leaving spark methods pre-eminent only in fields such as metallurgical analysis where matrix effects are
less important and where speed of analysis and simplicity of operation are of the greatest importance.
The intensity I of an atomic spectral line is related to the number n of atoms (not ions) present in the
discharge and to the temperature T of the discharge by the equation
where A is the transition probability, g 2 is a statistical weighting factor associated with the Maxwell-
Boltzmann equation (p. 275), h is Planck's constant (6.6 × 10 –^34 J s), ν is the frequency of the emitted
radiation, b is the diameter of the discharge in the direction of the detector, α is the degree of ionization,
∆E is the difference in energy between the two levels associated with the transition and B is a constant
at a given temperature. Under constant excitation conditions, n is proportional to C, the concentration of
the analyte and therefore
where k' is a constant.
Equation (8.2) also holds for an ion line under constant excitation conditions. In practice, an internal
standard should always be used because of the complex nature of the relation between I and C. The
internal standard line and the analyte line should have similar wavelengths and intensities so as to be
affected in a similar manner by changes in excitation conditions. A pair of lines fulfilling these
requirements is known as an homologous pair. Spectra of a series of standards each containing a fixed
amount of the internal standard are recorded. A major constituent of the sample sometimes fulfils the
role of an internal standard as its concentration can be considered to be constant. The ratios of readings
for the homologous pair are then plotted against the amount of analyte in the corresponding standard to
produce a calibration or working curve. Figure 8.6 shows such a curve for the determination of
magnesium using molybdenum as an internal standard. The homologous pair are Mg at 279.8 nm and
Mo at 281.6 nm. The corresponding ratios are calculated for samples and the concentration of
magnesium determined from the working curve. Precision is in the range 3–10%, direct reading
spectrometers and spark or plasma sources giving the most reliable data.
Applications of Arc/Spark Emission Spectrometry
Arc/spark emission methods have been widely used for the determination of metals and some non-
metals particularly as minor and trace constituents. In recent years, however, the technique has been
extensively displaced by atomic absorption spectrometry, and plasma emission methods. Detection
limits for many elements are of the order of 1–10 ppm (Table 8.3) and as