The relationship between the wavelength and frequency of electromagnetic waves is

Correlation formula:

1, Planck's law is sometimes written in the form of energy density spectrum:

Mi Fang Hertz). By integrating the whole frequency domain, the frequency-independent energy density can be obtained. The radiation field of blackbody can be regarded as photon gas, and the energy density at this time can be determined by the thermodynamic parameters of gas.

2. The energy density spectrum can also be written as a function of wavelength.

Many popular science books about quantum theory, even some physics textbooks, have made serious mistakes when discussing the history of Planck's blackbody radiation law. Although these misconceptions were pointed out by researchers in the history of physics more than forty years ago, it turns out that they are still difficult to eliminate.

Part of the reason may be that Planck's original motivation for quantizing energy cannot be explained clearly in a few words. The reason is quite complicated for modern people, and it is not easy for outsiders to understand. Danish physicist Helge Kla once published an article, which clearly explained how this error happened.

"Ultraviolet Catastrophe": In the classical statistical theory, the energy equipartition theorem predicts that the intensity of blackbody radiation will diverge to infinity in the ultraviolet region, which is seriously contrary to the facts.

First of all, although Planck gave the quantization expression of electromagnetic wave energy, Planck did not quantize electromagnetic waves, which can be seen from his 190 1 paper and the citation of his early literature in this paper.

He also explained in the book "Thermal Radiation Theory" that the Planck constant in the quantization formula (the basic constant in modern quantum mechanics) is just an ordinary constant suitable for Hertz oscillator.

The first person who really put forward light quantum in theory was Einstein who successfully explained photoelectric effect in 1905. He assumed that the electromagnetic wave itself has quantized energy, and the smallest unit that carries these quantized energy is called optical quantum. 1924, satyendra nath bose developed the statistical mechanics of photons, thus theoretically deducing the expression of Planck's law.

Another misunderstanding is that Planck's motivation for developing this law is not to try to solve the "ultraviolet disaster." The name "ultraviolet catastrophe" was put forward by paul ehrenfest in 19 1 1, which was ten years later than Planck's law.

Ultraviolet catastrophe means that when the energy equipartition theorem of classical statistical mechanics is applied to the cavity blackbody radiation (also known as cavity radiation or cavity radiation), the total energy of the system will become divergent and tend to infinity in the ultraviolet region, which is obviously inconsistent with the reality.

Planck himself never thought that the equipartition theorem of energy would hold forever, so he didn't notice the "catastrophe" of blackbody radiation at all-but only five years later, with the discovery of Einstein, Lord Rayleigh and Sir Jenkins, the problem became acute.