration of nickel is [Ar]3d⁸, and when it forms four bonds, it promotes two electrons from the 3d orbital to the 4s orbital, giving it the electronic configuration [Ar]3d⁸ 4s².

In sp³ hybridization, nickel's 4s and three 4p orbitals hybridize to form four sp³ hybrid orbitals. Each of these orbitals forms a sigma bond with one of the carbon monoxide ligands, resulting in a tetrahedral geometry for the complex ion.