where Iv is the intensity of the transmitted radiation at frequency ν and kν is the corresponding
absorption coefficient. The value of kν is determined by the concentration of atoms which can absorb at
frequency ν and is given by the expression
where m and e represent the mass and charge of the electron, Nν is the number of atoms per cm^3 capable
of absorbing radiation of frequency ν (i.e. ground state atoms) and f is the oscillator strength, defined as
the number of electrons per atom capable of being excited by the incident radiation. Hence, for
transitions from the ground state, the integrated absorption is proportional to Nν, which approximates to
the concentration of the element in the sample.
Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000–
3000 K, the overall line width is about 10–^2 nm which is extremely narrow when compared to
absorption bands observed for samples in solution. This is to be expected, since changes in molecular
electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with
solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall
width of an atomic absorption line is determined by:
(1) The natural width (about 10–^5 nm).
(2) Doppler broadening, caused by the thermally induced movement of atoms relative to the
spectrometer. (This is analogous to the apparent change in pitch of a train whistle as it approaches and
passes an observer.)
(3) Collisional or pressure broadening and resonance broadening. These are caused by collisions
between unlike and like atoms respectively in the sample vapour. Only the former is significant in
flames.
(4) Stark and Zeeman broadening caused by electric and magnetic fields respectively set up within the
sample vapour and which perturb atomic energy levels.
In flames, only Doppler and, to a lesser extent, collisional broadening contribute significantly to the
overall linewidth.
To make accurate measurements of the integrated absorption associated with such narrow lines requires
that the linewidth of the radiation source be appreciably smaller than that of the absorption line. In
practice, this could be achieved with a continuum source only if expensive instrumentation of extremely
high resolving power were used, and it is doubtful whether conventional photomultiplier detectors
would be sufficiently sensitive at the resulting low radiation intensities. An alternative arrangement is to