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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.
The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck constant. Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of ...
Planck in 1918, the year he received the Nobel Prize in Physics for his work on quantum theory. In 1900, Max Planck derived the average energy ε of a single energy radiator, e.g., a vibrating atomic unit, as a function of absolute temperature: [24] = / (), where h is the Planck constant, ν is the frequency, k is the Boltzmann constant, and T ...
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: =.
Lambda (Λ), commonly known as the cosmological constant, describes the ratio of the density of dark energy to the critical energy density of the universe, given certain reasonable assumptions such as that dark energy density is a constant. In terms of Planck units, and as a natural dimensionless value, Λ is on the order of 10 −122. [21]
The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =. Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 and for other elementary particles , neutral atoms and molecules in the years since.
The oscillation frequency of the standing wave, multiplied by the Planck constant, is the energy of the state according to the Planck–Einstein relation. Stationary states are quantum states that are solutions to the time-independent Schrödinger equation : H ^ | Ψ = E Ψ | Ψ , {\displaystyle {\hat {H}}|\Psi \rangle =E_{\Psi }|\Psi \rangle ...
where m e is the mass of the electron, k B is the Boltzmann constant, T is the temperature, ħ is the reduced Planck constant, and E I = 13.6 eV is the ionization energy of hydrogen. [5] Charge neutrality requires n e = n p, and the Saha equation can be rewritten in terms of the free electron fraction x e: