Precision of Flame Atomic Absorption Measurements of Arsenic, Cadmium, Calcium, Copper, Iron, Magnesium, Molybdenum, Sodium, and Zinc N. W. Bower and J. D. Ingle, Jr.* Department of Chemistry, Oregon State University, Corvallis, Ore. 9733 1
Procedures for evaluating the precision of atomic absorption measurements have been improved and applied to 9 elements. Measurementson a Varlan AA-6 spectrophotometerindicate that there are many similarities in the precision characteristics of different elements. For instance, analyte absorption flicker noise limits the measurement precision of most elements at moderate absorbances. The actual value of the measurement precision at a given absorbance and the dependence of measurement precision on absorbance depend upon the caiibration curve, the wavelength of analysis, the integrationtime, and the type of flame employed.
Precision characteristics of atomic absorption (AA) spectrophotometers for different elements must be established if analyte concentrations and the instrumental parameters are to be optimized for a maximum signal to noise ratio (S/N). A knowledge of the nature and sources of imprecision of an analysis are necessary if systematic improvements are to be made in the performance of the instrument. Based upon theoretical considerations ( I ), the authors have recently presented a procedure (2) for the determination of the precision characteristics of AA measurements. For copper, the magnitude of noise from each possible source was determined and the relative contribution of each noise source to the total precision was established under a variety of instrumental conditions. In this paper, the precision curves (plots of the relative standard deviation in absorbance ( ~ A / Avs.) absorbance ( A ) ) for a representative sampling of elements are presented to demonstrate the similarities and differences of the effects of various sources of noise under normal experimental conditions. The theoretical equations and evaluation procedure discussed allow one with a few measurements to predict accurately the experimental measurement precision as a function of absorbance. Typical values of noise parameters are given and should be applicable to most modern AA instruments.
EXPERIMENTAL A Varian AA-6 spectrophotometer was used with an external voltmeter and computer to obtain all the data. A Spectrum model 1021 amplifier was connected between the 100-mVAA analog output and the 100-kHdVV/F converter (Analog Devices 4701) to prevent loading of the analog output and to provide a factor of 10 amplification to yield 0.001 %T readout resolution. The V/F converter was connected to a frequency counter (Data Precision model 5740) whose BCD output was interfaced to a PDP-11/20 computer and processed as previously described (2). Instrumental variables (e.g. hollow cathode current, spectral bandpass) were generally those specified in the Varian manual and are summarized in Table I. The flame height was adjusted for maximum absorbance. Westinghouse hollow cathode tubes were used for all measurements. Thirty 1-s measurements were made for Ca, Fe, Mg, Na, Zn, Cd, Mo, and As solutions. Mg and Ca were run in both NzO/CzHz and air/CzHz flames to demonstrate the effect of the type of flame on noises due to the flame such as background emission, flame transmission, analyte emission, and analyte absorption noise. Ten 1-s and 574
*
ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
ten 10-s measurements were also made on Cu to demonstrate the effect of integration time on precision. Measurements of U A / Ain some cases were also made, as previously described ( 2 ) ,with filters between the hollow cathode tube and focusing lens to simulate analyte absorption. This provides a means to test the validity of Equation A-1 when certain noise sources are limiting as well as a way to separate experimentally the contributions from different noise sources. The evaluation procedure outlined previously (2) was followed, except where noted below, to obtain the precision plots presented here. The secondary emission factor (01) (step 16 in reference 2) was evaluated ( 3 , 4 )from the formula 01 = (6 - l ) - I where 6 is the gain of a dynode stage in a photomultiplier; 6 is found from the measured photomultiplier gain m and the formula m = g r l where n is the number of dynodes. In the original procedure ( 2 )it was suggested that the analyte absorption flicker factor, &, could be evaluated from Equation 15 in reference 2 and the experimental standard deviation in the sample signal (u,t), measured with a solution yielding an absorbance of 1.This procedure is not satisfactory because [3 varies with analyte concentration and absorbance. A better procedure is to evaluate €3 as before but at a concentration where the calibration curve is linear and analyte absorption noise is dominant. This is usually the case at an absorbance of about 0.2. 4 3 at other absorbances is calculated from the value of the flicker factor measured at an absorbance of 0.2 and the slope of the calibration curve as shown in Equation 1
where ( & ) A = o 2 = €3 at an absorbance equal to 0.2 and mA = measured slope (Le. dA/de) of calibration curve at given absorbance A or concentration e. The justification for Equation 1 can be seen from Figure 1. If one assumes that the relative standard deviation of the viewed analyte free atom population (u,,/no) is independent of the analyte concentration, and that analyte absorption flicker noise is related to fluctuations in the free atom population of the analyte (no)in the part of the flame viewed, f 3 (and hence UA/Aunder analyte absorption noise limited conditions) should be a constant for A a no (Le., a linear calibration curve). However, for calibration curves which exhibit a negative deviation, the fluctuations in the free atom population will have a smaller relative effect on the observed fluctuations in absorbance at absorbances where the calibration slope is smaller. In Figure 1, for example, the relative fluctuation in free atom population is assumed to be 0.1 and the curve is drawn so that the slope at no = 4 is half of that at no = 2 (mA at no = 4 is one-half of mA at no = 2). As can be seen, UA/Ais lower at the higher A . For this specific case, ( & ) A = o 2 = 0.1 and U A is the same at no = 2 and 4 while A increases by a factor of 1.6. The experimental precision plot is made exactly as specified with Equation 2 in reference 2. A calibration plot is also constructed from the mean absorbance values for each concentration,and the slope of the curve at each measured absorbance is estimated by calculating the slope from two values of the calibration curve which closely bracket the absorbance of interest. A theoretical plot is then made by evaluating Equation A-1 in the Appendix (Equation 1in reference 2) at different transmittances, where the variables are defined in the Appendix. All precision curves were plotted as U A / Avs. A although for a particular instrument and set of conditions a plot of uc/c vs. A or e would be more useful. UA/Aplots are more useful for comparing the different sources of noise between elements since the scale is the same. Also UA/A can be measured directly while U,/C must be calculated. Under analyte absorption noise limiting conditions in the data to be presented, the apparent increase in precision as absorbance in-
Table I. Instrumental Variables
Element
Wavelength nm
Na Ca Ca Cu Mo Mg Mg Fe Cd Zn As
589.0 422.7 422.7 324.8 313.3 285.2 285.2 248.3 228.8 213.9 193.7
Flame
Spectral bandpass, nm
Lamp current, mA
EPMT,"
Concn range, PPm
0.2 0.2 0.2 0.2 0.2 0.5 0.5 0.2 0.2 0.2
5 3 3 3 5 3 3 5 3 5 7
265 404 398 355 387 320 319 487 3551367 4281460 5781595
0.01-60 0.01-100 0.01-100 0.5-250 1-200 0.01-100 0.01-100 1-500 0.01-100 0.1-200 5-1000
1.0
v
For elements where the flame absorbs significantly, the voltage with and without the flame are given.
Table 11. Calculated Values8 mX lo3
Element Na Ca(Air) Ca(N20)
0.17 4.5 3.7 a 1.6 1.6
cu
Mo 3.1 Mg(Air) 0.74 Mg(N20) 0.74 Fe 16 Cd 1.612.0 Zn 6.2110.2 As 58/70
i,X
(Ur)q+,
10l3 ur( X lo4 urt X lo4 [I X lo4 240 8.8 11
2.5 7.0 9.3 4.8 3.1 7.0 3.5 3.5 15 5.0 8.5
25 25 13 54 54 2.5 25/20 6,413.9 0.6810.55 13
3.6 7.0 12 4.5 3.1 11
5.0 7.9 17 20 25 40
2.1 4.6 7.9 3.4 2.9 5.4 2.6 2.6 11
3.7 5.7
..
(2 X
lo4 f 2.6
... ... ... ...
