# Spectrum, Continuous

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## Spectrum, Continuous

a spectrum of electromagnetic radiation in which the energy distribution is characterized by a continuous function Φ(v) of the radiation frequency or by a continuous function Φ(v.) of the radiation wavelength. For a continuous spectrum, Φ(v) or *f* (ʎ) varies slightly over a broad range of *v* or ʎ. By contrast, in line and band spectra Φ(v) has, at discrete values of the frequency v = v_{1}, v_{2}, v_{3}, . . ., pronounced maxima that are very narrow for spectral lines and broader for spectral bands. When radiation in the optical region is decomposed into a spectrum by spectroscopic instruments, a continuous spectrum is obtained in the form of a continuous band (when the spectrum is visually observed or photographically recorded) or a smooth curve (when the spectrum is photoelectrically recorded). Continuous spectra are observed both in emission and in absorption. The equilibrium spectrum is an example of a continuous spectrum encompassing the entire range of frequencies and characterized by a definite spectral energy distribution. The equilibrium spectrum is characterized by Planck’s radiation law.

Superpositions of a line spectrum on a continuous spectrum are possible in some cases. For example, in solar and stellar spectra both a discrete absorption spectrum (Fraunhofer lines) and a discrete emission spectrum (in particular, the spectral emission lines of the hydrogen atom) may be superposed on a continuous emission spectrum.

According to quantum theory, a continuous spectrum arises when quantum transitions occur between two sets of energy levels; at least one of the sets must belong to a continuous sequence of levels—that is, to a continuous energy spectrum. An example is the continuous spectrum of the hydrogen atom resulting from bound-free transitions. In such transitions, electrons move from discrete energy levels with different values of the quantum number *n* to the continuous set of energy levels lying above the ionization limit. In absorption, a continuous spectrum corresponds to the ionization of a H atom—that is, to electronic transitions from a bound state to a free state. In emission, a continuous spectrum corresponds to the recombination of an electron and a proton—that is, to electronic transitions from a free state to a bound state. Free-free transitions also occur; they are transitions between different pairs of energy levels belonging to a continuous set of energy levels. The continuous spectra resulting from such transitions correspond to bremsstrahlung in the case of emission and to the reverse process in the case of absorption. Bound-bound transitions, on the other hand, give rise to a line spectrum; such transitions occur between different pairs of discrete energy levels.

Continuous spectra can be obtained for nonmonatomic molecules as a result of the superposition of a very large number of spectral lines of finite width when transitions occur between sets of discrete energy levels that are close to each other. Apparent continuous spectra may be obtained when the spectroscopic instruments used have insufficient resolving power. In this case, a line or band spectral structure merges into a continuous spectrum.

M. A. EL’IASHEVICH