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In 1905, "Einstein believed that Planck's theory could not be made to agree with the idea of light quanta, a mistake he corrected in 1906." [133] Contrary to Planck's beliefs of the time, Einstein proposed a model and formula whereby light was emitted, absorbed, and propagated in free space in energy quanta localized in points of space. [132]
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: =.
At the same time, investigations of black-body radiation carried out over four decades (1860–1900) by various researchers [50] culminated in Max Planck's hypothesis [51] [52] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = hν.
The photon having non-zero linear momentum, one could imagine that it has a non-vanishing rest mass m 0, which is its mass at zero speed. However, we will now show that this is not the case: m 0 = 0. Since the photon propagates with the speed of light, special relativity is called for. The relativistic expressions for energy and momentum ...
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.
Black-body radiation has a characteristic, continuous frequency spectrum that depends only on the body's temperature, [8] called the Planck spectrum or Planck's law. The spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, and at room temperature most of the emission is in the infrared ...
In particular, Planck assumed that electromagnetic radiation can be emitted or absorbed only in discrete packets, called quanta, of energy: = =, where: h is the Planck constant, ν is the frequency of light, c is the speed of light, λ is the wavelength of light.
Since emission can occur in all directions, atmospheric radiative transfer (like Planck's Law) requires units involving a solid angle, such as W/sr/m 2. At the most fundamental level, the absorption and emission of radiation are controlled by the Einstein coefficients for absorption, emission and stimulated emission of a photon ( B 12 , A 21 ...