Rayleigh Jeans law

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... 

However, in a classical theory, at low enough frequencies, one might be able to use the Rayleigh-Jeans law,... 

Equation 5.9 is called the Rayleigh-Jeans law, and can also be derived by taking the limit of Equation 5.7 as h approaches zero (Problem 5-2). 

Show that Equation 5.9, the Rayleigh-Jeans law, is identical to the Planck black-body distribution in the limit as h —> 0. 

Q.7.4 Show that (a) the Rayleigh-Jeans law is a special case of Planck distribution law for the blackbody spectrum. Show also that (b) the Wein displacement law can be derived from Planck s distribution law. 

Many physicists of the late nineteenth century tried to derive expressions consistent with the experimental intensity-versus-frequency curves for several temperatures, as shown in Fig. 3.19, but without success. In fact, the Rayleigh-Jeans law gives the expression that is derived according to the laws of nineteenth century physics as ... 

It can be seen that the Rayleigh-Jeans law reproduces the experimental data at low frequencies fairly well. However, at high frequencies, the Rayleigh-Jeans law diverges as v. Since the frequency increases in the ultraviolet region of the spectrum, this divergence was called the ultraviolet catastrophe, a phenomenon that classical physics was unable to explain theoretically. This was the first such phenomenon to be observed in physics and did in fact mark a major milestone in the annals of physics. 

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... 

In this expression, k is Boltzmann s constant, A is the wavelength, and T is the absolute temperature. The total energy per unit volume at a particular temperature is given by the integral of the above expression. Equation 9.20 is known as the Rayleigh-Jeans law. 

Other attempts were made to explain the nature of light in terms of blackbody radiation, but none were any more successful than the Rayleigh-Jeans law. The matter remained unsolved until 1900. All of the above unexplained phenomena... 

FIGURE 9.13 Early attempts at modeling the behavior of a blackbody included the Rayleigh-Jeans law. But as this plot illustrates, at one end of the spectrum the calculated intensity grows upward to infinity, the so-called ultraviolet catastrophe. 

The slope of the plot of energy versus wavelength for the Rayleigh-Jeans law is given by a rearrangement of equation 9.20 ... 

Determine under what conditions of temperature and wavelength the Rayleigh-Jeans law approximates Planck s law. 

According to the Rayleigh-Jeans law, at microwave frequencies the thermal radiation intensity is proportional to the absolute temperature and so... 

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). 

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. 

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