Radiation, electromagnetic amplitude

In the previous section we defined several characteristic properties of electromagnetic radiation, including its energy, velocity, amplitude, frequency, phase angle, polarization, and direction of propagation. Spectroscopy is possible only if the photon s interaction with the sample leads to a change in one or more of these characteristic properties. 

In the second broad class of spectroscopy, the electromagnetic radiation undergoes a change in amplitude, phase angle, polarization, or direction of propagation as a result of its refraction, reflection, scattering, diffraction, or dispersion by the sample. Several representative spectroscopic techniques are listed in Table 10.2. 

Figure 12.11 Electromagnetic waves are characterized by a wavelength, a frequency, and an amplitude, (a) Wavelength (A) is the distance between two successive wave maxima. Amplitude is the height of the wave measured from the center. (b)-(c) What we perceive as different kinds of electromagnetic radiation are simply waves with different wavelengths and frequencies.

You can appreciate why scientists were puzzled The results of some experiments (the photoelectric effect) compelled them to the view that electromagnetic radiation is particlelike. The results of other experiments (diffraction) compelled them equally firmly to the view that electromagnetic radiation is wavelike. Thus we are brought to the heart of modern physics. Experiments oblige us to accept the wave-particle duality of electromagnetic radiation, in which the concepts of waves and particles blend together. In the wave model, the intensity of the radiation is proportional to the square of the amplitude of the wave. In the particle model, intensity is proportional to the number of photons present at each instant. 

When two or more waves pass through the same region of space, the phenomenon of interference is observed as an increase or a decrease in the total amplitude of the wave (recall Fig. 1.20). Constructive interference, an increase in the total amplitude of the wave, occurs when the peaks of one wave coincide with the peaks of another wave. If the waves are electromagnetic radiation, the increased amplitude corresponds to an increased intensity of the radiation. Destructive interference, a decrease in the total amplitude of the waves, occurs when the peaks of one wave coincide with the troughs of the other wave it results in a reduction in intensity. 

The model fundamental to all analyses of vibrational motion requires that the atoms in the system oscillate with small amplitude about some defined set of equilibrium positions. The Hamiltonian describing this motion is customarily taken to be quadratic in the atomic displacements, hence in principle a set of normal modes can be found in terms of these normal modes both the kinetic energy and the potential energy of the system are diagonal. The interaction of the system with electromagnetic radiation, i.e. excitation of specific normal modes of vibration, is then governed by selection rules which depend on features of the microscopic symmetry. It is well known that this model can be worked out in detail for small molecules and for crystalline solids. In some very favorable simple cases the effects of anharmonicity can be accounted for, provided they are not too large. 

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... 

As noted above, for interaction to be possible between the electromagnetic radiation and the bonding system of a molecule, leading to uptake of energy and therefore to an increase in the amplitude of the appropriate stretching or bending vibration, two conditions have to be met ... 

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