Electromagnetic radiation quantization

Read materials assigned by your instructor on electromagnetic radiation, quantization of energy, and atomic spectra. 

Studies of black-body radiation led to Planck s hypothesis of the quantization of electromagnetic radiation. The photoelectric effect provides evidence of the particulate nature of electromagnetic radiation. 

Photoelectric effect The effect produced when electromagnetic radiation knocks electrons out of a metal. Einstein used this phenomenon to show that light was quantized and came in energy packets called photons. 

Finally, in the early 20th century Albert Einstein explained the photoelectric effect based on quantized packets of electromagnetic radiation called photons. These quickly led to the familiar relationships of the energy of a photon,... 

All spectra are due to the absorbance of electromagnetic radiation energy by a sample. Except for thermal (kinetic) energy, all other energy states of matter are quantized. Quantized transitions imply precise energy levels that would give rise to line spectra with virtually no line-width. Most spectral peaks have a definite width that can be explained in several ways. First, the spectral line-width can be related to the... 

The concept of quantization enabled physicists to solve problems that nineteenth-century physics could not. One of these involved the thermal properties of solids when they are heated to incandescence. The other involved the induction of electrical current in metals when they are exposed to only specific frequencies of electromagnetic radiation. 

Not really a spectroscopic technique in that the line spectrum produced does not arise from quantization of electromagnetic radiation. Of specialized interest only not further discussed here. 

The angular distribution of the intensity of electromagnetic radiation is given by specific analytic functions written in terms of an angle, W(Q,mi), relative to the quantization axis, Z, and the magnetic quantum number, mi. The patterns depend on the order of the multipole, dipole, quadra pole, and so forth, but they are the same for electric and magnetic transitions with the same order. For example, the angular distributions for dipole radiation are... 

The proportionality constant h has the dimensions of energy times time and has the value of 6.62 x 10 27 erg-sec. It is called Planck s constant and is the same for all types of electromagnetic radiation. Since energy seems to come in discrete units, this quantization thus permits us to view radiation also in terms of particles, the photons. Absorption of photons by atoms would increase their energy by an amount equivalent to hv per photon. 

A ramp changes height continuously, but stairs are quantized, changing height only in discrete amounts. In the same way, electromagnetic radiation is not continuous but is emitted only in discrete amounts. 

There are several reasons for starting this account with a discussion of electromagnetic radiation. Historically, it was in this area that the quantum theory first developed. It is easier here to understand the evidence for the theory, and to appreciate some of its paradoxical consequences, than it is in the quantum theory of matter. The applications of the light-quantum hypothesis, as it was first called, also provide key pieces of evidence for the quantization of energy in atoms and molecules. Studies of the absorption and emission of radiation—the field of spectroscopy—and of the effect of light on chemical reactions—photochemistry—are very important areas of modem chemistry, in which the quantum nature of radiation is crucial. 

Most other forms of spectroscopy do not involve emission of extra particles such as electrons, but the straightforward absorption or emission of photons. These processes increase or decrease the energy of an atom ex molecule, by an amount equal to the photon energy. The results all reinforce the conclusion of photoelectron spectroscopy that only discrete energy levels occur (see Fig. 1.12). For example, the line spectra of atoms, known since the early nineteenth century, only contain lines at certain well-defined wavelengths. The quantization of energy, not only in electromagnetic radiation but in material systems, is an inescapable conclusion rtf spectroscopy. 

The B cyclic theorem is a Lorentz invariant construct in the vacuum and is a relation between angular momentum generators [42], As such, it can be used as the starting point for a new type of quantization of electromagnetic radiation, based on quantization of angular momentum operators. This method shares none of the drawbacks of canonical quantization [46], and gives photon creation and annihilation operators self-consistently. It is seen from the B cyclic theorem ... 

In this chapter we introduce some of the fundamental concepts needed to understand how light interacts with matter. We start by examining a system of classical charged particles that interacts with a pulse of electromagnetic radiation. We then quantize the particle variables and develop the semiclassical theory of light interacting with quantized particles. The details of the derivations are not required for subsequent chapters. However, the resultant equations [Eqs. (1.50) to (1.52)] form the basis for the theoretical development presented in Chapter 2, which deals with both the interaction of weak lasers with molecules and with photodissociation processes. 

Now we will introduce quantum electrodynamics. Just as we quantized the atoms and molecules, we must also quantize the electromagnetic radiation field, to deal with field-molecule interactions properly [14,34],... 

This, plus the quantization of the normal modes of vibration of the electromagnetic radiation field (just demonstrated), form, together, the quantum-mechanical basis for the wave-particle duality A wave can become a particle, and vice versa, but you can never make a simultaneous experiment to test both the wave and the particle nature of the same system. 

In spectroscopy it is useful to consider the propagation of electromagnetic radiation in a quantitative manner. Light is transmitted as discrete packets or as a stream of particles of energy called photons. These photons have a specific energy and for spectroscopy are quantized and described by the following equation ... 

The next important development in the knowledge of atomic structure came when Albert Einstein (see Fig. 12.5) proposed that electromagnetic radiation is itself quantized. Einstein suggested that electromagnetic radiation can be viewed as a stream of particles now called photons. The energy of each photon is given by the expression... 

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