Correct increasing order of wavelength of absorption in visible region for complex is:

A. \([Ni(CN)_6]^{4-}\)

B. \([Ni(H_2O)_6]^{2+}\)

C. \([Ni(CO)_6]^{2+}\)

D. \([Ni(NH_3)_6]^{2+}\)

Choose the correct answer from the options given below:

\(C < A < D < B\)

The correct answer is option 2. \(C < A < D < B\).

In transition metal complexes, the ligands interact with the metal center and cause a splitting of the d-orbitals into different energy levels. This splitting leads to the absorption of visible light, which promotes electrons from a lower energy d-orbital to a higher energy d-orbital. The wavelength of light absorbed depends on the magnitude of this splitting, known as the ligand field splitting energy (\(\Delta_0\)):

Larger splitting energy (\(\Delta_0\)) corresponds to the absorption of light of shorter wavelength (higher energy).

Smaller splitting energy corresponds to the absorption of light of longer wavelength (lower energy).

Comparing Ligands and Their Field Strength

C. \([Ni(CO)_6]^{2+}\):

Ligand: Carbon monoxide \((CO)\)

Field Strength: \(CO\) is a strong field ligand.

Effect: \(CO\) causes a large splitting of the d-orbitals in the nickel center. As a result, \([Ni(CO)_6]^{2+}\) will absorb light of shorter wavelength (higher energy), meaning it absorbs in the blue or violet region of the spectrum, and reflects longer wavelengths (red).

A. \([Ni(CN)_6]^{4-}\):

Ligand: Cyanide \((CN^-)\)

Field Strength: \(CN^-\) is also a strong field ligand, but less strong than \(CO\).

Effect: \(CN^-\) causes significant splitting of the d-orbitals, but the splitting is not as large as that caused by CO. Therefore, \([Ni(CN)_6]^{4-}\) absorbs light of slightly longer wavelength (lower energy) compared to \([Ni(CO)_6]^{2+}\).

D. \([Ni(NH_3)_6]^{2+}\):

Ligand: Ammonia \((NH_3)\)

Field Strength: \(NH_3\) is a medium field ligand.

Effect: \(NH_3\) causes moderate splitting of the d-orbitals. Consequently, \([Ni(NH_3)_6]^{2+}\) absorbs light of longer wavelength (lower energy) than \([Ni(CO)_6]^{2+}\) and \([Ni(CN)_6]^{4-}\).

B. \([Ni(H_2O)_6]^{2+}\):

Ligand: Water \((H_2O)\)

Field Strength: \(H_2O\) is a weak field ligand.

Effect: \(H_2O\) causes the smallest splitting of the d-orbitals among the ligands listed. Thus, \([Ni(H_2O)_6]^{2+}\) absorbs light of the longest wavelength (lowest energy) compared to the other complexes.

Thus, the correct increasing order of wavelength of absorption (from shortest to longest wavelength) is:

1. \([Ni(CO)_6]^{2+}\) (shortest wavelength, highest energy)

2. \([Ni(CN)_6]^{4-}\)

3. \([Ni(NH_3)_6]^{2+}\)

4. \([Ni(H_2O)_6]^{2+}\) (longest wavelength, lowest energy)

Therefore, the correct option is: 2. \(C < A < D < B\)