Given below are two statements:
Statement-I: The \(\text{M}-\text{C}\) \(\sigma\) bond is formed by the donation of lone pair of electrons on the carbonyl carbon into a vacant d-orbital of the metal.
Statement-II: The \(\text{M}-\text{C}\) \(\pi\) bond is formed by the donation of a pair of electrons from a filled d-orbital of metal into the vacant antibonding \(\pi^*\) orbital of carbon monoxide.
In the light of the above statements, choose the correct answer from the options given below:

According to the bonding in metal carbonyls:

Statement-I is incorrect because the \(\text{M}-\text{C}\) \(\sigma\) bond is formed by the donation of a lone pair of electrons from the carbonyl carbon into a vacant hybrid orbital of the metal, not necessarily a vacant d-orbital. For example, in \(\text{Ni(CO)}_4\), the nickel atom is \(sp^3\) hybridized (\(3d^{10}\) configuration) and the \(\sigma\) bonds are formed by donation into vacant \(sp^3\) hybrid orbitals, with no vacant d-orbitals involved.

Statement-II is correct because the \(\text{M}-\text{C}\) \(\pi\) bond is formed by the back-donation of a pair of electrons from a filled d-orbital of the metal into the vacant antibonding \(\pi^{*}\) orbital of carbon monoxide. This is known as synergic bonding.

Therefore, Statement I is incorrect but Statement II is correct.

Answer: Statement I is incorrect but Statement II is correct