Energy element

In science, an energy element ε is the base energy unit of the total internal energy U of an irradiated, monochromatic, vibrating resonator, i.e. blackbody, defined to be proportional to the frequency ν of the emitted or absorbed radiation: [1]

ε = h ν

where h is Planck’s constant. The energy element postulate was developed, during the years 1889-1901, by German physicist Max Planck.

In 1894, German physicist Max Planck turned his attention to the problem of black-body radiation. He had been commissioned by electric companies to create maximum light from lightbulbs with minimum energy. The problem had been stated by Kirchhoff in 1859: how does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (e.g., the color of the light) and the temperature of the body? The question had been explored experimentally, but no theoretical treatment agreed with experimental values. Wilhelm Wien proposed Wien's law, which correctly predicted the behavior at high frequencies, but failed at low frequencies. The Rayleigh-Jeans law, another approach to the problem, created what was later known as the "ultraviolet catastrophe", but contrary to many textbooks this was not a motivation for Planck.

Planck's first proposed solution to the problem in 1899 followed from what Planck called the "principle of elementary disorder", which allowed him to derive Wien's law from a number of assumptions about the entropy of an ideal oscillator, creating what was referred to as the Wien-Planck law. Soon it was found that experimental evidence did not confirm the new law at all, to Planck's frustration. Planck revised his approach, deriving the first version of the famous Planck black-body radiation law, which described the experimentally observed black-body spectrum well. It was first proposed in a meeting of the German Physical Society (Deutsche Physikalische Gesellschaft, DPG) on 19 October 1900 and published in 1901. This first derivation did not include energy quantization, and did not use statistical mechanics, to which he held an aversion.

In November 1900, Planck revised this first approach, relying on Austrian physicist Ludwig Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law (Boltzmann had been discussing in a theoretical paper in 1877 the possibility that the energy states of a physical system could be discrete). As Planck was deeply suspicious of the philosophical and physical implications of such an interpretation of Boltzmann's approach, his recourse to them was, as he later put it, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics.”

The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition that the electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit ε = hν, where h is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and ν is the frequency of the radiation.

In 1901, in reference to the total internal energy U of a resonating blackbody, Planck stated: [2]

“It is necessary to interpret U not as a continuous, indivisible quantity, but as a discrete quantity composed of an integral number of finite equal parts … let us call each such part the energy element ε.”

Here, Planck was explaining the view that the internal energy U of a black body (resonator) could be divided into a discrete number of “energy elements” ε by the expression:

U = εP

where P is large integer. [1]

Einstein | Quantums
In 1905, German-born American physicist Albert Einstein, influenced by Planck, proposed that light itself was composed of quantums of energy, i.e. light quantums. These light quantums later came to be called “photons”, a term introduced in 1926 by American physical chemist Gilbert Lewis. These beginnings launched the later development of quantum thermodynamics.

1. Kuhn, Thomas S. (1987). Black-body Theory and the Quantum Discontinuity, 1894-12, (section: "Energy elements and energy discontinuity", pgs. 125-30). University of Chicago Press.
2. Planck, Max. (1901). "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff.

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