Rayleigh black-body radiation

Rayleigh scattering is named after its discoverer, John William Strutt (1842-1919), third Baron Rayleigh, an English physicist. He also did important work on acoustics and black-body radiation... 

Fig. 2.2 The intensity of black-body radiation as a function of angular frequency, to, for two different temperatures, and Tz, where T2> . The dashed curve gives the classical Rayleigh-Jeans law at temperature, T2.

Black-body radiation Figure 22 shows the frequency dependence of the intensity of the radiation that is emitted from a black body at two different temperatures, Tx and T2, where T2 > Tv We see that at high frequencies the emitted intensity, /, is much less than that predicted by the Rayleigh-Jeans law, namely... 

Planck wanted to understand black body radiation. The black body may be modeled by a box, with a small hole (shown in Fig. 1.1). We heat the box up, wait for the system to reach a stationary state (at a fixed temperature), and see what kind of electromagnetic radiation (intensity as a function of frequency) comes out of the hole. In 1900, Rayleigh and Jeans tried to apply classical mechanics to this problem, and they calculated correctly that the black body would emit the electromagnetic radiation with a distribution of frequencies. However,... 

The quantum hypothesis was derived by M.K.E.L. Planck from a discussion on the study of black-body radiation. A black body is a physical body that absorbs all incident electromagnetic radiation and emits the so-called black-body radiation with a spectrum depending only on temperature. For the spectrum of the black-body radiation, Wien (W.C.W.O.F.F. Wien) s Law (1886) and the Rayleigh-Jeans... 

Rayleigh and Jeans constructed a classical theory of black-body radiation. They defined as their system the set of standing electromagnetic waves that could exist inside a box made of electrically conductive material. An electric field cannot penetrate a perfect conductor (one with zero resistance), because a finite electric field would produce an infinite current. Electromagnetic waves must have nodes at perfectly conducting... 

Rayleigh-Jeans law A formula giving the intensity of black-body radiation at long wavelengths for a body at a particular temperature. It is an approximation to Planck s full formula for the black-body intensity based on quantum concepts. 

This is known as the Stefan-Boltzmaim law of radiation. If in this calculation of total energy U one uses the classical equipartition result = k T, one encounters the integral f da 03 which is infinite. This divergence, which is the Rayleigh-Jeans result, was one of the historical results which collectively led to the inevitability of a quantum hypothesis. This divergence is also the cause of the infinite emissivity prediction for a black body according to classical mechanics. 

Following the work of Kirchhoff on the connection between emission and absorption coefficients, it had been proved that the radiation inside a totally enclosed cavity maintained at a uniform temperature was a function of the temperature alone and was identical with the radiation which would be emitted by a perfectly black body at the same temperature. The spectral distribution of the radiation had been investigated experimentally and it was found that the intensity increased slowly with decreasing frequency until it reached a peak, after which it decreased very rapidly (Fig.1.1). However, all attempts to derive an equation giving the intensity as a function of frequency had failed. The most convincing approach made by Rayleigh and Jeans on the basis of classical thermodynamics gave the result... 

Theory of radiation of an ideal black body from the point of view of wave theory Rayleigh-Jeans formula... 

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