ments are obtained within a few seconds, the contribution of organic phosphate to the measured values should be very small. Further work on this aspect is under way. Ionic strength variations were seen to have little effect on the measured reaction rates. Phosphate standards prepared in 3000 ppm NaCl gave the same rate as deionized water standards. Alternate Analysis Procedures. The rate measurements described here can be made manually by determining the Comparable slopes of recorded absorbance vs. time curves. results can be obtained; but the automatic procedure is less time-consuming and less subject to operator bias. Alternatively, the variable time procedure (6) can be used in which (6) W. J. Blaedel and G. P. Hicks, “Advances in Analytical Chemistry and Instrumentation,” C. N. Reilley Ed., Vol. 3, Wiley, New York, 1964, pp. 130-3.
the time interval is measured for a fixed absorbance change. Generalizations. The automatic reaction rate method should be applicable to other phosphate-containing materials. In addition, it should be possible to eliminate many interferences in the classical molybdenum blue procedure by the rate method. For example, silicate reacts with molybdate and a reducing agent to give a similar blue product, whose rate of formation can be made negligibly slow in comparison to the rate with phosphate by proper control of pH. Hence a kinetic separation or a differential kinetic analysis of phosphate and silicate is possible. Preliminary work in this area is under way.
Received April 3, 1967. Accepted June 2, 1967. Presented at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1967.
Selection of Wavelengths for Atomic Absorption Spectrometry Marvin Margoshes Spectrochemical Analysis Section, National Bureau of Standards, Washington, D. C.
The theoretical basis for the absorption of light by atoms is examined for atomic absorption spectrometry A with a line source and with a continuum source. method is described for selection of wavelengths to be measured from published atomic constants. The most sensitive line can be selected; but if the absorbance measured with this line is too large, another line having an appropriate sensitivity can be chosen. The methods have been tested with published data for atomic absorption spectrometry with hollow cathode lamps and with new data for atomic absorption specIn both cases, trometry with a continuum source. the accuracies of the predictions are adequate for the purpose of line selection. Examples are discussed for which the theory does not agree with experiment.
20234
The purpose of this publication is to describe simple methods for predicting the relative sensitivities of two or more absorption lines of the same element. The predictions are shown to be in agreement with experimentally determined relative sensitivities in most cases. However, instances are also discussed of disagreement between predicted and measured relative sensitivities. Often, such differences can be anticipated when the causes of disagreement are understood. In general, the selection of lines by the methods here described can best guide for experimental measurements, rather than as replacement for experiment.
serve as a a
THEORY
for measurement in atomic abSelection of a wavelength sorption spectrometry is ordinarily based on published data on suitable lines or on direct measurements on a number of lines of the analyte (element being determined) of either the concentration required to give a selected absorbance or the absorbance at a fixed concentration. Direct measurements on many lines are time-consuming, and reliance on published data may not result in the selection of the best possible wavelength. Differences in instrumentation must be taken into account, and the necessary information may not be given in the literature. For example, the most sensitive line of an element may be in a wavelength region that was not accessible with the spectrometer employed in the original measurements. The particular filler gas in the hollow cathode lamp is an experimental variable which can affect the choice of wavelengths, because the gas may have emission lines nearly coincident with one or more lines of the analyte. When there are such adjacent interfering lines, either from the filler gas or the analyte, the spectral band pass of the spectrometer becomes an important factor. When two or more analytes are to be determined in the same solution, it will not always be possible to make use of the most sensitive line of each element, as only a limited concentration range can be covered with a particular absorption line. There has been little information published on wavelengths suitable for the determination of elements present at high concentrations.
