# Quantum

## Einstein's Light Quantum

In deriving his blackbody formula Planck assumed the complete validity of classical electromagnetism and, not having any theory of atomic structure, used the fact that the radiation was independent of the material of the radiator to assume that it would be sufficient to consider the cavity walls as modeled by a collection of simple harmonic oscillators, each capable of absorbing and emitting a particular frequency. He then calculated the average energy of such an oscillator in equilibrium with the cavity radiation, using a method previously developed by Boltzmann for the statistical treatment of an ideal gas. As an aid to calculating the various possible "partitions" of the total energy among the gas molecules, Boltzmann had assumed each to have one of a discrete set of energy values, but afterward had let the separation of the values tend to zero, so that the molecules could have a continuous range of energy. However, Planck found good agreement with the experimental frequency distribution only when the oscillator energy values, separated by *h* in his theory, remained separated by that amount, with *h* retaining the finite value that we have given above.

Several physicists criticized Planck's derivation, claiming that he had misapplied Boltzmann's method to his problem, and pointing out that Boltzmann had treated his molecules as distinguishable from one another. Planck's treatment implied that oscillators of a given frequency were indistinguishable. Einstein's view was that the derivation was questionable, but the formula was undoubtedly correct and this brought into question certain aspects of Maxwell's electromagnetic theory. Einstein also had other grounds for questioning Maxwell's theory. In the photoelectric effect, radiation (e.g., ultraviolet light) falls on a metal plate and ejects electrons. Below a certain threshold frequency, dependent on the metal, no electrons are ejected. Above that threshold, electrons are ejected with kinetic energies that increase linearly with the difference of the light frequency from the threshold. At a fixed frequency, increasing the light intensity causes more electrons to be emitted, without increasing the energy per electron. This phenomenon is best explained by assuming that the light consists of concentrations of energy that can be transferred to individual electrons, as in a collision of particles. However, that picture is totally inconsistent with the smooth continuous wave picture of Maxwell's electromagnetic theory of light.

Einstein conjectured that the cavity radiation treated by Planck was like a gas consisting of "particles" called light quanta, each having energy *hν.* (In 1926 the American chemist Gilbert N. Lewis named these particles "photons.") Arguing this way, Einstein obtained Planck's formula without having to make any arbitrary assumption concerning the cavity walls, such as their being modeled by simple harmonic oscillators. Einstein also regarded that this particulate aspect belonged to radiation in general, whether in an enclosure or in free space. That amounted to a revolutionary modification of the existing theory of optics and electromagnetism. Planck and others found Einstein's proposal very difficult to accept. Although it explained phenomena that were otherwise mysterious, it was hard to see how such optical phenomena as refraction or diffraction (the spreading of light around a sharp edge) that since the early nineteenth century had been treated with a wave
theory of light, could be reconciled with almost Newtonian particles of light. For at least two decades, the quantum achievements of Planck and Einstein were regarded with suspicion. The Nobel Prize Committee recognized Planck's great discovery only in 1918; Einstein's in 1921 (but awarded the prize in 1922).

## Additional topics

- Quantum - Neils Bohr And The "old Quantum Theory"
- Quantum - Planck's Paper Of 1900
- Other Free Encyclopedias

Science EncyclopediaScience & Philosophy: *Propagation* to *Quantum electrodynamics (QED)*Quantum - Planck's Paper Of 1900, Einstein's Light Quantum, Neils Bohr And The "old Quantum Theory"