Rayleigh-Jeans law
|
|
In physics, the Rayleigh-Jeans Law, first proposed in the early 20th century, expresses the energy density of blackbody radiation of wavelength λ as
- <math> f(\lambda) = 8\pi k\frac{T}{\lambda^4}<math>
where T is the temperature in kelvins, and k is Boltzmann's constant.
The law is derived from classical physics arguments. Lord Rayleigh first obtained the fourth-power dependence on wavelength in 1900; a more complete derivation, which included the proportionality constant, was presented by Rayleigh and Sir James Jeans in 1905. It agrees with experimental measurements for long wavelengths. However it disagrees with experiment at short wavelengths, where it diverges and predicts an unphysical infinite energy density. This failure is known as the ultraviolet catastrophe.
In 1900 Max Planck had obtained a different law:
- <math>f(\lambda) = \frac{8\pi hc}{\lambda^5}~\frac{1}{e^\frac{hc}{\lambda kT}-1}<math>
where h is Planck's constant and c is the speed of light. This is Planck's law of black body radiation expressed in terms of wavelength λ = c/ν. The Planck law does not suffer from an ultraviolet catastrophe, and agrees well with the experimental data, but its full significance was only appreciated several years later. In the limit of very high temperatures or long wavelengths, the term in the exponential becomes small, and so the denominator becomes approximately hc/λkT. This gives back the Rayleigh-Jeans Law.