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Blackbody Radiation

Everything emits and absorbs electromagnetic radiation: gamma rays, X-rays, ultraviolet, visible light, infrared, microwave and radio waves - in this case known as thermal radiation.

Humans, for example, are largely transparent to X- and Gamma- rays (except bones), but reflect and absorb visible light1, and absorb infrared.

Humans don't emit in the Gamma to UV range. Emitting in that range would be dangerous; we would give each other cancer. We don't emit in the visible range either; if we did we would appear to glow. However we do emit electromagnetic radiation in the infrared range, as heat. This radiation is what is detected by the police when they use infrared cameras to detect the body heat of a criminal in the dark.

An Ideal Emitter/Absorber

Suppose you have a hollow container, with the inside blackened, at the same temperature as its surroundings, which has a pinhole in it. Radiation entering the container and hitting the sides would have a very small probability of being reflected out of the container again, because the hole is so small in comparison to the size of the container. Eventually, all the radiation which goes in through the hole, is absorbed. Because the container is in thermal equilibrium (at the same temperature) with its surroundings, the radiation has to be re-emitted by the inside surface of the container. If it didn't do this, it would get hotter, and would stop being in thermal equilibrium. The only way that radiation can get out of the container is through the hole. When radiation comes out of the hole, it is radiation which has been emitted by the inside of the sphere. The container is not transparent to any frequency, and doesn't reflect, so it is black. This is a theoretical construct called black body. Black velvet is quite close to being a black body in real life.

If you were to measure the energy given out at each different wavelength and plot it as a graph, this would give you a black body radiation curve.

The hotter an object is, the higher the frequency at which the most energy is radiated. At about 600°C, the black body would glow reddish. As you increase the temperature, the colour changes from dull red to brighter red, getting up to 'white hot', and for very hot objects, such as the hottest stars, blue.

What Makes them Important?

Classical thermodynamics assumed that a black body would be equally likely to emit radiation at all frequencies. However, Gustav Kirchhoff (and independently Balfour Stewart) pointed out that that would mean that black bodies would emit more radiation in higher frequencies than lower frequencies. It's like if you had to pick any number at random, between zero and infinity. You would be more likely to choose a number greater than 1 million, because there are more numbers greater than 1 million. Kirchhoff suggested the picture of a closed container used above. Creating such a container was an experiment that one could perform, to get a very close approximation of the black body radiation curve. The curve did not, however, go to infinity at ultraviolet wavelengths, as classical theory suggested, hence this was called the Ultraviolet Catastrophe.

Both Lord Rayleigh and Wilhelm Wein both tried to come up with theoretical models to fit the experimental data. However Rayleigh's only fit the data at high frequencies, and Wein's only fit it at low frequencies.

Max Planck, when studying the problem, suggested that instead of being allowed to emit radiation continuously, to make a theory fit the empirical data, electromagnetic energy should only be allowed to be emitted in discrete 'particles', which he called quanta. He also said that the energy of these quanta should be proportional to the frequency of the emitted radiation. The energy of a quantum of radiation E is given by the formula E=hf where f is the frequency of the radiation, and h is a constant, known as Planck's constant. This means that it is harder for a black body to radiate at higher frequencies - it takes more energy, so the ultraviolet catastrophe doesn't happen using this model.

This was the birth of Quantum Physics, but most physicists of the time, including Planck himself, didn't want to believe it, even when Albert Einstein used this theory to explain the Photoelectric Effect.

Use in Astrophysics

The black body radiation curve is important to astrophysicists. Stars are opaque at all wavelengths; it is impossible to see their internal structure, regardless of which frequency you try to use. Also, stars emit so much radiation that any incident radiation, which may possibly be reflected, can be neglected. So a star, assuming that its temperature is not changing, is a good approximation of a blackbody, and by looking at the spectrum of light emitted by a star, one can get a good idea of a perfect black body spectrum. If you study the radiation curve of a star, you can compare it to the theoretical curve of a black body at a given temperature, to work out the temperature of the star.

A Question and Answer Session

  • Why does a blackbody radiate at all?

    Everything emits and absorbs radiation. Imagine if it didn't. We'd all get hotter and hotter, if nothing emitted any of the radiation it absorbed... or else we'd all be at absolute zero, because no energy would've been emitted in the first place and we wouldn't have been able to absorb any.

  • Where does the energy come from that the body absorbs to be in equilibrium?

    A black body is in thermal equilibrium with its surroundings. Assuming that its surroundings are not at absolute zero, they have energy, so the black body receives energy. The point about a blackbody is that it re-emits all the radiation that it receives.

  • Is black body radiation at a single frequency or a range of frequencies? What shape is the distribution curve?

    All frequencies. The distribution curve is different for each temperature. Click here to see blackbody radiation for different temperatures. The first thing on the page is the formula, which is a thing of no beauty, that's why Planck didn't believe it, really. For the shape of the distribution, go to the first applet, and use the mouse to set the temperature on the left thermometer, in black, (rectangle at the side of the graph) to around 9000, and the temperature on the right thermometer, in red to around 7500. You should notice that the black graph peaks higher and to the left of the red one.

  • Why is the concept important in physics, and particularly in astrophysics?

    It is particularly important in astrophysics because it means that if you know what frequency a star emits most of its light at, using the model you can work out what its temperature is.

  • What is the relationship between the temperature of the body and its radiation spectrum?

    Very complicated. In general, the hotter the body, the higher the frequency/lower the wavelength that the highest amount of radiation is re-emitted at.

  • Why do hot things glow, and at what temperatures?

    They emit their radiation at a frequency/wavelength we can see. Everything emits and absorbs radiation, but most things in everyday life are too cold to emit light that we can see. But it all does, people do, and that's why infrared cameras work.

1 If you reflected none and absorbed none, the light would let it pass straight through you, you would be invisible. If you reflected it all you would be perfect white. If you absorbed it all you would be completely black.

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Entry Data
Entry ID: A270037 (Edited)

Edited by:

Date: 05   July   2000

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Photoelectric Effect

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