Page 92 - An Introduction to Analytical Atomic Spectrometry - L. Ebdon

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If self-absorption is neglected for a system in thermodynamic equilibrium:

A similar result is more readily, if less rigorously, obtained if we assume that virtually all the atoms
remain in the ground state (the strength of this assumption can be seen in Table 4.1). Thus, Eqn. 4.2
becomes

and Eqn. (4.1) becomes

This is similar to Eqn. 4.5 for practical purposes and the reader may prefer this simplified derivation.

Thus, the intensity of atomic emission is critically dependent on the temperature. It also follows that
when low concentrations of analyte atoms are used (i.e. when self-absorption is negligible), the plot of
emission intensity against sample concentration is a straight line.

4.1.2 Broadening

The result of a radiative atomic transition from an upper to a lower energy level is radiation at a
particular wavelength, as defined by

where h is Planck's constant and c is the velocity of light in vacuo.

However, atomic lines are not infinitely thin as would be expected and their width is discussed by
talking about half-width (Dv cm ), illustrated in Fig. 4.2a.
-1
Natural broadening occurs because of the finite lifetime (t) of the atom in the excited state.
Heisenberg's uncertainty principle states that if we know the state of the atom, we must have
uncertainty in the energy level. We assume that t for the ground state is infinity and therefore for a
resonance line the natural width Dv = ½pt.
N
Doppler broadening arises from the random thermal motion of the atoms relative to the observer. The
velocity V of an atom in the line of sight will vary according to the Maxwell distribution, the atoms
x
moving in all directions relative to the observer. The frequency will be displaced by