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Blackbody Radiation

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A blackbody is an idealisation of a piece of matter that absorbs all incident radiation and is in equilibrium with radiation. Since a piece of matter in equilibrium with radiation emits the same amount of radiation it absorbs, a black body is said to be a "perfect emitter of radiation". The piece of matter is called a black body because a black piece of matter absorbs more radiation than matter of any other colour.

BBR-Cavity-Illust
A black body can be simulated by a cavity with a small hole through radiation can pass. Since radiation incident upon hole bounces around within the cavity until it is absorbed, the hole absorbs all radiation incident upon it and may therefore be used as a model of a black body.

In 1900, Max Planck presented the following empirical formula for the amount of energy per volume in a cavity for the frequency range: f and f+df:

 u( \nu ) d \nu = \frac{8\pi\nu^2}{c^3} \cdot \Bigg( \frac{h \nu }{e^{h \nu / k_{B}T} - 1}  \Bigg)

This formula was found to fit Observations better than we would expect of an empirical formula, and Planck had to find a fundamental justification for his formula. Although Planck considered electrons oscillating in the walls of the cavity, here we shall consider the standing waves within a cavity.

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