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:

ν is the frequency

I(ν)δν is the amount of energy per unit surface per unit time per unit solid angle emitted in the frequency range between ν and ν+δν;

h is Planck's constant,:

c is the speed of light and

k is Boltzmann's constant.

Max Planck originally produced this law in 1900 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 noted that if light could only be emitted in discrete packets with energy proportional to frequency, the new law would make perfect sense.

E = h ν

However, Planck avoided drawing further conclusions about the nature of light from this. This 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 showed that 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.