Show how two \(2 p\) atomic orbitals can combine to form a \(\sigma\) or a \(\pi\) molecular orbital.

Atomic orbitals are the regions around the nucleus of an atom where there is a high probability of finding an electron. Molecular orbitals, on the other hand, describe the electron distribution in a molecule. The combination of atomic orbitals forms molecular orbitals when atoms bond together in a molecule.

The 2p atomic orbitals are part of the second energy level and consist of three orbitals, denoted as 2p_x, 2p_y, and 2p_z. These orbitals have a dumbbell shape and are oriented along the x, y, and z axes, respectively.

The σ molecular orbitals are formed by the head-on or axial overlapping of atomic orbitals. For our case, when two 2p_z atomic orbitals from two different atoms overlap along the z-axis, it results in the formation of a σ molecular orbital. The electron cloud is symmetrically distributed around the internuclear axis. This process can be represented as: \[ 2p_zA + 2p_zB \rightarrow \sigma_{2p_z} \] Here, 2p_zA and 2p_zB represent the 2p_z orbitals from two different atoms A and B, and σ_{2p_z} represents the resulting sigma molecular orbital.

The π molecular orbitals are formed by the side-wise or parallel overlapping of atomic orbitals. For our case, when a 2p_x atomic orbital from one atom overlaps with a 2p_x atomic orbital from another atom along the x-axis, it results in the formation of a π molecular orbital. Similarly, the overlapping of two 2p_y atomic orbitals along the y-axis also results in a π molecular orbital. The electron cloud is localized above and below the internuclear axis. This process can be represented as: \[ 2p_xA + 2p_xB \rightarrow \pi_{2p_x} \] and \[ 2p_yA + 2p_yB \rightarrow \pi_{2p_y} \] Here, 2p_xA and 2p_xB represent 2p_x orbitals, and 2p_yA and 2p_yB represent 2p_y orbitals from two different atoms A and B, while π_{2p_x} and π_{2p_y} represent the resulting pi molecular orbitals.