9.0 3.8 7.0 8
20 23 31
lo4
x
1.3 5.4 4.9 3.4 1.1
4.6 2.3 2.3 9.8 3.7 6.3 18
uhe
uo( X lo4 u , , X ~ lo4
0.1 0.4 0.4
0.2 0.1 0.4 0.4 0.4 0.4 0.4 0.4 0.4
0.3 1.5 10 0.7 0.2 3.0 1.1 1.3 3.0 0.6 1.0 15
x
lo4
0.3 1.5 10 0.7 0.2 3.0 1.0 1.2
3.0 0.4 0.9 15
(t3)o 2 u, X
lo4
lo4
x
90 37 130 1.1 75 0.4 35 5.8 59 80 0 2.6 80 100 0 110 0 110 0 13.8 . . . 1.9 12 74
a Ten 1-s integrations. Ten 10-s integrations. For Cd, Zn, and As, the gain was increased to compensate for absorption losses to the flame. Calculated for an absorbance of 2.0, or for the highest concentration if A < 2.0. There is considerable error in the value (1 could not be calculated for As because ur( is totally limited by signal shot noise. f There is of for elements where = (u,)~+%; considerable error in the value of (2 where urt and ur( are within a factor of two; (2 was not calculated for some elements where urt = ur(. 8 E, = 1.00 V. G = 2.5 X los. K = 2.3-3.7 X A.
RESULTS AND DISCUSSION
OA
r
n0
Figure 1. Calibration curve demonstrating effect of negative deviation on u A / A
creases results in no real net improvementin precision for determining the analyte concentration (ue/c).From Equation 54 in reference 1, uc/c is equal to u,/A times AlmAc. Thus under analyte absorption noise limited conditions where UA/A= (3, o,/c = ( ( 3 ) ~ = 0 . 2 . Hence in Figure 1, Q/C would the same Le., 0.1) at both no = 2 and 4.
The precision plots for the elements tested are shown in Figures 2-5 and the pertinent calculated parameters and summary of experimental results are shown in Table I1 and 111, respectively. Table I1 provides a convenient means for comparing the magnitude of different noise sources for each element. Since the reference voltage is 1.0 V, urd, urt, E l , (2, (Ur)q+s, uOt,Ube and uod represent the noise in each component in terms of transmittance. Since ((s)a=o.z is expressed as a relative standard deviation in absorbance, its magnitude a t a given absorbance can be expressed in absolute transmittance units to compare to the other noises by multiplying by 2.3 A . This does not account for negative deviations however. If this calculation is made a t moderate absorbances, the dominance of analyte absorption noise over most of the absorbance range is clear. The theoretical calculations from Equation A-1 are plotted as smooth curves while the experimental data are plotted as individual points. Figure 2 shows typical precision curves for Na. The agreement between the theoretical plots a, b, and c and the experimental points is reasonably good which indicates the validity of the theory and usefulness of the evaluation procedure. The match for curve a is much better than previously obtained ( 2 ) when it was assumed that E3 was a constant. Comparison of curves a-d with each other makes it clear which noise sources are limiting. Analyte absorption flicker ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
575
I
1
zn
1.0
I
I
I
3.0
A Flgure 2. Precision plots for Na in air/CzHz flame (a) Precision with analyte solutions aspirating (all noise sources considered). (b) Precision with blank aspirating and absorbance simulated with filters (all noise sources except those due to the analyte considered). (c) Precision without flame and absorbance simulated with filters (all noise sources independent of flame considered). (d) Precision with all noise sources except analyte absorption noise considered
aio .07 .05
-
-
-
-
-
.O2
0.01
1
I
I
I
Figure 3. Solution precision plots (a) Mo. (b) Mg in air/CzH2 flame. (c) Mg in N20/C2H2flame. (d) Fe. (e) Cd. (f) Zn. (9) As
noise is limiting from about 0.1 to 2.0 absorbance units and analyte emission flicker noise is the second most significant noise from about 0.5 to 2.0 absorbance.units. Similar plots and agreement between theory and experiment were obtained for all other elements tested. Curves b and 576
ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
I
I
I
'"
2.0
3.0
A
11
Flgure 5. Precision plots for Cu in air/C2H2 flame (a) I-s integration time, all noise sources considered. (a') 10-s integration time, all noise sources considered. (b) I-s integration time, all noise sources except analyte absorption and emission noise considered. (b') 10-s integration time, all noise sources except analyte absorption and emission noise considered. (c) I-s integration time, all noise sources independent of flame considered. (c') IO-s integration time, all noise sources independent of flame considered
c are not included for most other elements but can be generated from the data in Table I1 and Equation A-1. T o construct curve a (included for all elements), the slope of the calibration curve and magnitude of the analyte emission noise over the desired absorbance range must be known. General Characteristics. The plots in Figures 2-5 indicate that all elements exhibit somewhat similar precision
