Porbitals

P orbitals are atomic orbitals with angular momentum quantum number l = 1. They appear in every electron shell with n ≥ 2 and, in hydrogen-like atoms, form a triplet of degenerate orbitals with magnetic quantum numbers m_l = -1, 0, +1. In many atoms these are described as three real orbitals: p_x, p_y, and p_z, oriented along the Cartesian axes.

A p orbital has a dumbbell shape with two lobes on opposite sides of the nucleus. It contains a nodal plane that passes through the nucleus and is perpendicular to the orbital’s axis (for example, p_z has the xy-plane as a node). The angular node reflects l = 1, and the radial distribution has n − l − 1 radial nodes, so 2p has zero radial nodes, 3p has one, etc.

Electron density in p orbitals is directional, making them anisotropic. This directionality influences chemical bonding: overlap of p orbitals can form sigma bonds when lobes align along the internuclear axis or pi bonds when lobes overlap sidewise above and below the axis.

In terms of energy, s orbitals in a given shell are generally filled before p orbitals (2s before 2p, 3s before 3p, etc.). In isolated hydrogen, np levels are degenerate with ns, but in multi-electron atoms the energies split due to shielding and penetration.

Transitions involving p orbitals obey the selection rule Δl = ±1.