How Planck explained black body radiation

[cnidocyte]

If I'm not mistaken he explained it with the theory that light energy can be released only in integer multiples of a constant times the frequency of the light. How did he come to this conclusion? Was it to do with the fact that the higher the temperature, the higher the frequencies of the light emitted?

 

[mathman]

Planck's idea was to get around what was called the ultraviolet catastrophe. The point was that without quantization, the blackbody spectrum would become infinite as wavelength -> 0.

 

[Sybren]

If I'm not mistaken he explained it with the theory that light energy can be released only in integer multiples of a constant times the frequency of the light. How did he come to this conclusion? Was it to do with the fact that the higher the temperature, the higher the frequencies of the light emitted?

the assumption of quantized amounts of photon energy is used to produce the black-body radiation spectrum. This result is the justification of that assumption.

 

[Born2bwire]

At the time, the limiting cases of the power spectrum were known via both experiment and theory. The Rayleigh-Jeans fit lower frequency radiance while the Wien fit the higher frequency (though Wien seemed to derive his equations more from empirical fitting than strong theoretical footing). The Rayleigh-Jeans distribution can be found using classical electrodynamics and classical statistical mechanics. However, as mathman stated, you end up with the ultraviolet catastrophe where the energy density suffers from an ultraviolet divergence. It was theorized at the time, by Rayleigh and others, that the fault laid in the classical equipartition theory.

Planck looked at the Wien and Rayleigh-Jeans results and proposed an interpolation between the two results. This was the same as the resulting Placnk distribution. It then took him several weeks to find a physical and theoretical reasoning behind this and this was done by throwing out the classical equipartition theory and devising a new one that required the energy to be quantized. Actually, quantization of energy was done by Boltzmann as a tool for derivations but with Boltzmann the quantization did not affect the final results. However, removing the quantization in Planck's derivation simply results in the Rayleigh-Jeans distribution again. Thus, Planck's use of quantization was essential. In addition to the quantization, Planck used a different method for counting the elements which is consistent with what is now called Bose-Einstein statistics (as opposed to the Maxwell-Boltzmann statistics that gave rise to the Rayleigh-Jeans).

So basically Planck found a way to fit an equation that matched the Wien and Rayleigh-Jeans distributions and was able to a posteriori derive this distribution by using a new equipartition theorem. This matched the suspicions of other physicists at the time that the classical statistical equipartition theory may be the problem.

Milonni has a few sections in his Quantum Vacuum book that discusses this in detail.

 

[sardar]

Max Planck's explanation of black body radiation was a groundbreaking contribution to the field of quantum mechanics. He proposed that the energy emitted by a black body, a theoretical object that absorbs all incoming radiation, is not continuous but rather comes in discrete packets, or quanta. This was a radical departure from the prevailing theory at the time, which stated that energy could be emitted and absorbed continuously.

Planck's insight was that the energy of a black body is related to the frequency of the light emitted. He theorized that the energy of each quantum of light, or photon, is proportional to the frequency of the light, with the proportionality constant being known as Planck's constant. This means that the higher the frequency of the light, the higher the energy of each photon.

But how did Planck come to this conclusion? It was actually a result of his attempts to explain a phenomenon known as the ultraviolet catastrophe. According to classical physics, as the temperature of a black body increases, the intensity of the emitted radiation should also increase exponentially at higher frequencies. However, experiments at the time showed that this was not the case, and the intensity actually decreased at higher frequencies.

Planck realized that in order to reconcile this discrepancy, he needed to assume that the energy of the emitted radiation was not continuous, but rather came in discrete packets. He then used mathematical equations to determine the relationship between the energy and frequency of these packets, which led to his famous equation E=hf.

In summary, Planck's explanation of black body radiation was based on the idea that energy is quantized, or comes in discrete packets, and that the energy of each packet is related to the frequency of the light emitted. This theory not only solved the ultraviolet catastrophe, but also laid the foundation for the development of quantum mechanics and our understanding of the behavior of matter and energy at the atomic level.