The Beer-Lambert law states that the absorbance, A, is equal to 0.43 abc, where 0.43 is the log u,e, a is the absorptivity, b is the absorption path length, and c is the concentration of the absorbing species. In practice, the factor 0.43 is often in-
corporated into the absorptivity. This law will hold only when the absorptivity is constant over the band pass of the spectrometer, and it will be only approximately correct for atomic absorption spectrometry where the band width, which is effectively determined by the width of the emission line from the hollow cathode lamp, is comparable to the absorption line width in the flame. If the absorbance is measured over the entire width of the absorption line, then a is equal to /,¡tc1 2/otc, where fa is the oscillator strength for the transition from the lower energy level, i, to the upper energy level, j, e, and m are charge and mass of the electron, and c is the velocity of light
. When the lower energy level is the ground state of the atom, the concentration of the absorbing species is simply the population in the flame of atoms in the ground state, N0. For absorption lines due to transitions from energy levels above the ground state with an energy Ei, the population, N{, of
(1) H. G. Kuhn, “Atomic Spectra,” Academic Press, New York, 1962, p. 63. VOL. 39, NO. 10, AUGUST 1967
·
1093
Figure 2. Relation between gf-values and absorbances at concentration of 50 ppm for absorption lines of molybdenum
a
Av is the width of the rectangular line in frequency units. In the limiting case of I 0, Av is called the equivalent width of the line. At low line intensities, the equivalent width is proportional to Nif¡i. At higher intensities the curve flattens out and the equivalent width increases only slowly with increasing Nf but at very high intensities the equivalent width becomes proportional to Nll2f. Identical statements can be made if, instead of selecting a hypothetical line for which / 0, a fixed Av is chosen and the fractional absorption is plotted in place of the equivalent width. This corresponds to and defines the shape of the analytical curve for atomic absorption spectrometry with a continuum source, provided that the band pass of the spectrometer is larger than the line width. In order to compare lines at different wavelengths, the variation of Av with wavelength must be taken into account. The frequency of light is inversely proportional to the wavelength, v c/ , so Av cA\/X2 by differentiation, and Equation 3 can =
Figure 1. Correction factor to be applied for wavelength-dependent error in the tables of gfvalues
atoms in the appropriate excited state is given by the Boltzmann
relationship:
Ni
=
Nfgi!g0)exp(— EJkT)
(1)
where gt and g„ are the statistical weights of the excited state and the ground state, k is Boltzmann’s constant, and T is the temperature of the flame. The Beer-Lambert law can now be rewritten in the form A
=
[email protected](— E(lkT)
(2)
where if is a constant equal to 0.43t:t2 3¡mc. K, g0, and b are all constants for a particular element and a given experimental arrangement, and it is possible that at a constant N0 (effectively a constant analyte concentration in the test solution) the absorbances for a series of lines of an element will be linearly proportional to gf exp (—EjkT). Similarly, the concentrations of the element which will produce a selected absorbance for a series of lines may be proportional to the same group of factors. The fit of experimental data to the prediction will be primarily a test of the validity of the assumption that the effective absorptivity is proportional to the oscillator strength. A different theory applies to atomic absorption spectrom-
etry with a continuum source. Absorption of light from a continuum by atoms is described by the curve of growth (2). The actual absorption line can be considered to be replaced by a hypothetical line of rectangular profile which will absorb the same amount of energy from the continuum. The energy absorbed by such a rectangular line, AE, is given by (3).
AE
=
[(Ia
-
I)/I0]Av
(3)
=
=
=
be rewritten as
E
=
c[(/„
-
/)//0]( / 2)
(4)
For a grating monochromator with very narrow slits, / should be approximately constant, and AEwill be proportional to [(/0 I)/I0)]/X. Therefore, a curve corresponding to the curve of growth may be obtained by plotting the fractional absorption (or the percent absorption) vs. NfX, or, introducing the Boltzmann relation, gfCX. —
RESULTS a test of the method outlined above for the selection of lines for the case of hollow cathode line sources, some measured values of relative sensitivities taken from the literature have been plotted as a function of the gf values given by Corliss and Bozman (4). The tables of Corliss and Bozman are the most extensive listings available of gf values, and they have a claimed accuracy as relative values of ± 40 to 50 %, which is adequate for this purpose. However, the values are known (5) to be too low at short wavelengths. A correction for this wavelength-
As
where I0 and I are the incident and transmitted intensities, and (2) L. Goldberg and L. H. Aller, “Atoms, Stars, and Nebulae,” The Blakiston Co., Philadelphia, 1943, pp. 102-12. (3) R. B. King and A. S. King, Astrophys. 87,24 (1938).
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ANALYTICAL CHEMISTRY
(4) C. H. Corliss and W. R. Bozman, “Experimental Transition Probabilities for Spectral Lines of Seventy Elements,” National Bureau of Standards Monograph 53, U. S. Government Printing Office, Washington, 1962. (5) C. H. Corliss, Spectrochim. Acta, 23B, in press.
