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Given that the hydrogen atom contains a nucleus and an electron, quantum mechanics allows one to predict the probability of finding the electron at any given radial distance . It is given by the square of a mathematical function known as the "wavefunction", which is a solution of the Schrödinger equation. The lowest energy equilibrium state of ...
This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to radium and some beyond. "ψ" graphs are shown with − and + wave function phases shown in two different colors (arbitrarily red and blue).
The radial parts of these atomic orbitals are sometimes numerical tables or are sometimes Slater orbitals. By angular momentum coupling many-electron eigenfunctions of J 2 (and possibly S 2) are constructed. In quantum chemical calculations hydrogen-like atomic orbitals cannot serve as an expansion basis, because they are not complete.
In Schrödinger's quantum-mechanical theory of the hydrogen atom, the Bohr radius is the value of the radial coordinate for which the radial probability density of the electron position is highest. The expected value of the radial distance of the electron, by contrast, is 3 2 a 0 {\displaystyle {\tfrac {3}{2}}a_{0}} .
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...
STOs have the following radial part: =where n is a natural number that plays the role of principal quantum number, n = 1,2,...,; N is a normalizing constant,; r is the distance of the electron from the atomic nucleus, and
Visualization of the hydrogen wave function, prominently used in several articles. Hydrogen is made of only one electron and one proton, so it's understanding forms a basis for the understanding of more complex elements (as evident in the use of this image in articles below). Articles in which this image appears
The spectral series of hydrogen, on a logarithmic scale. The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom.