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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.
Planck constant in eV/Hz ... atomic unit of electric charge density e/ ... NIST publishes the CODATA value of the elementary charge. [2]
[2] Planck constant: 6.626 070 15 × 10 ... Rydberg unit of energy: 2.179 872 361 ... reflects our lack of knowledge of the corresponding value as expressed in SI ...
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.
since / = 1.239 841 984... × 10 −6 eV⋅m [4] where h is the Planck constant, c is the speed of light, and e is the elementary charge. The photon energy of near infrared radiation at 1 μm wavelength is approximately 1.2398 eV.
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 .
As such, the fine-structure constant is chiefly a quantity determining (or determined by) the elementary charge: e = √ 4πα ≈ 0.302 822 12 in terms of such a natural unit of charge. In the system of atomic units , which sets e = m e = ħ = 4 πε 0 = 1 , the expression for the fine-structure constant becomes α = 1 c . {\displaystyle ...
where c is the speed of light and h is the Planck constant. [5] The relative uncertainty, 5 × 10 −8 in the 2006 CODATA recommended value, [6] is due entirely to the uncertainty in the value of the Planck constant. With the re-definition of kilogram in 2019, there is no uncertainty by definition left in Planck constant anymore.