=== Photoelectric effect ===

{{main|Photoelectric effect}}

The article "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" ("On a [[Heuristic]] Viewpoint Concerning the Production and Transformation of [[Light]]")<ref group=einstein name=einsta /> received 18 March and published 9 June, proposed the idea of ''energy quanta''. This idea, motivated by [[Max Planck]]'s earlier derivation of the law of [[black-body radiation]] (which was preceded by the discovery of [[Wien's displacement law]], by [[Wilhelm Wien]], several years prior to Planck) assumes that [[luminous energy]] can be absorbed or emitted only in discrete amounts, called ''[[Quantum|quanta]]''. Einstein states,

{{quote|Energy, during the propagation of a ray of light, is not continuously distributed over steadily increasing spaces, but it consists of a finite number of [[photon|energy quanta]] localised at [[Point (geometry)|points in space]], moving without dividing and capable of being absorbed or generated only as [[wikt:entity|entities]].}}

In explaining the photoelectric effect, the hypothesis that energy consists of ''discrete packets'', as Einstein illustrates, can be directly applied to [[black body|black bodies]], as well.

The idea of light quanta contradicts the wave theory of light that follows naturally from [[James Clerk Maxwell]]'s [[Maxwell equations|equations]] for [[electromagnetism|electromagnetic]] behavior and, more generally, the assumption of [[infinite divisibility]] of energy in physical systems.

{{quote|A profound formal difference exists between the theoretical concepts that physicists have formed about gases and other ponderable bodies, and Maxwell's theory of electromagnetic processes in so-called empty space. While we consider the state of a body to be completely determined by the positions and velocities of an indeed very large yet finite number of atoms and electrons, we make use of continuous spatial functions to determine the electromagnetic state of a volume of space, so that a finite number of quantities cannot be considered as sufficient for the complete determination of the electromagnetic state of space.

... [this] leads to contradictions when applied to the phenomena of emission and transformation of light.

According to the view that the incident light consists of energy quanta'' ..., ''the production of cathode rays by light can be conceived in the following way. The body's surface layer is penetrated by energy quanta whose energy is converted at least partially into kinetic energy of the electrons. The simplest conception is that a light quantum transfers its entire energy to a single electron ... .}}

Einstein noted that the photoelectric effect depended on the wavelength, and hence the frequency of the light. At too low a frequency, even intense light produced no electrons. However, once a certain frequency was reached, even low intensity light produced electrons. He compared this to Planck's hypothesis that light could be emitted only in packets of energy given by ''hf'', where ''h'' is the [[Planck constant]] and ''f'' is the frequency. He then postulated that light travels in packets whose energy depends on the frequency, and therefore only light above a certain frequency would bring sufficient energy to liberate an electron.

Even after experiments confirmed that Einstein's equations for the photoelectric effect were accurate, his explanation was not universally accepted. [[Niels Bohr]], in his 1922 Nobel address, stated, "The hypothesis of light-quanta is not able to throw light on the nature of radiation."

By 1921, when Einstein was awarded the Nobel Prize and his work on photoelectricity was mentioned by name in the award citation, some physicists accepted that the equation {{nowrap|(<math>hf = \Phi + E_k</math>)}} was correct and light quanta were possible. In 1923, [[Arthur Compton]]'s [[Compton scattering|X-ray scattering experiment]] helped more of the scientific community to accept this formula. The theory of light quanta was a strong indicator of [[wave–particle duality]], a fundamental principle of [[quantum mechanics]].<ref>Physical systems can display both wave-like and particle-like properties</ref> A complete picture of the theory of photoelectricity was realized after the maturity of quantum mechanics.