Max Planck derived a formula to describe the electromagnetic field inside a box when in thermal equilibrium in 1900.
His model consisted of a superposition of standing waves. In one dimension, the box has length L, and only sinusoidal waves of wavenumber
can occur in the box, where n is a positive integer (mathematically denoted by ). The equation describing these standing waves is given by:
where E is the magnitude of the electric field amplitude, and E is the magnitude of the electric field at position x. From this basic, Planck's law was derived.
In 1911, Ernest Rutherford concluded, based on alpha particle scattering, that an atom has a central pointlike proton. He also thought that an electron would be still attracted to the proton by Coulomb's law, which he had verified still held at small scales. As a result, he believed that electrons revolved around the proton. Niels Bohr, in 1913, combined the Rutherford model of the atom with the quantisation ideas of Planck. Only specific and well-defined orbits of the electron could exist, which also do not radiate light. In jumping orbit the electron would emit or absorb light corresponding to the difference in energy of the orbits. His prediction of the energy levels was then consistent with observation.
These results, based on a discrete set of specific standing waves, were inconsistent with the continuous classical oscillator model.
Work by Albert Einstein in 1905 on the photoelectric effect led to the association of a light wave of frequency  with a photon of energy . In 1917 Einstein created an extension to Bohrs model by the introduction of the three processes of stimulated emission, spontaneous emission and absorption (electromagnetic radiation).