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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.
Stoney chose his units so that G, c, and the electron charge e would be numerically equal to 1. [4] In 1899, one year before the advent of quantum theory, Max Planck introduced what became later known as the Planck constant. [5] [6] At the end of the paper, he proposed the base units that were later named in his honor.
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: =.
reduced Planck constant in eV⋅s ħ = 6.582 119 569... × 10 −16 eV⋅s: u r (ħ) = 0 [12] k: Boltzmann constant: k = 1.380 649 × 10 −23 J⋅K −1: u r (k) = 0 [13] KJ: Josephson constant: K J = 483 597.8484... × 10 9 Hz⋅V −1: u r (K J) = 0 [14] NA: Avogadro constant: N A = 6.022 140 76 × 10 23 mol −1: u r (N A) = 0 ...
reduced Planck constant: 1.054 571 817... × 10 −34 J⋅s: 0 [4], Boltzmann constant: 1.380 649 × 10 −23 J⋅K −1: 0 [5] Newtonian constant of gravitation: 6.674 30 (15) × 10 −11 m 3 ⋅kg −1 ⋅s −2: 2.2 × 10 −5 [6] cosmological constant: 1.089(29) × 10 −52 m −2 [c]
For example, in Stoney units, the elementary charge is set to e = 1 while the reduced Planck constant is subject to measurement, ħ ≈ 137.03, and in Planck units, the reduced Planck constant is set to ħ = 1, while the elementary charge is subject to measurement, e ≈ (137.03) 1/2.
This value is then used to calculate a new approximation to A r (e), and the process repeated until the values no longer vary (given the relative uncertainty of the measurement, 2.1 × 10 −9): this happens by the fourth cycle of iterations for these results, giving A r (e) = 5.485 799 111 (12) × 10 −4 for these data.