Table 111. Summary of Results Best value of “AIA,
Element
%
A at which best value occurs
Na Ca(Air) Ca(N20) Cu(1 s) Cu(10 s) Mo Mg(Air) Mg(N2O) Fe Cd Zn
0.40
1.9
0.33
0.4 0.2
As
0.70
1.5 0.18
1.7
0.58 0.48
0.5 2.0 1.9 1.3 1.6
0.38 0.17 0.20
Limiting noises, 0.2 < A < 1.0
Limiting noises, A
> 1.0
1.7
0.07 0.50
Limiting noises,“ A < 0.2
1.1 0.6
If Criterion for limiting noises was that to be significant, a noise must have a variance at least noise.
characteristics. From about 0 to 0.1 absorbance unit, UA/A continually decreases and a combination of flame transmission flicker noise, source flicker noise, and signal shot noise limit precision. As can be seen from Table I1 by comparing the magnitudes of (1, (2, and ( c , ) ~ +all ~ , three noises are about the same size for most of the elements. However, for elements with resonance lines near 200 nm (As, Zn, Cd) where the flame exhibits significant absorption, flame transmission flicker noise is larger ((2 2 2 X lo-:?) and dominant. For such cases, the decrease in D A / Awith increasing absorbance is seen to be more gradual in the precision plots. For most elements, from about 0.1 t o 1 or 1.5 absorbance units, analyte absorption noise (&j) is limiting. Over this region U A / Awill be relatively constant, gradually decrease, or rapidly dip depending on the shape of the calibration curve. For instance, for elements such as Mg, Cu, and Na, which have calibration curves that are reasonably linear up to an absorbance of 1.0 or above, UAIAis essentially constant for moderate absorbances. At higher absorbances where the calibration curves decreases. For elements with calibration curves bend off, ~ A / A with a marked negative deviation before A = 1 (Cd, Fe, Zn), O A / A will continually decrease with absorbance correspondingly. Eventually a t higher absorbances of about 1.0-1.5, UA/A begins to continually increase with increasing absorbance as measurements become 0% T noise ( arlt)or analyte emission noise (ne) limited. In all cases, 0% T noise was totally or primarily limited by background emission noise ((T,,~ > no() and hence dark current noise and amplifier noise make little contribution to the precision of AA measurements for our apparatus. The absorbance a t which uAIA begins to increase varies considerably with the element as shown in the Figures and Table 111, and is a function of the relative amounts of background emission noise (variable from 0.003-0.15% T ) and analyte emission noise (variable from 0.00 to 0.74% T ) . Background emission noise is expected to be particularily large for elements whose resonance lines overlap regions of strong background emission from the flame or for elements with lower intensity lamps where higher photomultiplier gains or larger slit widths are required. The contribution to the noise due to flame background emission may also be significant for elements with small analyte absorption noise a t higher absorbances and for elements with weaker analyte emission (Le,, so that analyte emission noise does not dominate a t higher absorbances). Background emission noise should in general be greater for a N20/CzH2 flame than an air/CnH2 flame because of its higher background emission. The data in Table I1 support these predictions. In most cases, Uhe will be no more
I/{
of that of the most significant
than a factor of 2 to 4 greater than ur,(. utle is particularily large for Cain a N20/CzH2 flame because the Ca line sits on top of is large because 313 nm a strong emission band. For Mo, is in the intense OH radical bandheads, and for As and Fe it is large because of the large P M T gain and/or spectral bandpass required. Analyte emission noise ( ( l e ) increases with the size of the analyte emission signal and hence from the Boltzmann distribution will be more significant for elements with longer wavelength resonance lines. Experimentally its presence can be simply verified by demonstrating that the noise with analyte aspriating is larger than with blank aspirating when the lamp is off. In general ae will be significant for elements with h > 300 nm and increasingly more significant as h increases. Comparing the magnitude of ae in Table I1 to Dot confirms the above. Its effect will be relatively significant if other important noises at higher absorbances such as analyte absorption noise and background emission noise are small. Other factors besides wavelength are involved. For example, even though Na is a stronger emitter than Ca, the relative effect of analyte emission noise is less for Na because the