Quantum physics-rayleigh jeans/wien's law

[dado1307]

Show that the Rayleigh-Jeans radiation law is not consistent with Wien displacement law,
λmax T=constant, or vmax is proportional to T.

 

[Gordianus]

The displacement law states that at any temperature T the black body spectrum reaches its peak at a wavelength given by the displacement law.
If you happen to plot the Rayleigh-Jeans formula, you'll find there is no maximum. The shorter the wavelength, the higher the spectral power. This is known as the "ultra-violet catastrophe" and, in the search of a "cure", Planck came up with his famous proposal.

 

[dado1307]

Thank you very much...))
That makes perfect sense...

 

[hankaaron]

The displacement law states that at any temperature T the black body spectrum reaches its peak at a wavelength given by the displacement law.
If you happen to plot the Rayleigh-Jeans formula, you'll find there is no maximum. The shorter the wavelength, the higher the spectral power. This is known as the "ultra-violet catastrophe" and, in the search of a "cure", Planck came up with his famous proposal.

Actually, Planck developed his work as a refinement of Wien's law and was not attempting to solve the Ultra-violet catastrophe problem. In fact I believe his work (which included what is now know as Planck's constant) before or right around the same time as Rayleight-Jeans proposal.

 

[paranormal]

I can confidently say that the Rayleigh-Jeans radiation law and Wien displacement law are two different approaches to understanding the relationship between temperature and the wavelength or frequency of a blackbody radiation.

The Rayleigh-Jeans law, developed by Lord Rayleigh and Sir James Jeans, predicts that the energy emitted by a blackbody radiation is directly proportional to the temperature and the frequency of the radiation. This means that as the temperature increases, the intensity of the radiation also increases, and as the frequency increases, the intensity also increases.

On the other hand, the Wien displacement law, developed by Wilhelm Wien, states that the wavelength of maximum intensity (λmax) of a blackbody radiation is inversely proportional to the temperature. This means that as the temperature increases, the wavelength of maximum intensity decreases.

It is clear that these two laws are not consistent with each other. In fact, the Rayleigh-Jeans law predicts that the intensity of the radiation increases infinitely as the frequency increases, which is not observed in reality. This is known as the "ultraviolet catastrophe."

In contrast, the Wien displacement law accurately describes the behavior of blackbody radiation at high frequencies and temperatures, and it is consistent with experimental observations.

Therefore, it can be concluded that the Rayleigh-Jeans radiation law is not consistent with the Wien displacement law, and the latter is a more accurate and reliable approach in describing the relationship between temperature and the wavelength or frequency of blackbody radiation.