The hybridization of an atom refers to the mixing of atomic orbitals to form new hybrid orbitals, which have different shapes and energies than the original atomic orbitals. In the case of tetracarbonyl nickel, the nickel atom is bonded to four carbon monoxide (CO) ligands.

The central nickel atom in tetracarbonyl nickel is surrounded by four ligands, which means it has a coordination number of 4. In order to determine the hybridization of the nickel atom, we can use the concept of the Valence Shell Electron Pair Repulsion (VSEPR) theory.

According to VSEPR theory, the electron pairs around the central atom will arrange themselves in a way that maximizes the distance between them, resulting in a geometry that minimizes electron-electron repulsion. In the case of tetracarbonyl nickel, the four CO ligands are arranged in a symmetrical tetrahedral geometry around the central nickel atom.

To determine the hybridization of the nickel atom, we can count the number of electron pairs around it. In tetracarbonyl nickel, there are four sigma bonds between the nickel atom and the four CO ligands, as well as four lone pairs on the nickel atom. This gives a total of eight electron pairs around the nickel atom.

The hybridization of an atom is determined by the number of sigma bonds and lone pairs around it. In this case, since there are four sigma bonds and four lone pairs, the nickel atom in tetracarbonyl nickel is sp3 hybridized.

The sp3 hybrid orbitals are formed by the mixing of one s orbital and three p orbitals on the nickel atom. These hybrid orbitals are oriented in a tetrahedral arrangement, pointing towards the four CO ligands.

In summary, the hybridization of the nickel atom in tetracarbonyl nickel is sp3, as there are four sigma bonds and four lone pairs around the central atom.