The spectral lines observed in the absorption and emission spectra of atoms or molecules are the result of transitions occurring between different energy levels as electromagnetic radiation is absorbed or emitted. The frequency ()and wavelength (&lgr;) of this electromagnetic radiation are related through the following equation: = c/&lgr;, where c is the speed of light. Thus, UV light absorbed at 3,000 angstroms (Å) corresponds to a frequency of (2.96 x 10 10 cm/sec) / 3 x 10-5 cm = 1015 sec-1 = 1015 hertz (Hz).
The variable that can be most accurately measured is &lgr;. However, it is the frequency that is directly related to the energy, so spectroscopists usually locate the position of spectral lines using a unit called the wavenumber, which is inversely proportional to the wavelength and is represented by . Thus, if &lgr; is measured in cm, is then measured in cm-1 and is equal to the number of waves in one centimeter. A wavelength of 3,000 Å is then equal to: the number of angstroms in one cm/&lgr; = 108 /3 x 103 = 33,333 cm-1 .
A typical spectrum consists of a recording of the intensity of spectral lines as a function of wavelength. The position of the observed spectral lines will depend on the energies associated with the transition. Planck's equation, E = h, where h is Planck's constant, states that electromagnetic radiation of frequency occurs in small, discrete units called quanta, or photons, and that the amount of energy any one of these quanta contains, h, is directly proportional to the frequency. Thus, if electromagnetic radiation is absorbed by a molecule or atom, the energy of the quantum absorbed is equal to the difference in energy between two states of the molecule or atom. A wavelength of 3,000 Å then corresponds to an energy equal to E = 6.626 x 10-34 joule sec x 1015 sec-1 = 6.626 x 10-19 joule. The absorption of electromagnetic radiation at 3,000 Å will then result in observation of a spectral line, which is the result of a transition between energy levels separated by the above calculated energy and whose width is determined by the Heisenberg uncertainty principle. The spectral lines will be observed unless forbidden by the transition selections rules which that are for the most part governed by symmetry and formulated within the framework of molecular orbital theory.
The spectral lines are always broadened, partly due to the finite resolution of the measuring spectrometer and partly due to Doppler and pressure broadening. Doppler broadening is due to the thermal motion of the emitting atoms or ions. For a Maxwellian velocity distribution, the line shape is Gaussian; the full width at half maximum intensity (FWHM) is, in Å, equal to: FWHM= (7.16 x 10-7 &lgr; (T/M)1/2 ).
Where T is the temperature in K, and M the atomic weight in atomic mass units (amu). Pressure broadening is due to collisions of the emitters with neighboring particles and the lineshapes are often Lorentzian.
The electromagnetic spectrum ranges from the higher energy far ultraviolet (&lgr; = 10 to 200 nm; = 30,000 to 1,500 x 10-12 Hz) to the lower energy microwave region (&lgr; = 300,000 to 106 nm; = 1 to 0.0003 Hz). The absorption of radiation from the more energetic region, i.e., the far UV, near UV and visible regions, by molecules or atoms will result in electronic transitions, i.e. the promotion of their electrons to higher energy electronic levels. Absorption of lower energy photons, i.e., from the infrared region will result in vibrational or rotational motion of the constituent atoms of a molecule. Thus, the spectral lines observed in UV visible spectroscopy are due to electrons being promoted to higher energy levels while those recorded by infrared spectroscopy correspond to bond bending and stretching vibrations. The spectral lines observed in spectra thus provide information about the electrons and their arrangement in a given atom or molecule, just as the lines recorded in a vibrational spectrum will be indicative of the molecular geometry of the material. As such, they represent one of the most powerful tools available to investigate the fundamental properties of matter.
Some specific examples are the atomic spectral lines observed for a given gas which can reveal its elemental composition and concentration, since there is a direct relationship between the intensity of spectral lines and the amount of absorbing or emitting species present. This is how the composition of intergalactic gases has been identified.
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