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The Planck constant, or Planck's constant, denoted by , [1] is a fundamental physical constant [1] of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.
In other natural unit systems, the unit of charge is defined as , with the result that =, where α is the fine-structure constant, c is the speed of light, ε 0 is the electric constant, and ħ is the reduced Planck constant.
This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where E is the photon's energy; λ is the photon's wavelength; c is the speed of light in vacuum; h is the Planck constant; The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J, which is equal to 4.135 667 697 × 10 −15 eV.
The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical ...
When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equal to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 revision of the SI, this sets 1 eV equal to the exact value 1.602 176 634 × 10 −19 J. [1]
Planck considered only the units based on the universal constants G, h, c, and k B to arrive at natural units for length, time, mass, and temperature, but no electromagnetic units. [7] The Planck system of units is now understood to use the reduced Planck constant, ħ, in place of the Planck constant, h. [8]
A set of base units in the atomic system as in one proposal are the electron rest mass, the magnitude of the electronic charge, the Planck constant, and the permittivity. [6] [9] In the atomic units system, each of these takes the value 1; the corresponding values in the International System of Units [10]: 132 are given in the table.
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.