The curve of black-body radiation for highest (blue), intermediate, and less-high temperatures (red)

Black-body radiation is radiation produced by heated objects, particularly from a kind of special object that is made so it will absorb all radiation (visible light, infrared light, ultraviolet light, etc.) that falls on it, and which means that it will also radiate at all frequencies that heat energy produces in it.

This part of the story of radiation was first explained by James Clerk Maxwell via wave theory but the predicted and actual intensity vs. frequency curves did not go together right. At higher frequencies classical physics predicted that more and more energy would be radiated from the body until the energy became infinite. This broke the first law of thermodynamics which is a fundamental part of all physics. This was called the ultraviolet catastrophe.

When it was realised that classical physics did not work for black-body radiation, the German physicist Max Planck explained their relationship by saying that there are individual things (he did not try to guess what kind of things) that vibrate, each at its own frequency. Each wave of each frequency has its own special energy level. A single x-ray is very high energy and can go right through the human body. A single wave of infrared light is very low energy, cannot go through the human body, and can only warm it. Planck's good thinking was to realize that in order to get a single wave at the x-ray frequency, it was necessary to have a big enough package of energy (or "quantum") to make such a strong wave. So if a black-body took in a single wave at the x-ray frequency, then it could give off an x-ray at some later time. But if the black-body only took in infra-red light it would not matter how much of it was absorbed. It could only give off infra-red light and could not give off even ordinary red light, much less any higher energy light such as ultraviolet light or x-ray radiation. Planck said that the total energy given off by a black-body at any particular frequency is equal to the number of the "vibrating things" (see above), n, that were vibrating at a given frequency, f times a special constant, h, that turns frequency units into energy units. The equation is:

E = n h f

The constant he made, h, is called the Planck constant.

The idea that a unit of light at a given frequency always has the same energy, the idea that there is a quantum of energy for each unit of light at a given frequency, became the doorway into quantum mechanics, so the idea of a black-body is something that is basic to modern physics. It shows up in discussions of a wide variety of physics topics having to do with energies and frequencies.