Black Body Radiation

Radiation from heated bodies depends to some extent on the body heated. In order to understand the concept of a black body, we need to understand more closely how radiation is absorbed, transmitted, reflected and emitted. Let us back up momentarily and consider how differently different materials absorb radiation.

How is Radiation Absorbed?

·        Some, like glass, seem to absorb light hardly at all – the light goes through. For a shiny metallic surface, the light isn't absorbed either, it gets reflected.

·        For a black material like soot, light and heat are almost completely absorbed, and the material gets warm.

·        How can we understand these different behaviors in terms of light as an electromagnetic wave interacting with charges in the material, causing them to oscillate and absorb energy from the radiation?

·        In the case of glass, evidently this doesn't happen, at least not much.

A full understanding of how this works needs quantum mechanics, but the general idea is as follows:

·        There are charges – electrons – in glass that are able to oscillate in response to an applied external oscillating electric field, but these charges are tightly bound to atoms, and only oscillate at certain frequencies.

·        It happens that for ordinary glass none of these frequencies correspond to those of visible light, so there is no resonance with a light wave, and hence little energy absorbed.

·        Glass is opaque at some frequencies outside the visible range (in general, both in the infrared and the ultraviolet).

·        These are the frequencies at which the electrical charge distribution in the atoms or bonds can naturally oscillate.

·        A piece of metal has electrons free to move through the entire solid. This is why metals can conduct electricity. It is also why they are shiny.

·        These unattached electrons oscillate together with large amplitude in response to the electrical field of an incoming light wave.

·        They themselves then radiate electromagnetically, just like a current in an antenna. This radiation from the oscillating electrons is the reflected light. In this situation, little of the incoming radiant energy is absorbed, it is just reradiated, that is, reflected.

·        Soot, like a metal, will conduct an electric current, although not nearly so well.

·        There are unattached electrons, which can move through the whole solid, but they keep bumping into things – they have a short mean free path.

·        When they bump, they cause vibration, like a pinball machine, so they give up energy into heat.

·        Although the electrons in soot have a short mean free path compared to that in a good metal, they move very freely compared with electrons in atoms, so they can accelerate and pick up energy from the electric field in the light wave.

·        They are therefore effective intermediaries in transferring energy from the light wave into heat.

Absorption and Emission

·        Heated bodies radiate by processes just like the absorption described above operating in reverse.

·        Thus, for soot, heat causes the lattice to vibrate more vigorously, giving energy to the electrons (imagine them as balls in a pinball machine with strongly vibrating barriers, etc.) and since the electrons are charged they radiate away excess kinetic energy.

·        On the other hand, the electrons in a metal have very long mean free paths, the lattice vibrations affect them much less, so they are less effective in radiating away heat.

 

·        It is evident from considerations like this that good absorbers of radiation are also good emitters.

·        At sufficiently high temperatures, all bodies become good radiators.

·        Items heated until they glow in a fire look much more similar than they do at room temperature.

·        For a metal, this can be understood in terms of a shortening of the mean free path by the stronger vibrations of the lattice interfering with the electron's passage.

Black Body Radiation

In physics, a black body is an object that absorbs all electromagnetic radiation that falls onto it. No radiation passes through it and none is reflected, yet in classical physics, it can theoretically radiate any possible wavelength of energy.

A black body is matter which absorbs all electro-magnetic energy incident upon it and does not reflect nor transmit any energy. According to Kirchhoff's law, the ratio of the radiated energy from an object in thermal equilibrium, to the absorbed energy is constant and only dependent on the wavelength and the temperature T. A black body shows the maximum radiation as compared with other matter. Therefore a black body is called a perfect radiator.

Despite the name, black bodies are not actually black as they radiate energy as well. The amount and type of electromagnetic radiation they emit is directly related to their temperature. Black bodies below around 700 K (430 °C) produce very little radiation at visible wavelengths and appear black (hence the name). Black bodies above this temperature, however, begin to produce radiation at visible wavelengths starting at red, going through orange, yellow, and white before ending up at blue as the temperature increases.

The term "black body" was introduced by Gustav Kirchhoff in 1862. The light emitted by a black body is called black-body radiation, and has a special place in the history of quantum mechanics.

Explanation:

In the laboratory, the closest thing to black-body radiation is the radiation from a small hole entrance to a larger cavity. Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped and is almost certain to be absorbed by the walls in the process, regardless of what they are made of or the wavelength of the radiation (as long as it is small compared to the hole). The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the spectrum of the hole's radiation (i.e., the amount of light emitted from the hole at each wavelength) will be continuous, and will not depend on the material in the cavity (compare with emission spectrum). By a theorem proved by Kirchhoff, this curve depends only on the temperature of the cavity walls.

As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.

Calculating this curve was a major challenge in theoretical physics during the late nineteenth century. The problem was finally solved in 1900 by Max Planck as Planck's law of black-body radiation.

Einstein built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the photoelectric effect. These theoretical advances eventually resulted in the superseding of classical electromagnetism by quantum electrodynamics. Today, these quanta are called photons.

The temperature of a Pahoehoe lava flow can be estimated by observing its colour. The result agrees nicely with the measured temperatures of lava flows at about 1,000 to 1,200o C.

The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan-Boltzmann law. So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature.

The radiance or observed intensity is not a function of direction. Therefore a black body is a perfect Lambertian radiator.  Real objects never behave as full-ideal black bodies, and instead the emitted radiation at a given frequency is a fraction of what the ideal emission would be. The emissivity of a material specifies how well a real body radiates energy as compared with a black body. This emissivity depends on factors such as temperature, emission angle, and wavelength. However, it is typical in engineering to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the grey body assumption.

Interestingly, this means that every object around you is emitting electromagnetic waves with wavelengths of all values. Every object in the universe has heat, even the emptiness of space, and when the particles that make up an object vibrate on a microscopic level they radiate electromagnetic waves. These wavelengths are predominantly infrared (heat), but there is also a minute amount of visible light like red, yellow, green and blue. So, right now, you and everything around you is emitting visible light. The reason this light cannot be seen is that it has a very low intensity.

When dealing with non-black surfaces, the deviations from ideal black body behavior are determined by both the geometrical structure and the chemical composition, and follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.

In astronomy, objects such as stars are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect black-body spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is black-body radiation emitted by black holes.

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