REPORT FOR ANALYTICAL CHEMISTS where : ΩΒ =
NOW 160 L/M—WAS 140 L/M Welch Duo-Seal No. 1402B IxKMTORR
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ANALYTICAL CHEMISTRY
solid angle of emission radiation collected by the measurement system (4ir is the number of steradians in a sphere). AF. T h e integrated energy ab sorbed per unit time per unit area, IA, for a continuum source is given by combining E q u a t i o n 7 with E q u a t i o n 6 for low optical densities and E q u a t i o n 8 with E q u a t i o n 6 for high optical density, just as in AA. T h e value of IA for a line source is given by combining E q u a t i o n 13 with E q u a t i o n 6 for low optical densities, and Equation 14 with E q u a t i o n 6 for high optical densities, just as in AA. T h e flame area for absorption in A F is, of course, given b y (L X I') and the area for fluores cence is given by (I X /')· The self-absorption factor, /„, is defined (3) (for the experimental system described by Figure 1) by : 2\/fa2 Λ = —7= X V Trk0L Δ λ 0 f ~[1 - exp(-kvL)] Jo
d\'
(20)
T h e integral in Equation 20 is given by E q u a t i o n 7 for low optical densi ties and by Equation 8 for high optical densities, assuming only resonance absorption-fluorescence, i.e., λο = λο'. If stepwise or directline fluorescence (18) is of importance (λο' > λ 0 ), then the k0 in E q u a t i o n 20 is different from the k0 for the ab sorption process, i.e., the λ0 and λ 0 ' for the primary absorption process and for the self-absorption of fluores cence differ. The Final Intensity Expressions for Low and High Optical Densities I n Table I, the intensity expres sions are given in terms of funda mental spectral parameters for low and high optical densities in AE, in AA (with line and continuum sources), and in A F (with line and continuum sources). These expres sions are obtained by combining the above expressions and simplifying. Discussion of Intensity Expressions
The Expressions. T h e variation of integrated intensities of absorption, emission, and fluorescence with various spectral, flame composi tional, and instrumental factors can
be readily determined by the expres sions in Table I. For any given atom and any given absorption, emission or fluorescence line, m a n y of the parameters in the intensity expressions are either constant (e.g., X, c, λ0, and / ) , are not extremely dependent on small changes in flame gas composition and temperature (e.g., a, A\D, and φ), or are dependent only on the instrumental system (e.g., I, L, V, Ioc, IL, ΩΒ, ΩΓ and s). The term δ (α, ν) depends not only on flame gas composition and tempera ture b u t also on the half-width (25) of the line source (see Equation 12). The only parameter which is ex tremely sensitive to flame tempera ture is Ιχ0Β (see Equation 18). Growth Curve Plots. I n Figures 3 and 4, growth curves for AA, AE, and A F are given for a typical atom in a typical analytical flame. The growth curves consist of plots of integrated intensity (IE V In2/I^B X Δ λ β in AE, a in AA, and IF/(Ωί./47Γ)φ Ioc Δ λ 0 with a continuum source orIF/(QF/4:w) IL with a line source in AF) vs. some function of atomic concentration (N0fl/b, where b =
TTCAXO/X^VMÎ).
For all three flame spectrometric methods, the growth curves h a v e a slope of unity for low optical densities which is the most useful analytical region. No a t t e m p t was made to extend any of the growth curves to the limiting detectable atomic concentration since they depend upon the specific instrumental system used for measurement {26-28). Growth Curves in AA. When using a line source, the growth curve is essentially independent of instrumental conditions (except for t h e source line half-width, Δλ 5 ), whereas when using a continuum source, the vertical position of the grcwth curve depends directly on the spectral bandwidth, s, (see Figure 3). When using a line source in AA, the growth curve in the high density case asymptotically approaches an a of unity. However, when using a continuum source in AA, the growth curve appears to be approaching a n a of unity with a slope of 0.5. This, of course, is not correct, since ex's greater t h a n unity are not possible, and so our equation for AA with a continuum source at high optical densities must be invalid for a's near unity. For very high optical densi-
