EMISSION AND ABSORPTION OF ENERGY

As described above, each atom has a number of possible energy levels or states. Emission or absorption of radiation originates from an electron transition between particular pairs of these states. Which transitions are 

Einstein s theory of radiation is a method of classifying and explaining the relative line intensities. According to the radiation theory the intensity of a line corresponding to a particular transition will be directly proportional to its transition probability. The calculations are based on the rules of quantum mechanics, are complex, and only possible when simplifying assumptions are made. 

Einstein has derived several useful relationships between the Ay-, Bjj-, and. fijj-coefficients by assuming thermodynamic equilibrium between the radiation and the atoms and comparing it with the equilibrium of a black-body radiator at the same temperature  

Oscillator strength values are usually given as -values, which refer to 

The number of transitions or photons per second for a spontaneous emission is AyN. The intensity of the corresponding emission line is  

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An ideal blackbody exhibits perfect emission and absorption of energy at all wavelengths and at all angles. The total radiant energy of such a body is a function only of its temperature. This ideal is shown in Figure 5. 

FRET is a nonradiative process that is, the transfer takes place without the emission or absorption of a photon. And yet, the transition dipoles, which are central to the mechanism by which the ground and excited states are coupled, are conspicuously present in the expression for the rate of transfer. For instance, the fluorescence quantum yield and fluorescence spectrum of the donor and the absorption spectrum of the acceptor are part of the overlap integral in the Forster rate expression, Eq. (1.2). These spectroscopic transitions are usually associated with the emission and absorption of a photon. These dipole matrix elements in the quantum mechanical expression for the rate of FRET are the same matrix elements as found for the interaction of a propagating EM field with the chromophores. However, the origin of the EM perturbation driving the energy transfer and the spectroscopic transitions are quite different. The source of this interaction term... 

The carrier-phonon interaction decreases with the lowering of temperature, since the emission and absorption of phonons by carriers is proportional to the number of final states available to carriers and phonons. At sufficiently low temperatures, the interaction between the two subsystems can be so weak that there is no thermal equilibrium between them, and the energy is distributed among electrons more rapidly than it is distributed to the lattice, resulting in a different temperature for electron and phonon subsystems, giving rise to the so-called electron-phonon decoupling . 

This expression provides the basis of a spectroscopic method The transition of electron or nuclear spins between energy levels ("change of spin") may be associated with the emission or absorption of energy in the form of radiation with the appropriate frequency. Since the frequency is proportional to the applied field, spin spectra can in principle be studied in any region of the electromagnetic spectrum, merely by choosing an appropriate field strength. For practical reasons the fields are normally of the order of 1.5 tesla for nuclei and 0.3 tesla for electrons. 

By 1903. llie wave theory of light based oil Maxwell s equations was well established, but certain phenomena would not fit in. It seemed that emission and absorption of hght occur discontinuously. This led Einstein to (lie view that the energy is concentrated in discrete particles. It was a revolutionary idea, very hard to understand, as the successes of the wave theory were undeniable. It seemed that light had to be understood sometimes as waves, sometimes as particles, and physicists had to get used to it, The idea was incorporated into Bohr s theory of the hydrogen atom and forms an essential part of it. 

In Section I, the spectra of e"(ai) consist of Dirac 5 peaks (1.79). In a real crystal these peaks are broadened by static disorder, thermal fluctuations, and excitation-relaxation processes. Discarding for the moment the static disorder, we focus our attention on broadening processes due to lattice phonons, which may be described alternatively in terms of fluctuations of the local energies of the sites, or in terms of exciton relaxation by emission and absorption of phonons. These two complementary aspects of the fluctuation-dissipation theorem64 will allow us to treat the exciton-phonon coupling in the so-called strong and weak cases. The extraordinary (polariton) 0-0 transition of the anthracene crystal will be analyzed on the basis of these theoretical considerations and the semiexperimental data of the Kramers-Kronig analysis. 

The Kinetics of Collision and Ionization.—In the last section we have been considering the emission and absorption of radiation as a mechanism for the transfer of atoms or molecules from one energy level to another. The other important mechanism of transfer is that of collisions with another atom, molecule, or more often with an electron. In such a collision, the colliding particles can change their energy levels,... 

Electronic transitions (both in emission and absorption) of either acidic or basic substances in solution may show shifts of the band maximum upon H bond formation. In absorption spectra both, positive and negative shifts, Ai a> have been observed. These shifts correspond to energies, AAi/a> usually of the order of, but smaller than, H bond energies. In absorption spectra, no pronounced change of absorption coefficient accompanies the shift, but vibrational fine structure may become diffuse. 

In a real radiation source this perfect equilibrium cannot exist and there are losses of energy as a result of the emission and absorption of radiation, which also have to be considered. However, as long as both only slightly affect the energy balance, the system is in so-called local thermal equilibrium and ... 

Heat is transferred from points of high temperature to points of lower temperature by direct contact of particles of matter or the emission and absorption of radiant energy. The three classifications of heat transfer are ... 

Thus we see that the energy levels allowed by the old quantum theory are integral multiples of hv0, as indicated in Figure 6-1. The selection rule An = 1 permits the emission and absorption of light of frequency v0 only. 

There have been developed two essentially different wave-mechanical perturbation theories. The first of these, due to Schrodinger, provides an approximate method of calculating energy values and wave functions for the stationary states of a system under the influence of a constant (time-independent) perturbation. We have discussed this theory in Chapter VI. The second perturbation theory, which we shall-treat in the following paragraphs, deals with the time behavior of a system under the influence of a perturbation it permits us to discuss such questions as the probability of transition of the system from one unperturbed stationary state to another as the result of the perturbation. (In Section 40 we shall apply the theory to the problem of the emission and absorption of radiation.) The theory was developed by Dirac.1 It is often called the theory of the variation of constants the reason for this name will be evident from the following discussion. 

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