section_path: Properties/Electron energy levels
section_name: Electron energy levels
paragraph_text: Electron energy levels
  
  The ground state energy level of the electron in a hydrogen atom is −13.6 eV, equivalent to an ultraviolet photon of roughly 91 nm wavelength.
  
  The energy levels of hydrogen can be calculated fairly accurately using the Bohr model of the atom, in which the electron "orbits" the proton, like how Earth orbits the Sun. However, the electron and proton are held together by electrostatic attraction, while planets and celestial objects are held by gravity. Due to the discretization of angular momentum postulated in early quantum mechanics by Bohr, the electron in the Bohr model can only occupy certain allowed distances from the proton, and therefore only certain allowed energies.
  
  A more accurate description of the hydrogen atom comes from a quantum analysis that uses the Schrödinger equation, Dirac equation or Feynman path integral formulation to calculate the probability density of the electron around the proton. The most complex formulas include the small effects of special relativity and vacuum polarization. In the quantum mechanical treatment, the electron in a ground state hydrogen atom has no angular momentum—illustrating how the "planetary orbit" differs from electron motion.