Planck's law of black body radiation

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In physics, the intensity spectrum of electromagnetic radiation from a black body at temperature T is given by the Planck's law of black body radiation:

<math>I(\nu) =\frac{2h\nu^{3}}{c^2}\frac{1}{\exp\left(\frac{h\nu}{kT}\right)-1}<math>

where:

I(ν) is the amount of energy per unit time per unit surface area per unit solid angle per unit frequency. Units are e.g. [W m^-2 Hz^-1 sr^-1];

ν is the frequency

T is the temperature of the black body

h is Planck's constant,:

c is the speed of light

k is Boltzmann's constant.

Max Planck originally produced this law in 1900 (published in 1901) in an attempt to interpolate between the Rayleigh-Jeans law (which worked at long wavelengths) and Wien's law (which worked at short wavelengths). He found that the above function fit the data for all wavelengths remarkably well.

The Rayleigh-Jeans law was particularly significant, since it was built on a strong theoretical framework, but suffered a serious flaw known as the ultraviolet catastrophe. This suggested that the theoretical framework of thermodynamics was faulty. Planck now attempted to produce a better fundamental theory which would supplement thermodynamics. He calculated that if the sum of different modes of charged oscillators in matter could only be counted where these oscillators have energy proportional to frequency, the new radiation law would fit all spectroscopic measurements.

Contrary to popular opinion Planck did not quantize light. It is plain in his writing in his original 1901 paper and in the references in this paper to his earlier work. It is also plainly explained in his book "Theory of Heat Radiation" where he explains that his constant refers to Hertzian oscillators. The idea of quantisation was developed by others into what we now know as quantum mechanics. The next step along this road was made by Albert Einstein, who, by studying the photoelectric effect proposed a model and equation whereby light was not only emitted but also absorbed in packets or photons.

From the Planck's law of black body radiation we derive today the Stefan-Boltzmann law.

External link and references

Planck, Max, "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff (1901).
Radiation of a Blackbody - interactive simulation to play with Planck's law
Scienceworld entry on the Planck Law

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