Na lamp is more intense and a smaller P M T gain can be used. For As, although the resonance line is below 200 nm, the use of a larger P M T gain and spectral bandpass and a 1000-ppm solution a t the highest absorbance measured results in significant analyte emission a t the highest absorbances. For Ca it can be seen from Figure 4 that use of the hotter N20/CzHz flame is disadvantageous with respect to precision of analyses because of the greater magnitude of background and analyte emission noise. The emission noise from Ca is so large that a ~ 1 Abegins to increase before A = 1 in both flames. The magnitude of all noises would be expected to decrease for longer integration times (smaller noise equivalent bandpasses) until the point is reached where drift is significant over the time required to make the measurements to calculate standard deviations. This improvement is demonstrated for Cu for 1-and 10-s integration times as shown in the precision plots in Figure 5 and the tabulated noises in Table 11.Thirty consecutive 1-s measurements (not given) resulted in essentially the same precision plot as obtained for ten consecutive 1-s measurements. Shot noise in the lamp signal, background emission signal, and analyte emission signal would be expected to decrease by m a t the longer integration time because they are white noises. From Table 11, both background emission noise (“be) and analyte emission noise (a,) do decrease by about flas expected since the noises a t the modulation frequency should be primarily white noises. For non-fundamental flicker noises which often are l / f in character, the ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
577
improvement in precision would be expected to be less than fi.The data show that there is little improvement in lamp flicker noise ((1) but about a 50%decrease in analyte absorption noise. The effect of integration time on flame transmission flicker noise could not be determined here since it was not measurable a t either integration time. Since for most of the absorbance range, the precision of Cu measurements is limited by analyte absorption noise, 0% T noise (primary background emission noise), and analyte emission noise, the longer integration time provides a factor of 2-3 improvement in precision as seen in Figure 5. A similar improvement in precision with integration time has been noted by others (5). Specific Noise Sources. Lamp flicker noise, (1, is seen to vary from about 2-9 X lo-* for the elements tested. (1 might be expected to vary with lamp current, but for Na, (1 was essentially constant for lamp currents from 2 to 8 mA. For many elements ort > ur(, which indicates flame transmission noise is significant. In other words, the noise observed in the signal from the lamp increases when the flame is turned on. For most elements, 52 is no more than a factor of 2 to 3 greater than (1. For a given wavelength, ( 2 is expected to depend on the fuel and oxidant used, the fuel/oxidant ratio, and flame height. A Hz hollow cathode lamp was used to measure the flame transmission flicker factor (&) a t the As and Zn wavelengths with the same procedure used for metal hollow cathodes. The values of (2 measured agree well with the values obtained with the respective metal hollow cathodes. The source flicker factor ((1) for the Hz lamp is about 1 X and hence this lamp cannot be used to evaluate (2 for most elements since ( 2 < 1 X (1 for the H2 lamp is very dependent on lamp position in the turret holder and appears to be less for larger slit widths, possibly because a larger part of the sourue image is viewed. The flame transmission flicker factor was also measured for As in the air/CzHz flame and found to be 1.4 X lo+. This clearly points out the disadvantage of the air/CzHz flame compared to the more transmitting NzO/CzHZ flame for As and the general trend that & increases with flame absorbance. Analyte absorption noise is very important since it is limiting at moderate absorbances for all the elements measured except As. For As, flame transmission, background emission, and analyte emission noise are so large that analyte absorption noise is not observed. This flicker noise ( ( & ) ~ = 0 2 ) can be estimated for most elements to be about 0.5-1% for 1-s integrations a t absorbances of about 0.2 and to be independent of element type and flame. T h e variations of E3 with concentration can be estimated from slopes calculated from Calibration curves. The source of analyte absorption noise is elusive and it may actually be caused by a number of phenomena such as fluctuating solution aspiration rate, nebulization variations (i.e., different number or size of droplets entering the