Radiation classical theory

In the classical theory of scattering (Cohen-Tannoudji et al. 1977, James 1982), atoms are considered to scatter as dipole oscillators with definite natural frequencies. They undergo harmonic vibrations in the electromagnetic field, and emit radiation as a result of the oscillations. 

According to classical theory, in Eq. (16.16), the first term represents an oscillating dipole that radiates light of frequency v0, that is, Rayleigh scattering. The second term is associated with the Raman scattering of frequency v0 - vm (Stokes process) and v0 + vm (anti-Stokes process). If (daldq)0 is zero, the vibration is not Raman active (Ferraro and Nakamoto, 1994). 

In the classical theory of electrodynamics, electromagnetic radiation is emitted when an electron moves in its orbit but, ac cording to the Bohr theory of the atom,... 

In view of the complexity associated with equation (48), approximate methods are needed for applications. References [6] and [33]-[38] may be consulted for these approximations. While scattering may be important in combustion situations involving large numbers of small condensed-phase particles, often the effects of scattering may be approximated as additional contributions to emission and absorption, thereby eliminating the integral term. Two classical limits in radiation-transport theory are those of optically thick and optically thin media the former limit seldom is applicable in combustion, while the latter often is. In the optically thin limit, gas-phase... 

A familiar device in modem technology is the photocell or electric eye, which mns a variety of useful gadgets, including automatic door openers. The principle involved in these devices is the photoelectric effect, which was first observed by Heinrich Hertz in the same laboratory in which he discovered electromagnetic waves. Visible or ultraviolet radiation impinging on clean metal surfaces can cause electrons to be ejected from the metal. Such an effect is not, in itself, inconsistent with classical theory since electromagnetic waves are known to carry energy and momentum. But the detailed behavior as a function of radiation frequency and intensity cannot be explained classically. 

FIGURE 4.6 The dependence of the intensity of blackbody radiation on wavelength for two temperatures 5000 K (red curve) and 7000 K (blue curve). The sun has a blackbody temperature near 5780 K, and its light-intensity curve lies between the two shown. The classical theory (dashed curves) disagrees with observation at shorter wavelengths. 

All the considerations that follow are only valid for radiation that is stimulated thermally. Radiation is released from all bodies and is dependent on their material properties and temperature. This is known as heat or thermal radiation. Two theories are available for the description of the emission, transfer and absorption of radiative energy the classical theory of electromagnetic waves and the quantum theory of photons. These theories are not exclusive of each other but instead supplement each other by the fact that each describes individual aspects of thermal radiation very well. 

Here, h = (6.626 068 76 0.000 000 52)-10 34 Js is the Planck constant, also known as Planck s action quantum v is the frequency of the photons. Quantum theory is required to calculate the spectral distribution of the energy emitted by a body. Other aspects of heat transfer can, in contrast, be covered by classical theory, according to which the radiation is described as the emission and propagation of electromagnetic waves. 

In view of the experimental difficulties a theory for radiation properties is desirable. The classical theory of electromagnetic waves from J.C. Maxwell (1864), links the emissivity e x with the so-called optical constants of the material, the refractive index n and the extinction coefficient k, that can be combined into a complex refractive index n = n — ik. The optical constants depend on the temperature, the wavelength and electrical properties, in particular the electrical resistivity re of the material. In addition, the theory delivers, in the form of Fresnel s equations, an explicit dependence of the emissivity on the polar angle / , whilst no dependence on the circumferential angle ip appears, as isotropy has been assumed. 

This picture is developed to a high level of sophistication within the classical theory of the electromagnetic field, where dynamics is described by the Maxwell equations. Some basics of this theory are described in Appendix 3 A. Here we briefly outline some of the important results of this theory that are needed to understand the nature of the interaction between a radiation field and a molecular system. 

Compton (1922) investigated the scattering of X-rays by a block of paraffin, and found that the radiation scattered at an angle of less than 90° possesses a greater wave-length than the primary radiation, so that the v of the scattered wave, contrary to the prediction of the classical theory, is smaller than the v of the... 

From another point of view, the statistical interpretation of wave functions suggests how the radiation emitted by the atom may be calculated on wave-mechanical principles. In the classical theory this radiation is determined by the electric dipole moment p of the atom, or rather by its time-rate of variation. By the correspondence principle, this connexion must continue to subsist in the wave mechanics. Now the dipole moment is easily calculated by wave mechanics if we adhere to the analogy with classical atomic mechanics, it is given by... 

If, contrary to the order of historical development, we have discussed the quantum theory of the atom before quantum statistics, we have our reasons. In the first place, the failure of- the classical theory displays itself in atomic mechanics—for instance, in the explanation of line spectra or the diffraction of electrons—even more immediately than in the attempts to fit the law of radiation into the frame of classical physics. In the second place, it is an advantage to understand the mechanism of the individual particles and the elementary processes before proceeding to set up a system of statistics based upon the quantum idea. 

What are the limitations of classical theories, such as electromagnetics, optics, and thermodynamics, for thermal radiation and what fact originally prompted the modern theory of radiation State briefly the foundations of the modem theory. 

In Section 3 a very brief discussion of the classical theory of the radiation of energy from accelerated charged particles has been given, in order to have a foundation for later discussions of this topic. Mention is made of both dipole and quadrupole radiation. 

The Correspondence Theorem is a formal expression of the requirement that the radiation calculated hy quantum theory must agree in frequency, intensity and polarization with that calculated by classical theory when the difference between the initial and final quantum states tends asymptotically to zero. This condition is met when the difference between the two values of a particular quantum number is small compared with the absolute value. 

The appeal to classical theory is avoided in a theory of radiation due to Dirac [35] in which the same formula for intensities is derived by the application of pert urbation theory to a weakly interacting system of atoms and radiation. A serious objection to the theory, however, is that for higher approximations to the perturbation interaction entirely meaningless results-diverging integrals—-are obtained. A fuller discussion of these difficulties is given in Chapter IX. 

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