The Planck relation [1] [2] [3] (referred to as Planck's energyâfrequency relation, [4] the PlanckâEinstein 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: The constant of proportionality, h, is known as the Planck constant. Several equivalent forms of the relation exist, including in terms of angular frequency Ď: where . Written using the symbol f for frequency, the relation is
The relation accounts for the quantized nature of light and plays a key role in understanding phenomena such as the photoelectric effect and black-body radiation (where the related Planck postulate can be used to derive Planck's law).
Light can be characterized using several spectral quantities, such as frequency ν, wavelength Îť, wavenumber , and their angular equivalents ( angular frequency Ď, angular wavelength y, and angular wavenumber k). These quantities are related through so the Planck relation can take the following "standard" forms: as well as the following "angular" forms:
The standard forms make use of the Planck constant h. The angular forms make use of the reduced Planck constant ħ = h/2Ď. Here c is the speed of light.
The de Broglie relation, [10] [11] [12] also known as de Broglie's momentumâwavelength relation, [4] generalizes the Planck relation to matter waves. Louis de Broglie argued that if particles had a wave nature, the relation E = hν would also apply to them, and postulated that particles would have a wavelength equal to Îť = h/p. Combining de Broglie's postulate with the PlanckâEinstein relation leads to or
The de Broglie relation is also often encountered in vector form where p is the momentum vector, and k is the angular wave vector.
Bohr's frequency condition [13] states that the frequency of a photon absorbed or emitted during an electronic transition is related to the energy difference (ÎE) between the two energy levels involved in the transition: [14]
This is a direct consequence of the PlanckâEinstein relation.
The Planck relation [1] [2] [3] (referred to as Planck's energyâfrequency relation, [4] the PlanckâEinstein 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: The constant of proportionality, h, is known as the Planck constant. Several equivalent forms of the relation exist, including in terms of angular frequency Ď: where . Written using the symbol f for frequency, the relation is
The relation accounts for the quantized nature of light and plays a key role in understanding phenomena such as the photoelectric effect and black-body radiation (where the related Planck postulate can be used to derive Planck's law).
Light can be characterized using several spectral quantities, such as frequency ν, wavelength Îť, wavenumber , and their angular equivalents ( angular frequency Ď, angular wavelength y, and angular wavenumber k). These quantities are related through so the Planck relation can take the following "standard" forms: as well as the following "angular" forms:
The standard forms make use of the Planck constant h. The angular forms make use of the reduced Planck constant ħ = h/2Ď. Here c is the speed of light.
The de Broglie relation, [10] [11] [12] also known as de Broglie's momentumâwavelength relation, [4] generalizes the Planck relation to matter waves. Louis de Broglie argued that if particles had a wave nature, the relation E = hν would also apply to them, and postulated that particles would have a wavelength equal to Îť = h/p. Combining de Broglie's postulate with the PlanckâEinstein relation leads to or
The de Broglie relation is also often encountered in vector form where p is the momentum vector, and k is the angular wave vector.
Bohr's frequency condition [13] states that the frequency of a photon absorbed or emitted during an electronic transition is related to the energy difference (ÎE) between the two energy levels involved in the transition: [14]
This is a direct consequence of the PlanckâEinstein relation.