# Line spectrum

Alpha spectrum of the plutonium isotopes 242 Pu, 239 Pu / 240 Pu and 238 Pu

A line spectrum is a physical spectrum that shows separate ( discrete ) points of increased intensity, so-called spectral lines . Under certain circumstances, these points can appear next to or superimposed with continuous components .

Light spectra can show absorption or emission lines . Also particle may have a line spectrum; the particles then have discrete kinetic energies , as is the case with alpha radiation .

Spectrum of a low pressure mercury vapor lamp. Upper picture with a 256-pixel line sensor . Lower shot with a camera

## Origin of the lines in light and X-ray spectra

Every material and every atom or molecule has characteristic, discrete energy levels at which electrons can "stay". The transition from one to another energy level occurs through the absorption (transition from the lower to the higher state) or emission (transition from the higher to the lower state) of a photon with the energy

${\ displaystyle E = h \ cdot \ nu}$

(with the frequency of  the radiation and Planck's quantum of action ). The energy difference between the energy levels corresponds exactly to the energy of the photon, and the energy of a photon together with the speed of light determines its wavelength ${\ displaystyle \ nu}$ ${\ displaystyle h}$${\ displaystyle c}$

${\ displaystyle \ lambda = {\ frac {c} {\ nu}}}$.

Of all the possible energy states of a material, only a few pairs of energy states are generally preferred absorbers or emitters.

If a material is located between a radiation source with a continuous spectrum and a spectrometer (e.g. for measuring the spectrum), it absorbs photons of the energies given by the energy states of the material. The absorbed photons are then missing in the observed spectrum of the source; this causes dark absorption lines to appear.

An excited atom or molecule returns to a lower energy state after a short period of time. A photon is emitted, the energy of which corresponds to the energy difference between the higher and lower energy state. If this material is observed from the side, i.e. without the radiation source being visible, these photons of a certain energy (and thus wavelength) appear as emission lines in the spectrum.

## Gaining information from line spectra

Line spectra of atoms were an important source of information for the discovery of quantum mechanics . The particularly simple spectrum of the hydrogen atom gave rise to Bohr's atomic model . More detailed investigations of the hydrogen spectra later made it clear that this atomic model does not adequately describe reality and that the theories of Werner Heisenberg and Wolfgang Pauli provide a more precise description.

In astronomy , line spectra are a source of information about the universe. The line spectra are characteristic of the respective atom or molecule, so the elements occurring in space can be determined from the light. In this way, for example, helium was first found on the sun before it could also be detected on earth.

Line spectra have a further application in astronomy: Since the exact energies of the spectra of the elements are known and the elements can be identified using the pattern of the lines, the redshift of its light can be determined from the line spectrum of a star . For closer objects, this allows the speed of the object in the direction of the line of sight to be determined using the Doppler effect . This fact is used in the search for exoplanets as a radial velocity method. For objects that are further away, the redshift based on Hubble's law gives the distance of the object from the earth.

The line spectra of the gamma radiation allow the detection of small amounts of a radionuclide in many cases .

## Line spectrum in acoustics and electrical engineering

An acoustic line spectrum contains one or more discrete frequencies (DIN 13320). Periodic sound processes generate a line spectrum, aperiodic or stochastic sound processes a continuous spectrum (band spectrum). A typical example of a line spectrum is the sound spectrum or a periodic signal (voltage or current).

With the line spectrum, each partial frequency of the signal is symbolized by a discrete spectral line. The frequency is represented by the position on the abscissa (frequency axis); the length of such a line represents the amplitude of the oscillation (amplitude spectrum) or the strength of a sound process (level spectrum). The frequency scale is usually divided logarithmically. Each spectral line (constant frequency, constant amplitude) represents an ideal harmonic (i.e. sinusoidal) oscillation (that is, for example, voltage). The associated phase spectrum represents the phase information (zero phase angle), e.g. B. the amplitudes of a voltage or a current. The amplitude and phase spectrum together describe a signal equivalent to its time domain representation.

## literature

• Dieter Meschede: Gerthsen Physics. 23rd edition, Springer-Verlag, Berlin Heidelberg New York 2006, ISBN 978-3-540-25421-8 .
• Thomas Görne: Sound engineering. 1st edition, Carl Hanser Verlag, Leipzig 2006, ISBN 3-446-40198-9 .