The average or bulk properties of electromagnetic radiation interacting with matter are systematized in a simple set of rules called radiation laws. These laws apply when the radiating body is what physicists call a blackbody radiator. Generally, blackbody conditions apply when the radiator has very weak interaction with the surrounding environment and can be considered to be in a state of equilibrium. Although stars do not satisfy perfectly the conditions to be blackbody radiators, they do to a sufficiently good approximation that it is useful to view stars as approximate blackbody radiators.

Planck Radiation Law

The primary law governing blackbody radiation is the Planck Radiation Law, which governs the intensity of radiation emitted by unit surface area into a fixed direction (solid angle) from the blackbody as a function of wavelength for a fixed temperature. The Planck Law can be expressed through the following equation.

The behavior is illustrated in the figure shown above. The Planck Law gives a distribution that peaks at a certain wavelength, the peak shifts to shorter wavelengths for higher temperatures, and the area under the curve grows rapidly with increasing temperature.

The Wien and Stefan-Boltzmann Laws

The behavior of blackbody radiation is described by the Planck Law, but we can derive from the Planck Law two other radiation laws that are very useful. The Wien Displacement Law, and the Stefan-Boltzmann Law are illustrated in the following equations.

The Wien Law gives the wavelength of the peak of the radiation distribution, while the Stefan-Boltzmann Law gives the total energy being emitted at all wavelengths by the blackbody (which is the area under the Planck Law curve). Thus, the Wien Law explains the shift of the peak to shorter wavelengths as the temperature increases, while the Stefan-Boltzmann Law explains the growth in the height of the curve as the temperature increases. Notice that this growth is very abrupt, since it varies as the fourth power of the temperature.

The following figure illustrates the Wien law in action for three different stars of quite different surface temperature. The strong shift of the spectrum to shorter wavelengths with increasing temperatures is apparent in this illustration.

For convenience in plotting these distributions have been normalized to unity at the respective peaks; by the Stefan-Boltzmann Law, the area under the peak for the hot star Spica is in reality 2094 times the area under the peak for the cool star Antares.

Temperatures and Characteristic Wavelengths

By the Planck Law, all heated objects emit a characteristic spectrum of electromagnetic radiation, and this spectrum is concentrated in higher wavelengths for cooler bodies. The following table summarizes the blackbody temperatures necessary to give a peak for emitted radiation in various regions of the spectrum.

Some Blackbody Temperatures
Region Wavelength
Blackbody Temperature
Radio > 10 < 10-5 < 0.03
Microwave 10 - 0.01 10-5 - 0.01 0.03 - 30
Infrared 0.01 - 7 x 10-5 0.01 - 2 30 - 4100
Visible 7 x 10-5 - 4 x 10-5 2 - 3 4100 - 7300
Ultraviolet 4 x 10-5 - 10-7 3 - 103 7300 - 3 x 106
X-Rays 10-7 - 10-9 103 - 105 3 x 106 - 3 x 108
Gamma Rays < 10-9 > 105 > 3 x 108

Blackbody radiation corresponds to radiation from bodies in thermal equilibrium. We will consider later the emission of non-thermal radiation, which doesn't follow a blackbody law. Such radiation is often produced by violent collisions rather than equilibrium heating. For example, in astrophysical environments radiation at the long and short wavelength ends of the above table is more likely to be produced by non-thermal processes.

Java Virtual Experiments: Blackbody Radiation

Here are three Java applets illustrating some important properties of blackbody radiation.

You may use these virtual experiments to gain some experience with how Planck distributions evolve with temperature.

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