flame per unit time), fluctuating flame gas flow rates, fluctuating flame temperature, flame movement, and fluctuating air entrainment. Another possible cause is a quantum or shot effect mentioned as a possible cause of noise in flame emission (6) which is due to the statistical distribution of the finite number of droplets in the viewed part of the flame. If Poisson statistics applied, then there would be a relative fluctuation of 1%if the mean number of droplets in the viewed part of the flame was 10 000. If the number of droplets was reduced, then the relative fluctuation in droplets and hence the analyte absorption noise should increase. For our system under normal conditions, the calculated relative standard deviation due to the above effect is about 0.2% (0.2 mL/min of solution into 100 L/min of hot flame gases, 2 pm droplet size, 0.4 cm3 viewed flame volume). 578
ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
The latter hypothesis was tested by varying the nebulizer flow rate (with a variable nebulizer or forced feeding) and by rotating the slot burner. The analyte concentration was increased to maintain the absorbance. Even though in both experiments the mean number of viewed droplets was reduced, there was no change in precision. Hence analyte absorption flicker noise must be limited by other factors. Classification of Elements. From the precision data for the different elements, it appears that most elements can be classified in groups with their precision characteristics dependent upon the resonance absorption wavelength. This classification is intended only to provide an overview. In general, analyte absorption noise will limit the precision a t moderate absorbances independent of the wavelength. The remaining significant noises are more wavelength related. For longer wavelength resonance lines (alkali metals, most of the rare and alkaline earths, and group 3B) the precision will be totally limited a t higher concentrations by analyte emission noise. Similarily, a t these wavelengths, flame background emission and hence background emission noise is small, and transmission is essentially loo%, so flame transmission flicker noise will be small. Thus, for small absorbances, flame transmission flicker will dominate the noise only if lamp flicker and signal shot noise are also relatively small. Generally, all of the above noises are comparable, though for heavier group 1and 2A elements the hollow cathode intensities are lower and the signal shot noise will therefore be greater. Also, since higher gains are required for the heavier elements, analyte emission noise may be relatively higher. For the lanthanides, because N20/CzH:, flames are used and because of some low intensity lamps, and therefore high gains or wide slits, the emission noises will also be relatively important. For intermediate wavelengths, 230-370 nm, a different class of elements (mostly the transition elements) becomes apparent. Here, flame transmission flicker noise is increasingly important a t low absorbances, while analyte emission noise is less important, which makes background emission noise the more important at the high absorbances. The last group of elements are those with resonance absorbance wavelengths below 230 nm (Le., some group 2B, 4A, 5A, and 6A elements). Here, flame absorption is significant and flame transmission noise becomes dominant a t low absorbances. Analyte emission noise is usually negligible, and intensities of many of the lamps are low. The flame absorbance, lower lamp intensities and reduced photomultiplier sensitivity must be compensated for with higher lamp currents (leading to decreased element sensitivity and negative deviations), wider slit widths, and higher gains. The last two requirements make the background emission noise more significant. For these elements, flame transmission noise, analyte absorption noise, and background emission noise are the dominant noise sources. CONCLUSIONS These studies show that variation of the measurement precision of flame atomic absorption measurements with absorbance can be expressed theoretically and that the limiting noise sources at a given absorbance can be identified. The effect of lamp current and intensity, type and composition of flame, burner height, and other variables can be evaluated in the context of precision. From a practical point of view, the precision plots presented provide a means to determine over what concentration range samples should be adjusted for maximum measurement precision. For most elements, the dependence of precision on absorbance is generally t h e same and analyte absorption noise is limiting over a large part of the absorbance range.
