where the electric field
(1.3)
where ν is the frequency of the oscillation, measured in units of s−1 = Hz. In Eqs. (1.1) and (1.2), k is the wave vector (or momentum vector) of the electromagnetic wave, defined by Eq. (1.4):
Here, λ is the wavelength of the radiation, measured in units of length, and is defined by the distance between two consecutive peaks (or troughs) of the electric or magnetic fields. Vector quantities, such as the electric and magnetic fields, are indicated by an arrow over the symbol or by bold typeface.
Since light is a wave, it exhibits properties such as constructive and destructive interference. Thus, when light impinges on a narrow slit, it shows a diffraction pattern similar to that of a plain water wave that falls on a barrier with a narrow aperture. These wave properties of light were well known, and therefore, light was considered to exhibit wave properties only, as predicted by Maxwell's equation.
Figure 1.1 Description of the propagation of a linearly polarized electromagnetic wave as oscillation of electric (
In general, any wave motion can be characterized by its wavelength λ, its frequency ν, and its propagation speed. For light in vacuum, this propagation speed is the velocity of light c (c = 2.998 × 108 m/s). (For a list of constants used and their numeric value, see Appendix 1.) In the context of the discussion in the following chapters, the interaction of light with matter will be described as the force exerted by the electric field on the charged particles, atoms, and molecules (see Chapter 3). This interaction causes a translation of charge. This description leads to the concept of the “electric transition moment,” which will be used as the basic quantity to describe the likelihood (that is, the intensity) of spectral transition.
In other forms of optical spectroscopy (for example, for all manifestations of optical activity, see Chapter 10), the magnetic transition moment must be considered as well. This interaction leads to a coupled translation and rotation of charge, which imparts a helical motion of charge. This helical motion is the hallmark of optical activity, since, by definition, a helix can be left‐ or right‐handed.
1.2 Blackbody Radiation
From the viewpoint of a spectroscopist, electromagnetic radiation is produced by atoms or molecules undergoing transitions between well‐defined stationary states. This view obviously does not include the creation of radio waves or other long‐wave phenomena, for example, in standard antennas in radio technology, but describes ultraviolet, visible, and infrared radiation, which are the main subjects of this book. The atomic line spectra that are employed in analytical chemistry, for example, in a hollow cathode lamp used in atomic absorption spectroscopy, are due to transitions between electronic energy states of gaseous metal atoms.
The light created by the hot filament in a standard light bulb is another example of light emitted by (metal) atoms. However, here, one needs to deal with a broad distribution of highly excited atoms, and the description of this so‐called blackbody radiation was one of the first steps in understanding the quantization of light.
Any material at a temperature T will radiate electromagnetic radiation according to the blackbody equations. The term “blackbody” refers to an idealized emitter of electromagnetic radiation with intensity I(λ, T) or radiation density ρ(T, ν) as a function of wavelength and temperature. At the beginning of the twentieth century, it was not possible to describe the experimentally obtained blackbody emission profile by classical physical models. This profile was shown in Figure 1.2 for several temperatures between 1000 and 5000 K as a function of wavelength.
Figure 1.2 (a) Plot of the intensity I radiated by a blackbody source as a function of wavelength and temperature. (b) Plot of the radiation density of a blackbody source as a function of frequency and temperature. The dashed line represents this radiation density according to Eq. (1.5).
M. Planck attempted to reproduce the observed emission profile using classical theory, based on atomic dipole oscillators (nuclei and electrons) in motion. These efforts revealed that the radiation density ρ emitted by a classical blackbody into a frequency band dν as function of ν and T would be given by Eq. (1.5):