Electromagnetic radiation wave theory

Bulk viscosity parameter in granular theory (kg/m s) Erequency of electromagnetic radiation wave (s )... 

The oscillating dipole is a source of electromagnetic radiation of the same frequency, polarized in the direction of the oscillations. At large distances, the wave is spherical. According to the electromagnetic theory, the resulting electric vector at a point in the equatorial plane of the dipole is a>2/ r c2 times the moment of the dipole at time t — r /c. The amplitude of the spherically scattered wave at unit distance in the equatorial plane is therefore... 

We shall apply the time-dependent perturbation theory of the last section to a system exposed to electromagnetic radiation. Before doing so, we review the classical wave theory of light.2... 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

A full explanation of the properties of light requires both the wave theory of electromagnetic radiation and the quantum theory. Most photochemical processes are best understood in terms of the quantum theory, which says that light is made up of discrete particles called quanta or photons. Each quantum carries an amount of energy, S, determined by the wavelength of the light, A. Equation 13.1, in which h is Planck s constant and c is the speed of light in a vacuum,... 

By the end of the nineteenth century it was realized that the wave theory of electromagnetic radiation could not by itself explain the form of the black-body radiation shown in Fig. 1.9. In particular, it was predicted that the energy distribution should rise indefinitely as the wavelength became shorter, rather than falling to zero as found. This alarming prediction, known as the ultraviolet catastrophe, gave the first serious clue that the theory was in need of modification,... 

In 1900 Max Planck proposed a solution to the problem of black-body radiation described above. He suggested that when electromagnetic radiation interacts with matter, energy can only be absorbed or emitted in certain discrete amounts, called quanta. Planck s theory will not be described here, as it is highly technical. In any case, Planck s proposal was timid compared with the theory that followed. He supposed that quanta were only important in absorption and emission of radiation, but that otherwise the wave theory did not need to be modified. It was Einstein who took a more radical step in 1905 (the year in which he published his first paper on the theory of relativity and on several other unrelated topics). Einstein s analysis of the photoelectric effect is crucial, and has led to a complete change in the way we think of light and other radiation. 

It turns out that electromagnetic waves exhibit properties of both waves and particles, or equally valid, electromagnetic waves are neither waves nor particles. This fundamental paradox is at the heart of quantum theory. You can perform experiments that unequivocally demonstrate light is definitely a wave. You can also perform experiments that unequivocally demonstrate light is definitely a particle. Nonetheless, there is one important relationship that allows the energy of electromagnetic radiation to be calculated if the frequency or wavelength is known ... 

The theory gives rise to a concept of atomic or molecular orbital, ie the wave-function, which depends explicitly on the spatial coordinates of only one electron and the quantum numbers that define energy, spin, orbital momentum, and symmetry properties of the two last wavefunctions. Quantum numbers of the wavefunc-tions in lower and upper states determine the possible interaction of the entity with electromagnetic radiation [1],... 

THE PHYSICS OF WAVES, William C. Elmore and Mark A. Heald. Unique overview of classical wave theory. Acoustics, optics, electromagnetic radiation, more. Ideal as classroom text or for self-study. Problems. 477pp. 5b 8b. 

If you recall from the beginning of this chapter, some of the work that led to the development of the modem atomic theory was done by scientists Max Planck, Albert Einstein, Louis de Broglie, Werner Heisenberg, Niels Bohr, and Erwin Shrodinger. The first work centered around light (electromagnetic radiation), while the later work focused on the wave-like nature of matter. The AP test does not probe too deeply into the theoretical considerations of any of these scientists, but some calculations have popped up on previous tests. Therefore, let s turn our attention to some of the equations associated with these scientists work. 

De Broglie s theory was proven by experiment when streams of electrons produced diffraction patterns similar to those produced by electromagnetic radiation, which was already known to travel in waves. 

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