IRON CONCENTRATION, ppm Figure 3. Relation between gf exp(—E/kT) and iron concentration required to give an absorbance of 0.1
dependent error has been developed by Corliss (5), as shown in Figure 1. The gf values in the tables of Corliss and Bozman are apparently unaffected by the error to wavelengths as short as 2450 Á but are too low by a factor of about 50 at wavelengths near 2100 Á. Multiplying the listed gf values by correction factors taken from Figure 1 has been found to give reasonable results in this application. Figure 2 is a plot of the gf values for a series of lines of molybdenum as a function of the absorbances given by David (6) for a fixed molybdenum concentration of 50 ppm. All lines originate from the ground state, so it is not necessary to include the exponential term. The points lie on a straight line within the claimed accuracy of the gf values. Figure 3 is a plot of gf exp (—E/kT) vs. the concentration of iron in ppm required to give an absorbance of 0.1, according to the data of Allan (7). Because of the large range of values covered, a logarithmic plot has been made. A flame temperature of 2000° K was assumed. Again, the data fit a straight line of unit slope within the accuracy of the gf values. Figure 4 is a plot for cobalt, with the data of Harrison (8) on the absorbance at a fixed cobalt concentration of 50 ppm. For this element, three lines gave absorbances which were significantly lower than would be expected from their gf values. The largest deviation is for the cobalt line at 2309.02 Á, which is nearly coincident with a line at 2309.16 A from the argon filler gas in the hollow cathode lamp used by Harrison. The second largest deviation is for the line at 2274.49 Á, which is close to another cobalt line at 2274.61 A which does not have the ground state as the lower energy level. Such interferences can be predicted, if the resolving power of the spectrometer is known, by reference to standard tables of spectral lines. The third line for which there is a large deviation, at 3474 A, represents a more complex case. There is a pair of coincident cobalt lines at this wavelength, one of which has the ground state as the lower energy level while the other has a lower energy level at 4690 K (9). Corliss and Bozman, in calculating the gf (6) D. J. David, Analyst, 86, 730 (1961). (7) J. E. Allan, Spectrochim. Acta, 15, 800 (1959). (8) W. W. Harrison, Anal. Chem., 37, 1168 (1965). (9) W. F. Meggers, C. H. Corliss, and B. F. Scribner, “Tables of Spectral Line Intensities. Part I. Arranged by Elements,” National Bureau of Standards Monograph 32, U. S. Government Printing Office, Washington, 1961.
Figure 4. Relation between gf exp (—E/kT) and absorbance at a cobalt concentration of 50 ppm
Figure 5. Relation between g/XC and per cent absorption for six lines of manganese, using a continuum source
values from emission intensities, assigned all of the intensity to the lower-energy transition (10), so that the gf value is incorrect. Fortunately, such instances of coincident lines are rela-
tively rare. No suitable data could be found in the literature on the relative sensitivities with various lines of an element with a continuum light source. As a test of the theory for this case, measurements were made for a series of six resonance lines of manganese, one group of three lines near 2795 A and another group of three near 4030 A. The measurements were made with solutions containing 0.03, 0.1, 0.3, 1, 3, and 10 ppm of manganese sprayed into a total-consumption burner with an oxygen-acetylene flame. The light source was a high-pressure xenon lamp, and the monochromator was a 0.75-m FastieEbert mount with a 1200 groove/mm grating and 10-µ entrance and exit slits, giving a measured resolution of about 0.15 Á. Figure 5 shows the results of the experiment. The curve closely approximates the curve of growth, except that the expected region showing a dependence of the per cent absorption on C1/2 was not found. At the high concentrations needed to produce these large per cent absorption values, it may be that the band pass of the spectrometer is too narrow to take in the (10) C. H. Corliss, National Bureau of Standards, Washington,
D. C., private communication, 1966.
VOL. 39, NO. 10, AUGUST 1967
1095
0 and exp(—E/kT) straight line, with one fixed point at E 1. It is therefore necessary to calculate the exponential term for only one value of E at the appropriate flame temperature in order to prepare the graph. It is not necessary to use an exact temperature, since the predictions are only approximate. In preparing Figures 3 and 4, a flame temperature of 2000° K was =
Table I.
