Ultraviolet catastrophe

The catastrophe ultraviolet , formulated in second half of the 19th century and thus named by the Austrian Physicist Paul Ehrenfest, is a against-factual prediction of the classical theories of physics - electromagnetism and Physique statistics: a black Corps with the thermodynamic balance is supposed to radiate a infinite Flux. More precisely, the energy radiated by band of Wavelength must tend towards the infinite one when the wavelength tends towards zero, “in the Ultraviolet” for the Physicien S of the time, since neither the X-rays nor the Gamma rays were then known.

This anomaly showed the failure of the classical theories of physics in certain fields and constituted one of the motivations for the design of the Quantum physics: in 1900, max Planck threw the premises of them, making it possible to solve the problem of the radiation of the black body with its Loi of Planck.

Traditional resolution of the black body

A black body is modelled by a cavity containing of energy in the form of an electromagnetic field. Because of the boundary conditions, the field takes the form of a standing wave admitting a discrete whole of modes. For example, the horizontal modes of a box can have for Fréquence only

$\backslash ,\; \backslash \; naked\; =\; nc/L$

where L is the length of the box, N a Entier naturalness not no unspecified and C the Speed of light. In electromagnetism, one shows more generally than the number of modes per unit of frequency of the cavity is proportional to the square of the frequency:

$\backslash ,\; \backslash \; frac\; \{\backslash \; mathrm\; \{D\}\; NR\}\; \{\backslash \; mathrm\; \{D\}\; \backslash \; naked\}\; \backslash \; propto\; \backslash \; nu^2$.

By applying the Theorem of equal division of energy, each mode must contain an energy kT /2, where K is the Boltzmann constant and T the Température of the system. It results from it that energy per unit of frequency follows the Loi of Rayleigh-Jean:

$\backslash \; frac\; \{\backslash \; mathrm\; \{D\}\; E\}\; \{\backslash \; mathrm\; \{D\}\; \backslash \; naked\}\; \backslash \; propto\; T\; \backslash \; nu^2$.

Thus energy per unit of frequency tends towards the infinite one when the frequency tends towards the infinite one and total energy is infinite.

Quantum resolution of the black body

TBW .

Related articles

• History of quantum mechanics
• other settings at fault of traditional physics
• photoelectric Effect
• Spectral line
• Duality wave-particle of the light
• fields of the physique concerned
• Thermodynamic electromagnetism
• and Physical statistics
• Quantum physics
• authors
• Paul Ehrenfest
• max Planck

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