The hydrogen atom's orbitals, solutions to the Schrödinger equation, are fully specified by three quantum numbers (n, l, m_l) and are characterized by radial probability distributions (probability of finding the electron at a given distance from the nucleus) and nodal structure — points or surfaces of zero electron probability. Total nodes equal n−1, angular nodes equal l (producing nodal planes with no radial dependence, characteristic of orbitals with nonzero angular momentum such as p orbitals), and radial nodes equal n−l−1; a fourth quantum number, electron spin (m_s = ±1/2), is required for a complete description of an electron and underlies the Pauli exclusion principle that no two electrons in an atom share all four quantum numbers. This is part of quantum mechanical atomic structure theory within physical chemistry, extending single-electron (hydrogen) orbital theory toward the treatment of multi-electron atoms.
The hydrogen atom's orbitals, solutions to the Schrödinger equation, are fully specified by three quantum numbers (n, l, m_l) and are characterized by radial probability distributions (probability of…