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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: =.
Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.
In addition, the law may be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. In the limit of low frequencies (i.e. long wavelengths), Planck's law tends to the Rayleigh–Jeans law , while in the limit of high frequencies (i.e. small wavelengths) it tends to ...
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.
Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. [3] [4] The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). For a modulated wave, wavelength may refer to the carrier wavelength of the signal.
By applying the differentials to the energy equation and identifying the relativistic momentum: = then integrating, de Broglie arrived at his formula for the relationship between the wavelength , λ , associated with an electron and the modulus of its momentum , p , through the Planck constant , h : [ 14 ] λ = h p . {\displaystyle \lambda ...
In frequency (and thus energy), UV rays sit between the violet end of the visible spectrum and the X-ray range. The UV wavelength spectrum ranges from 399 nm to 10 nm and is divided into 3 sections: UVA, UVB, and UVC. UV is the lowest energy range energetic enough to ionize atoms, separating electrons from them, and thus causing chemical reactions.
In 1900 Max Planck empirically obtained an expression for black-body radiation expressed in terms of wavelength λ = c/ν (Planck's law): =, where h is the Planck constant, and k B is the Boltzmann constant. Planck's law does not suffer from an ultraviolet catastrophe and agrees well with the experimental data, but its full significance (which ...