Cavity radiation

No such thing as photon-photon collision has ever been observed, and to all practical purposes photons must be considered as non-interacting particles the collisional cross-section of the photon has been estimated from theory to be less than 10 70 cm2. This means that electromagnetic radiation (even cavity radiation) cannot be compared with a gas of molecules that can reach thermodynamic equilibrium through collisions which result in exchange of momentum and energy. 

This implied that for some reason the cavity radiated light only in packets (later called photons) with energy hv. A specific value of h (today called Planck s constant) gave perfect agreement with experiment. We also sometimes use frequency in units of radians per second (co) instead of cycles per second (v), as we discussed in Chapter 1, but we can convert readily between the two if we define h = h/ln. ... 

Without going beyond thermodynamics and the electromagnetic theory of light, we can deduce two laws regarding the way in which black body radiation (or, as it is also called, cavity radiation) depends on the temperature. Stefan s law (1879) states that the total emitted radiation is proportional to the fourth power of the temperature of the radiator the hotter the body, the more it radiates. Proceeding a step further, W. Wien found the displacement law (1893) which bears his name, and which states that the spectral distribution of the energy density is given by an equation of the form... 

If therefore we know the mean energy of an oscillator, we know also the spectral intensity distribution of the cavity radiation. 

Attempts have been made to remedy this very conspicuous failure in the theory by the following hypothesis. Suppose that, as in chemistry, a finite reaction time is needed before equilibrium is attained, and let the reaction velocity in the case of cavity radiation be very small, so that a very long time must elapse before equilibrium is reached, during which time the system as a whole, in consequence of external influences, will in general, we may well imagine, have completely changed. But this certainly does not go to the root of the matter ... 

We now return to the law of cavity radiation. We have seen in the preceding section that Planck s hypothesis has been brilliantly successful not only for cavity radiation, but also in the theory of specific heats. The latter success furnishes additional strong support for the quantum theory. 

We can also try to deduce the radiation formula, not as above from the pure wave standpoint by quantisation of the cavity radiation, but from the standpoint of the theory of light quanta, that is to say, of a corpuscular theory. For this we must therefore develop the statistics of the light-quantum gas, and the obvious suggestion is to apply the methods of the classical Boltzmann statistics, as in the kinetic theory of gases the quantum hypothesis, introduced by Planck in his treatment of cavity radiation by the wave method, is of course taken care of from the first in the present case, in virtue of the fact that we are dealing with light quanta, that is, with particles (photons) with energy hv and momentum Av/c. It turns out, however, that the attempt to deduce Planck s radiation law on these lines also fails, as we proceed to explain. 

Thus we see that the classical statistical methods fail, not only in the case when we deal with the statistics of cavity radiation from the wave point of view ( 3, p. 201), but also when we try to set up a statistical theory of the light quantum gas. The question therefore arises of what changes must be made in the classical statistics in order that it may become possible to deduce Planck s radiation law by purely statistical reasoning, without making use of the roundabout road by way of an absorbing and enoitting oscillator. 

FIGURE 7.12 Applications of net radiation exchange between two surfaces (a) a small, convex surface and large, isothermal surroundings (b) an isothermal cavity radiating into cold, black surroundings. 

An optical instrument is modeled as a spherical cavity of diameter Dc inside a metal block at temperature T and surface emissivity e (Fig. 9P-fi). The cavity radiates to an ambient at Too through a small opening of diameter Do and of negligible length. The effective emissivity of the cavity, o f is defined by... 

Svoboda V, Kotaskova Z, Lenger V, et al. 1979. Effect of 239Pu on mouse hemopoietic stem cells in different types of bone marrow cavities. Radiat Environ Biophys 16 339-345. 

With each jump, each electron emits a photon of characteristic energy. The jumps, and so the photon energies, are limited by Planck s constant. Subtract the value of a lower-energy stationary state W2 from the value of a higher energy stationary state fVj and you get exactly the energy of the light as hv. So here was the physical mechanism of Planck s cavity radiation. 

Figure 5 Idealized blackbody cavity radiator. From Grum and Becherer (1979).

The average spectral energy density in a blackbody cavity radiator, ct) is given in eqn [1],... 

The photoelectric effect and the properties of cavity radiation show that the classical idea that electromagnetic radiation is a form of wave motion is defective. Interference and diffraction phenomena, in which electromagnetic radiation behaves as though the photons are governed by a wave motion, are understandable in the enhancement and enfeeblement of waves of probability of finding photons in particular localities. These phenomena are shown in Figure 1.5. 

The nature of electromagnetic radiation was described in terms of quanta or photons, and evidence for such a description is given from Planck s explanation of cavity radiation and the photoelectric effect. 

The anti-crystal holes should be permeated by the photons obeying the frequency distribution function with an upper limit. This is due to the interface between the anti-crystal hole and the ordered part be able to act as a filter for the photons. The molar photon energy loss of the anti-crystal holes, AUh, due to the cavity radiation from Tb to T/ is given... 

For 2nlQ mode reflectometers, an inverted CPC can be used in front of cavity radiation sources (46, 54) in order to reduce the non-Lambertian properties of such sources at larger angles. The HDR 100 hemiellipsoidal reflectometer from Surface Optics Corporation uses a reflective cone above a cavity radiation source (55). 

Previously calibrated standards of similar reflectance and BRDF as the samples to be measured can be used to estimate the size of the interreflection uncertainty. However, this approach is limited by the a priori knowledge of the sample s reflectance and BRDF, as well as the availability of standards. The interreflection error can be directly minimized by using detectors (0/2ti) or cavity radiation sources 2nlB) having a low reflectance. 

The easiest bodies of matter to treat theoretically were called blackbodies. A blackbody is a perfect absorber or emitter of radiation. The distribution of absorbed or emitted radiation depends only on the absolute temperature, not on the blackbody material. A blackbody can be approximated as a small, hollow cavity with only a tiny hole for light to escape (Figure 9.11). Light emitted by blackbodies is sometimes referred to as cavity radiation. 

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