Ultraviolet catastrophe In physics, the ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, is the classical prediction, first made in the late 19th century, that an ideal black body at thermal equilibrium will emit radiation with infinite power. As this is clearly shown by observation to be false, it was one of the first clear indications of problems with classical physics. In 1900, Max Planck's solution of this problem led to one of the early portions of quantum mechanics. It was called the "ultraviolet" catastrophe because ultraviolet radiation had the highest frequencies of any radiation known at the time (X-rays and gamma rays had not been discovered yet). It was also sometimes called the "violet catastrophe" for short. Since the first appearance of the term, it has also been used for other predictions of a similar nature, e.g. in quantum electrodynamics (also used in those cases: ultraviolet divergence). The ultraviolet catastrophe results from the equipartition theorem of classical statistical mechanics which states that all modes (degrees of freedom) of a system at equilibrium have an average energy of $kT/2$. According to classical electromagnetism, the number of electromagnetic modes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the Rayleigh-Jeans law, and be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power go to infinity as higher and higher frequencies are considered: this is clearly an impossibility. Max Planck resolved this issue by postulating that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to the frequency (as given by Planck's law). This has the effect of reducing the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy at those frequencies by application of the equipartition theorem. The radiated power eventually goes to zero at infinite frequencies, and the total predicted power is finite. The formula for the radiated power for the idealized system (black body) was in line with known experiments, and came to be called Planck's law of black body radiation. Based on past experiments, Planck was also able to determine the value of its parameter, now called Planck's constant. The packets of energy later came to be called photons, and played a key role in the quantum description of electromagnetism. References Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. (W. H. Freeman and Company: New York, 1980). See chapter 4. Claude Cohen-Tannoudji, Bernard Diu, and Franck Laloë, Quantum Mechanics: Volume One (Hermann: Paris, 1977), pp. 624 —626. FAVORITE ARTICLES: History of the World    History of the United States    History of Europe    Ancient History    History    Military History    World War I    Bombing of Dresden    California    US Constitution    Frank Sinatra    Boston    Marbury v. Madison This article is licensed under the GNU Free Documentation License at http://www.gnu.org/copyleft/fdl.html You may copy and modify it as long as the entire work (including additions) remains under this license. You must provide a link to http://www.gnu.org/copyleft/fdl.html To view or edit this article at Wikipedia go to http://www.wikipedia.org/wiki/Ultraviolet_catastrophe">follow this link. All other content is copyright © 2000-2005 by WorldHistory.com. All rights reserved.

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