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Atomic Emission Lines Shapes

Emission intensity and absorption

In optical spectroscopy we usually consider a “spectrum” to be an intensity measurement as function of the wavelength of frequency. Here we can distinguish between an emission spectrum, and an absorption spectrum. In both cases we describe the light intensity as a function of the wavelength or frequency. The term spectrum is, however, used more generally. In XRD (X-ray diffraction) the radiation intensity is expressed as a function of the diffraction angle, the radiation used for the experiment being monochromatic. Mass spectrometry expresses the ion count rate as function of the ion mass, more precisely as a function of mass to charge ratio, the result is called a mass spectrum. In mathematics, a spectrum is understood as a collection of pairs of numbers associated with a mathematical object, i.e. an operator.
A typical optical emission spectrum is composed of lines, wavelength (of frequency) intervals showing an intensity significantly different from zero, or the background radiation. These lines are characterised by their shape: how the intensity varies with the frequency (wavelength) and their “overall intensity”, which is often expressed as the peak, or maximum, intensity or alternatively as the integral intensity or line intensity.

Emission spectra

If we consider atomic optical emission spectra, the lines are caused by atomic transitions emitting photons of a given energy. Each line observed, may be caused by a single transition or by several transitions generating photons of “similar” energies which can not be distinguished by the spectrometer used for the experiment.
The emission intensity ‘IL of a given line in the spectrum, not considering absorption for the moment and concentrating on single transition lines, depends on the population of the upper state and different factors specific for each transition:

  • Einstein coefficient for spontaneous emission or oscillator strength
  • Multiplicity of the states involved in the transition

The emission intensity varies with the emission frequency. As line intensity ‘IL‘ we define the frequency integral of the frequency dependent emission intensity.

Lineshape factorLineshapefactor

We can now define a dimensionless magnitude, the line shape factor ‘L(n)’, as given by the equation to the left.

The line shape factor can be understood as normalised emission intensity, its frequency integral is unity by definition.
The line shape factor becomes interesting when dealing with spectra composed of lines with having all the “same” shape. It allows characterising the multitude of observed lines by their individual line intensity and the common line shape factor.
A different use of the line shape factors is when the actual line shape, but not the line intensity is of interest. This is the case for example when different “broadening” effects are studied such as pressure broadening, Stark broadening, Doppler broadening. The effect of absorption on the line shape factor is being discussed later.

 typical lineshapes

[Line profiles: Gaussian, Lorentzian, Voigt]

The natural width (Lorentzian profile) of an emission line is governed by the Heisenberg uncertainty principle and is determined by the lifetime of the excited state. The lifetime in turn depends on the sum of all the ATPs from the level. The physical linewidth (Voigt profile) is the natural width plus various broadening processes such as Doppler (Gaussian) and pressure broadening (Lorentzian). The measured linewidth is the physical width plus the effect of the spectrometer slits.

When we scan across an emission line with a spectrometer, there are many factors that determine the shape of the line we see.

At the origine is the natural line shape, which can be altered by the Doppler effect and pressure broadening. These are linked to the object we are looking at. The spectrometer used for the observation will again alter this line shape.

First published on the web: 09. 01. 2008.

Author: Thomas Nelis. The text resumes topics presented by Prof. E.B Steers during the first GLADNET Training course held in Antwerp, Be, in September 2007.