Rayleigh Jeans result

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. 

Laws of classical physics can be used to derive an equation which describes the intensity of blackbody radiation as a function of frequency for a flxed temperature -the result is known as the Rayleigh-Jeans law. Although the Rayleigh-Jeans law agrees with experimental data for low frequencies (long wavelengths), it diverges... 

Combining the two expressions of the number of mode of vibration with the average energy of vibration and reported to the volume of the enclosure of blackbody, results the expression of the density of spectral energy, as Rayleigh-Jeans formula (RJ)... 

By about 1968 the microwave region of the background spectrum had been fairly well covered by ground-based measurements. The results were consistent with the Rayleigh-Jeans tail of a blackbody spectrum with a temperature of roughly 2.7 . There was even some evidence that the spectrum was beginning to show the proper... 

This Rayleigh-Jeans law matches the experimental results fairly well at low frequencies (in the infrared region) but is in strong disagreement with experiment at higher frequencies (in the ultraviolet region). 

We see from equation (1.1) and Fig. 1.1 that the intensity predicted by the Rayleigh-Jeans law increases indefinitely at higher frequencies, the well-known ultraviolet catastrophe, in complete contradiction with the experimental results. 

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... 

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