pOrbitalen

pOrbitalen refers to the set of atomic orbitals with angular momentum quantum number l = 1 in quantum mechanics and chemistry. They are the p-type orbitals and, in a spherically symmetric atom, come in three degenerate orientations corresponding to m_l = -1, 0, +1. In Cartesian terms these three orbitals are commonly described as px, py, and pz. Each p orbital has a dumbbell shape with a nodal plane that passes through the nucleus and is perpendicular to its axis: the px orbital has a nodal plane at x = 0, and similarly for py and pz. The three orbitals are related by rotation and together they account for the p-type electron density in an atom.

The angular part of the p orbitals is described by the spherical harmonic Y_1^m, and the full wavefunction is written as ψ_n1m(r) = R_n1(r) Y_1^m(θ, φ) with l = 1. The radial part R_n1(r) depends on the principal quantum number n and ensures that p orbitals appear only for n ≥ 2. In hydrogen-like atoms they are degenerate with other orbitals having the same principal quantum number, but in multi-electron atoms their energies are lifted by electron–electron interactions and shielding.

Each p orbital can hold up to two electrons with opposite spins, giving a total capacity of six electrons for the three p orbitals. In chemistry, p orbitals participate in covalent bonding through overlap with orbitals on neighboring atoms, forming sigma and pi bonds. The orientation of px, py, and pz influences molecular geometry and bonding patterns.

The designation p orbital stems from historical spectroscopic notation for atomic lines (s, p, d, f), which corresponds to angular momentum values l = 0, 1, 2, 3.