| Revision as of 12:16, 4 July 2007 editTaemyr (talk | contribs)Extended confirmed users2,632 edits Getting rid of ambigous reference to energy density by copy-pasting from Planck's law← Previous edit | Revision as of 07:42, 5 July 2007 edit undoEep² (talk | contribs)7,014 editsm link fixNext edit → | ||
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| where ''T'' is the ] in ]s, and ''k'' is ]. | where ''T'' is the ] in ]s, and ''k'' is ]. | ||
| The law is derived from classical physics arguments. ] 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 ] in 1905. It agrees with experimental measurements for long wavelengths. However it predicts an energy output that diverges towards ] as wavelengths grow smaller. |
The law is derived from classical physics arguments. ] 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 ] in 1905. It agrees with experimental measurements for long wavelengths. However it predicts an energy output that diverges towards ] as wavelengths grow smaller. This was not supported by experiments and the failure has become known as the ]. | ||
| In 1900 ] had obtained a different law: | In 1900 ] had obtained a different law: | ||
Revision as of 07:42, 5 July 2007
In physics, the Rayleigh-Jeans Law, first proposed in the early 20th century, attempts to describe the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature. For wavelength λ, it is;
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 predicts an energy output that diverges towards infinity as wavelengths grow smaller. This was not supported by experiments and the failure has become known as the ultraviolet catastrophe.
In 1900 Max Planck had obtained a different law:
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.