The success of various techniques to improve precision will depend on the absorbance range and the limiting noise sources. Increasing the integration time from 1 to 10 s (reducing the noise bandwidth) appears to be somewhat successful over the whole absorbance range. The actual improvement will depend on the noise power spectrum of the limiting noises. Under source flicker noise limiting conditions, modest improvement is likely because of the l / fcharacter of this noise. From the detection limit to about 0.1 A, signal shot noise, source flicker noise, and/or flame transmission noise will be limiting and usually are about the same magnitude. Hence, to improve precision at low absorbances, one would need to use a combination of techniques. Higher light throughput (i.e., larger lamp current, larger slit width) can be used to reduce the relative signal shot noise. A double-beam system will reduce lamp flicker noise, and wavelength modulation (7) and sample modulation (8) may reduce lamp and flame transmission noise. This should be particularly successful for elements with resonance lines near 200 nm (larger flame transmission flicker factors). Use of less absorbing flames, and simultaneous background correction could also reduce flame transmission flicker noise. Background correction systems presently used are unlikely to result in increased precision because of the high source flicker of H2 lamps. At moderate absorbances, where analyte absorption noise is limiting, improvements other than through increased integration times will result only if the cause of analyte absorption noise is determined and design changes can be implemented to reduce its magnitude. I t appears the nebulization variations are a major cause of this noise. At higher absorbances, the relative amount of background and analyte emission noise must be reduced to improve precision. This can be accomplished by increasing the ratio of the lamp signal (i,) to the background and analyte emission signal by using a larger lamp current and smaller slit width or by using a smaller duty signal for lamp modulation to reduce the time that the flame is viewed. Use of larger integration times and cooler (less emitting) flames would also help. Although these studies have been performed on one instrument, we feel the general results can be extended to other manufacturers' instruments. The light throughput, flame, and nebulizer characteristics should be about the same in most modern AA spectrophotometers. Experimental aA/A vs. A plots reported for other instruments (5, 9) exhibit a region where ~ A / isA constant at moderate absorbances and hence analyte absorption noise limited conditions. APPENDIX
+
UA/A= [(-E,lnT)-2 [KmGE,(l T-l) (uJT)' 2Er2(Ei2 62') 2(1 + T-2 - T - ' ) ( U ~ ~ + ~ )[32]1/2 ~]
+ +
+
+
A = absorbance, dimensionless. UA = standard deviation in absorbance measurement, dimensionless. T = transmittance, dimensionless. E , = 100% T or reference signal due to source radiation transmitted by the flame with the blank aspirating, V. i, = reference signal photocathodic current due to transmission of source radiation by flame with the blank solution aspirating into the flame, A. E ~ M=Tphotomultiplier voltage used when the blank is aspirating, V. m = current gain of the photomultiplier, dimensionless. = amplification factor for amplifier-readout system, V A-l. G takes into account the response of the amplifier readout system to the rms photoanodic signal and is frequency dependent. = source flicker factor or the relative standard deviation of the source spectral radiance over the measurement bandwidth due to flicker noise, dimensionless. E2 = flame transmission flicker factor or relative standard deviation of transmission characteristics of the flame over the measurement bandwidth, dimensionless. 53 = analyte absorption flicker factor or the relative standard deviation in the absorption or atomization characteristics of the analyte, dimensionless. K = bandwidth constant, A. (ar)q+s= (mGKE,)'12 = rms shot noise in E,, V. a