Comparison of Theory with Experiment for Atomic Absorption Spectrometry with a Plasma Torch Ratio of Ratio of sensitivities Absorption
Element
lines, A
gf values
(73)
A1
3092.7 3961.5
2.5
1.0
Ti
3642.7 4667.6
21
0.75
3635.5 5173.8
14
1.0
3653.5 4681.9
20
0.75
Y
3620.9 4102.4
1.1
1.0
4077.4 4643.7
9.1
1.0
wings of the lines, so that the theory no longer applies. However, it is the lefthand side of the curve which is most important for atomic absorption spectrometry, and the theory seems to apply here within the errors of the gf values. The systematic difference between the results obtained for the two sets of lines may reflect errors in the gf values. When a similar plot is made with the gf values for manganese reported by Ostrovskii and Penkin (1 /), an equally good fit is obtained but the points for the lines near 4030 A fall to the left of the points for the lines near 2795 A.
DISCUSSION
The theories derived and experimentally demonstrated above provide the basis of an easy and reasonably accurate prediction of which line or lines of an element would be most suitable for atomic absorption spectrometry. If the most sensitive line of the analyte is too strongly absorbed at the range of analyte concentrations in the samples, a line having appropriately smaller sensitivity can be quickly chosen. It must be recognized that the criterion for sensitivity adopted in this study, and most often employed in atomic absorption spectrometry, is less meaningful than measurement or calculation (72) of the limit of detection in terms of the concentration required to give a chosen ratio of signal to noise. In many cases, however, either criterion will lead to the selection of the same line. Rather than calculating exp(— E/kT) for each lower energy level above the ground state, it is helpful to prepare a graph of the exponential term as a function of E. A plot of the exponential term on a logarithmic scale vs. E on a linear scale is a (11) Yu. I. Ostrovskii and N. P. Penkin, Op!. i Speklroskopiya, 3, 193 (1957). (12) J. D. Winefordner and T. J. Vickers, Anal. Chem., 36, 1939 (1964).
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ANALYTICAL CHEMISTRY
=
assumed.
The simple theories outlined above cannot predict relative sensitivities for different elements or for different experimental arrangements. The proportionality between the analyte concentration in solution and the number of atoms in the flame is different depending on the element and on the construction of the atomizer, the temperature of the flame, and other factors. No attempt has been made to correlate sensitivities for atom and ion lines of the same element, but this would be possible if the degree of ionization in the flame were known. The theory does not correctly predict the measured relative sensitivities for atomic absorption spectrometry with a plasma torch, as given by Wendt and Fassel (73). The temperature of the torch is not known, so that not all of the data given by Wendt and Fassel can be used for this comparison. Table I lists the data for those line pairs measured by Wendt and Fassel which share a common lower energy level. For each pair, the table lists the ratios of the measured sensitivities (concentrations to give 1 % absorption) and the ratio of the gf values. Both ratios should be the same within the errors of the gf values. Of the six pairs listed, only one gives satisfactory agreement. The disagreement between theory and experiment cannot be explained by any identifiable error in the measured sensitivities. In several cases, there are other lines close to the lines being measured that would be emitted by the hollow cathode lamp and that could affect the measurements. However, tracings of the emission spectra of the hollow cathode lamps show that, in all cases, the possible interfering lines are much lower in intensity than the lines being measured (14), and therefore cannot account for the discrepancies. It is possible that, for the conditions in the plasma torch, the assumption is not valid that the absorbance is equal to /,·< 62/ me, even though Figures 2, 3, and 4 indicate that the assumption is valid for normal flames. This assumption will be invalid, for example, if the widths of the absorption and emission lines are not similar.
ACKNOWLEDGMENT
I am grateful to V. A. Fassel for providing detailed information on the emission spectra of the hollow cathode lamps employed in the atomic absorption measurements with the plasma torch. Received for review March 2,1967. Accepted May 17, 1967. (13) R. H. Wendt and V. A. Fassel, Ibid., 38, 337 (1966). (14) V. A. Fassel, Iowa State University, Ames, Iowa, private
communication, 1967.
