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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.
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h /2 π , also known as the reduced Planck constant or Dirac constant . Quantity (common name/s)
1.438 776 877... × 10 −2 m⋅K: 0 [12] [e] Wien wavelength displacement law constant: 2.897 771 955... × 10 −3 m⋅K: 0 [13] ′ [f] Wien frequency displacement law constant: 5.878 925 757... × 10 10 Hz⋅K −1: 0 [14] Wien entropy displacement law constant 3.002 916 077... × 10 −3 m⋅K: 0
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 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: =.
In SI units, the values of c, h, e and k B are exact and the values of ε 0 and G in SI units respectively have relative uncertainties of 1.6 × 10 −10 [16] and 2.2 × 10 −5. [17] Hence, the uncertainties in the SI values of the Planck units derive almost entirely from uncertainty in the SI value of G.
Three years later, Bohr would use similar equations with different interpretation. Bohr took the Planck constant as given value and used the equations to predict, a, the radius of the electron orbiting in the ground state of the hydrogen atom. This value is now called the Bohr radius. [14]: 197
The proportionality constant has become known as the Planck constant. In the range of kinetic energies of the electrons that are removed from their varying atomic bindings by the absorption of a photon of energy h ν {\displaystyle h\nu } , the highest kinetic energy K max {\displaystyle K_{\max }} is K max = h ν − W . {\displaystyle K_{\max ...