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Wednesday, January 11, 2012

The Black Body Radiation

This topic maybe tend more to physics than chemistry, but I think we should know this one. Electron has dualism property: As particle or wave. Waves have its energy due to its wavelength. See the picture as follows:

(Source: http://www.antonine-education.co.uk/physics_gcse/Unit_1/Topic_5/em_spectrum.jpg)

Some matter can absorb perfectly the wave that accepted by it. Others not or even absolutely not absorb the wave. Black Body is the matter that can absorb or emit radiation perfectly. As an example: When you shined the light into the hole of a box, you will see that the box still dark. (Sorry I didn't find the picture until now).

There are 3 persons who found the relation between Intensity of wave and its wavelength: Wien, Rayleigh - Jeans, and Max Planck.

Wien's displacement law states that the wavelength distribution of thermal radiation from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced on the graph. Apart from an overall T3 multiplicative factor, the average thermal energy in each mode with frequency ν only depends on the ratio ν / T. Restated in terms of the wavelength λ = c / ν, the distributions at corresponding wavelengths are related, where corresponding wavelengths are at locations proportional to 1 / T. Blackbody radiation approximates to Wien's law at high frequencies.

where λmax is the peak wavelength, T is the absolute temperature of the black body, and b is a constant of proportionality called Wien's displacement constant, equal to 2.8977685(51)×10−3 m·K.

The Rayleigh–Jeans law agrees with experimental results at large wavelengths (or, equivalently, low frequencies) but strongly disagrees at short wavelengths (or high frequencies). This inconsistency between observations and the predictions of classical physics is commonly known as the ultraviolet catastrophe. The ultraviolet catastrophe can be described as these examples: If the Rayleigh-Jeans law is true, we will be dead because of the sun's radiation. We will be dead with just a small bonfire.

where p(v, T) is the energy density related with temperature.

Planck's law describes the amount of energy emitted by a black body in radiation of a certain wavelength (i.e. the spectral radiance of a black body). The law is named after Max Planck, who originally proposed it in 1900. The law was the first to accurately describe black body radiation, and resolved the ultraviolet catastrophe. It is a pioneer result of modern physics and quantum theory.

where B is the spectral radiance, T is the absolute temperature of the black body, kB is the Boltzmann constant, h is the Planck constant, and c is the speed of light. However these are not the only ways to express the law; expressing it in terms of wavenumber rather than frequency or wavelength is also common, as are expression in terms of the number of photons emitted at a certain wavelength, rather than energy emitted. In the limit of low frequencies (i.e. long wavelengths), Planck's law becomes the Rayleigh-Jeans law, while in the limit of high frequencies (i.e. small wavelengths) it tends to the Wien approximation.

The graph below shows the relation between Wavelength, Temperature, and Intensity of a wave:

(Source: http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod/uvcatas.gif)

(Source: http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod/bb7b.gif)

Further Reading . . .

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