To determine the hybridization involved in the complex \([Ni(CN)_4]^{2-}\), we must follow a systematic approach considering the electronic configuration of the central metal atom and the ligand involved.
Step 1: Determine the oxidation state of Nickel:
- The complex is \([Ni(CN)_4]^{2-}\).
- Let the oxidation state of Nickel be \(x\).
- Each CN ligand carries a charge of \(-1\). Therefore, for four CN ligands, the total negative charge is \(-4\).
- The overall charge on the complex is \(-2\).
- The equation for oxidation state is:
x + 4(-1) = -2 。
- Solving for \(x\), we get \(x = +2\).
Step 2: Determine the electronic configuration of Ni\(^{2+}\):
- Neutral Nickel (\(Ni\)) has an atomic number of 28, hence its electronic configuration is
\text{[Ar]} 3d^{8} 4s^2.
- For \(Ni^{2+}\), we remove two electrons from the 4s orbital:
\text{[Ar]} 3d^{8} 4s^{0}.
Step 3: Determine the hybridization in the presence of cyanide ligands:
- CN\(^-\) is a strong field ligand, which causes pairing of electrons in the \(\text{3d orbital}\).
- This pairing results in the configuration:
\text{[Ar]} \, 3d^{10} 4s^0 4p^0 with all 3d electrons paired.
- To form four coordination bonds, the electron orbitals used are 4s, 4p, and one 3d orbital:
- The hybridization is thus \(dsp^2\).
Conclusion:
The hybridization of the complex \([Ni(CN)_4]^{2-}\) is dsp^2. This means the complex forms a square planar geometry.