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Later, in 1924, Satyendra Nath Bose developed the theory of the statistical mechanics of photons, which allowed a theoretical derivation of Planck's law. [155] The actual word 'photon' was invented still later, by G.N. Lewis in 1926, [156] who mistakenly believed that photons were conserved, contrary to Bose–Einstein statistics; nevertheless ...
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.
Conversely, an electron that absorbs a photon gains energy, hence it jumps to an orbit that is farther from the nucleus. Each photon from glowing atomic hydrogen is due to an electron moving from a higher orbit, with radius r n, to a lower orbit, r m. The energy E γ of this photon is the difference in the energies E n and E m of the electron:
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 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 ...
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.
The Planck postulate (or Planck's postulate), one of the fundamental principles of quantum mechanics, is the postulate that the energy of oscillators in a black body is quantized, and is given by E = n h ν , {\displaystyle E=nh\nu \,,}