Planck Constant

The Planck constant, or Planck’s constant, is the quantum of electromagnetic action that relates a photon’s energy to its frequency. The Planck constant multiplied by a photon’s frequency is equal to a photon’s energy. The Planck constant is a fundamental physical constant denoted as  , and of fundamental importance in quantum mechanics.

The Planck constant is related to the quantization of light and matter. It can be seen as a subatomic-scale constant. In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency. Atomic unit systems are based (in part) on the Planck constant. The physical meaning of the Planck constant could suggest some basic features of our physical world. 

The Planck constant is one of the smallest constants used in physics. This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant (the quantum of action) is very small. One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.

The Planck constant is defined to have the exact value  = 6.62607015×10−34 J⋅s in SI units.

At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but predictions of the frequency distribution of the radiation by then-existing theories diverged significantly at higher frequencies. In 1900, Max Planck empirically derived a formula for the observed spectrum.

He assumed a hypothetical electrically charged oscillator in a cavity that contained black-body radiation could only change its energy in a minimal increment,   that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, , from the experimental measurements, and that constant is named in his honor.

The black-body problem was revisited in 1905, when Rayleigh and Jeans (on the one hand) and Einstein (on the other hand) independently proved that classical electromagnetism could never account for the observed spectrum. These proofs are commonly known as the “ultraviolet catastrophe”.

They contributed greatly (along with Einstein’s work on the photoelectric effect) in convincing physicists that Planck’s postulate of quantized energy levels was more than a mere mathematical formalism. The first Solvay Conference in 1911 was devoted to “the theory of radiation and quanta”.

Einstein’s explanation for observations of photoelectric effect was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small “packets” or quanta. The size of these “packets” of energy, which would later be named photons, was to be the same as Planck’s “energy element”, giving the modern version of the Planck–Einstein relation:

The Planck constant also occurs in statements of Werner Heisenberg’s uncertainty principle. Given numerous particles prepared in the same state, the uncertainty in their position,  and the uncertainty in their momentum , obey

where the uncertainty is given as the standard deviation of the measured value from its expected value.

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