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.