Black Body Radiation Essay

Black Body Radiation Essay

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BLACK-BODY RADIATION 1. What is Black-body? When a smooth surface completely reflects all incident rays, as is approximately the case with many metallic surfaces, it is termed “reflecting.” When a rough surface reflects all incident rays completely and uniformly in all directions, it is called “white.” A rough surface having the property of completely transmitting the incident radiation is described as “black.\" According to G. Kirchhoff it denotes a body which has the property of allowing all incident rays to enter without surface reflection and not allowing them to leave again. A body must satisfy three conditions to be a blackbody. First, the body must have a black surface in order to allow the incident rays to enter without reflection. Second, the black body must have a certain minimum thickness depending on its absorbing power, in order to insure that the rays after passing into the body shall not be able to leave it again at a different point of the surface. Third, the black body must have a vanishingly small coefficient of scattering. Otherwise the rays received by it would be partly scattered in the interior and might leave again through the surface. A black body is an ideal body which absorbs whole incident radiation within itself. The radiation can be of any wavelength and have any angle of incidence. So in other words it can be described as an ideal absorber of incident radiation. 2. Properties of Black-body 1. Black-body emits exactly same amount of radiation as it absorbs. Let us consider a black-body placed inside a fully insulated cavity of arbitrary shape, whose walls are also blackbodies at constant temperature (which is different from the temperature of the body). Then the black-body absorbs whole incident radiation as an ideal absorber. After some time black-body and cavity will have common equilibrium temperature. Then the black-body will emit exactly the same amount of radiation as it absorbed initially. 2. Black-body absorbs maximum radiation incident at any angle or any direction and when it emits the radiations are in the very same direction as they were initially because of its property of isotropy. 3. Black-body is an ideal emitter at any wavelength. But the intensity of the emitted radiation is not uniform because of its ‘white noise’ property. 4. Emission of radiations from black-body only depends on its nature, not on the properties of the cavity. 5. The total radiation properties are the function of the temperature only. If temperature of the cavity changes then the temperature of the body inside it will also change to maintain the equilibrium. And when the system becomes isothermal then body emits the same energy of radiation which was initially absorbed. But the magnitude of the radiation may differ with the temperature. 6. The total energy of radiation emitted by the black-body is proportional to the function of thermodynamic temperature only. If we consider two infinite ideal black-bodies parallel to each other. And upper body is maintained at higher temperature then the lower body. Now if we consider that the emission increases with the decrease in temperature, then lower body will emit more energy. Since both of them will absorb whole radiation given by the other body because they are black. To maintain the temperature the upper body has to emit the radiation per unit time and absorbed by the lower body. But this violates the second law of thermodynamics (i.e. energy transfer from cold surface to hot one is impossible). Therefore, the radiations emitted by the black-body increases with the temperature. 7. The more absorbing a body is, the smaller the value of this minimum thickness, while in the case of bodies with vanishingly small absorbing power only a layer of infinite thickness may be regarded as black. 3. History of Black-body It was the middle of the nineteen century when scientist had started to study the radiation of the heated bodies. Until that time the Newtonian physics was the only physics that people used to know. And then people had started to think about quantum mechanics. It was Kirchhoff who took first two steps in this direction. At the first Kirchhoff said the spectrum of light emitted and absorbed by a substance corresponds to that particular substance only. And this theory led to the discovery of a new branch ‘Spectroscopy’ (spectral analysis of the substance). And at the second he said the radiation spectrum of the heated bodies only depends on their temperature not on the chemical composition of the emitting substance. Kirchhoff considered theoretically the radiation inside a closed cavity in a rigid body, whose walls possess some particular temperature. There he found the walls emit same amount of energy as much as it has absorbed earlier. He found out under these conditions the energy distribution in the radiation spectrum does not depend on the material the walls were made of but the temperature. Such a radiation was called ‘absolutely (or ideally) black’ Figure 1. Classical experimental model of black-body source In 1895, W. Wien and O. Lummer suggested the development of ideal black-body to verify Kirchhoff’s theory. This model was manufactured as a hollow sphere with internal reflecting surface and a narrow hole in the wall, the hole is comparatively very small to the diameter of the sphere. So, any light undergoes multiple reflection inside the sphere, actually, cannot exit through the hole. At the same time, if the walls are at high temperature the hole will brightly shine (if the process is in optical band) owing to the electromagnetic radiation issuing from inside the cavity. It was this particular test model of a black-body radiation on which the experimental investigations to verify thermal radiation laws were carried out and temperature (Planck formula) was established quantitatively. The success of this experiment was so significant that for a long time, it was considered as a unique example of black-body in general physics textbooks. And, thus, some illusion of black-body exclusiveness with respect to natural objects arises. In reality, however the natural world around us is virtually saturated with physical objects which are very close to black-body models in their characteristics. A blackbody is a theoretical idealized object described as something \"absorbing all incident radiation\" commonly imagined as a cavity or empty bottle/ box or hole in which photons are bouncing back and forth between walls of that bottle at a certain temperature defining the temperature of the cavity. The bottle has a little peephole through which radiation is escaping to be observed. A blackbody is assumed to capture an essential aspect of the radiation from a real body like the visible glow from a lump of iron at 1000 C, the Sun at 6000 C or the invisible infrared faint glow of a human body at 37 C. Figure 2. Blackbody as a cavity filled with photons bouncing back and forth. First of all, the source of black-body radiation is the star nearest to the Earth – the Sun. The direct radar experiments, performed, in the 1950s and 1960s, have indicated completed absence of a radio-echo within the wide wave-length band – in centimetre, in millimetre and decimetre ranges. The spectral studies of solar radiation in the optical and IR bands have indicated the presence of the thermal black-body radiation with a brightness temperature of 5800K at the Sun. In other bands of electromagnetic field the situation is complicated, due to presence of non-stationary quasi-noise radiation (flares, storms), in thermal radiation terms. The second is our own home planet, the Earth, which possesses radiation close to black-body radiation with a temperature of
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