# Optical Spectrum

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## Spectrum, Optical

a spectrum of electromagnetic radiation encompassing the infrared, visible, and ultraviolet regions. The following types of optical spectra are distinguished: emission spectra, absorption spectra, scattered-light spectra, and reflection spectra.

To obtain emission spectra, the radiation from a light source is separated into its various wavelength components by means of a spectroscopic instrument. An emission spectrum can be characterized by the function f(λ) giving the energy distribution of the emitted light with respect to wavelength ʎ. Absorption, scattered-light, and reflection spectra are usually obtained by passing light through a substance and then separating the light into its wavelength components. To characterize these spectra, the following functions are used: for absorption spectra, k(λ), the fraction of light energy absorbed at each wavelength; for scattered-light spectra, α(λ), the fraction of light energy scattered at each wavelength; and for reflection spectra, R(ʎ), the fraction of light energy reflected at each wavelength. In the case of the scattering of monochromatic light of wavelength ʎ0, the Raman spectrum obtained is characterized by the energy distribution of the scattered light with respect to the changed wavelengths ʎ ≠ ʎ0 [f’(ʎ)]. Thus, any spectrum can be characterized by some function f(λ) giving the absolute or relative energy distribution with respect to ʎ. Here, the energy is considered over a certain range of ʎ. The function f(λ) can be replaced by the function Φ(v) giving the energy distribution with respect to frequency v = c/ʎ, where c is the speed of light. The energy is then considered over a certain range of v.

Optical spectra are registered by photographic and photoelectric means. Other methods and instruments may also be used—for example, quantum counters in the ultraviolet region and thermocouples and bolometers in the infrared region. Spectra may be observed visually in the visible region.

According to their appeararfce, optical spectra are classified as line, band, or continuous spectra. Line spectra consist of separate spectral lines corresponding to discrete values of λ. Band spectra are made up of separate bands, each covering a certain range of λ. Continuous spectra cover a large range of λ. Strictly speaking, an individual spectral line does not correspond to a single definite value of λ; instead, a line always has a finite width corresponding to a narrow range of λ.

Optical spectra are a result of quantum transitions between the energy levels of atoms, molecules, solids, and liquids. Emission spectra correspond to allowed transitions from upper energy levels to lower levels, and absorption spectra correspond to allowed transitions from lower levels to upper levels.

The appearance of an optical spectrum depends on the state of the substance. If for a given temperature the substance is in a state of thermodynamic equilibrium with the radiation, the substance emits a continuous spectrum whose energy distribution with respect to λ or v is given by Planck’s radiation law. Usually, however, the substance is not in thermodynamic equilibrium with the radiation, and the optical spectrum can have various forms. Atoms, for example, are characterized by line spectra produced by quantum transitions between electronic energy levels (seeATOMIC SPECTRA). Simple molecules have band spectra resulting from transitions between electronic, vibrational, and rotational energy levels (seeMOLECULAR SPECTRA).

For optical spectra, to different regions of λ or, consequently, of v there correspond different photon energies hv = ℰ1 – ℰ2, where h is Planck’s constant and ℰ1 and ℰ2 are the energy levels between which the transition occurs. Table 1 gives for the three regions of electromagnetic waves in optical spectra the approximate ranges of wavelengths ʎ, frequencies v, wave numbers vie, photon energies hv, and temperatures T. Here, T is the temperature characterizing the photon energy in accordance with the equation kT = hv, where k is the Boltzmann constant.

Optical spectra are widely used to investigate the structure and composition of substances.

Table 1. Ranges of various quantities characterizing the regions of optical spectra
Spectral regionʎ(μ m)v (sec–1)v/c (cm–1)hv (eV)T (°K)
Infrared . . . . . . . . . . . . . . .103–0.743.0 × 1011–4.0 × 101410–1.35 × 1041.25 × 10–3 –1.714–2.0 × 104
Visible . . . . . . . . . . . . . . .0.74–0.404 × 1014–7.5 × 10141.35 × 104–2.5 × 1041.7–3.12.0 × 104–3.6 × 104
Ultraviolet . . . . . . . . . . . . . . .0.40–0.0017.5 × 1014–3.0 × 10162.5 × 104–1063.1–1253.6 × 104–1.4 × 106

### REFERENCES

Landsberg, G. S. Optika, 4th ed. (Obshchii kurs fizika, part 3.) Moscow, 1957.
Frish, S. E. Opticheskiespektry atomov. Moscow-Leningrad, 1963.

M. A. EL’IASHEVICH

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