J. Phys. Chem. 1985,89, 4815-4821
4815
Lyman-a! Photometry: Curve of Growth Determination, Comparison to Theoretical Oscillator Strength, and Line Absorption Calculations at High Temperature R. G. Maki; J. V. Michael,* and J. W. Sutherland Department of Applied Science, Brookhaven National Laboratory, Upton. New York I I973 (Received: October 10, 1984; I n Final Form: May 1.5, 1985)
Absolute concentrationsof H atoms in the absorption region of an atomic resonance photometer have been accurately determined with a chemical kinetic technique that is based on the H + NO2 reaction. Subsequently,the curve of growth for the Lyman-a transition (H(’P3/%1/2) H(2Sl,,)) has been determined with a resonance lamp that is essentially a microwave-drivenelectrodeless discharge plasma. Additional experiments have been performed in order to measure the temperature and [HI in the resonance lamp plasma. Thus, simplified theoretical calculations of the curve of growth could be made from first principles using no adjustable parameters. These calculations agreed with experiment within experimental error, and therefore, the theoretical oscillator strength, as calculated from the known wave functions for H, is experimentally confirmed for the H(’P3 2,1/2) H(ZS1/2)transition. Confidence can now be placed in line absorption calculations and, hence, in measurements of [HI, at high absorber temperatures such as those encountered in flames, plasmas, and shock tubes where the atomic resonance absorption spectroscopic (aras) technique is commonly used. +
+
Introduction Atomic absorption and fluorescence spectroscopy are well-established techniques for monitoring low concentrations of atoms in chemically reacting systems.’-* The principal advantage in using these methods is that their high sensitivity for atom detection allows experimental conditions to be chosen so that the kinetic complications of atom-atom and/or atom-radical processes can be neglected. These techniques have been used in a relative fashion in most chemical kinetic investigations particularly for first-order processes, where only relative changes in absorbance and in fluorescence signal are needed to determine the first-order rate constant. Obviously, absolute atom concentrations in chemically reacting systems can be measured by absorption spectroscopy provided the absorption cross section and its dependences on concentration, temperature, and pressure are known. This has led to the development of several calibration procedures of varying c~mplexity.~”~~-~~ The sensitivity of an atomic resonance absorption photometer depends critically on the emission profile of the resonance lamp.14 It is therefore difficult to transfer the experience and the results from one particular study to another because the output of a resonance lamp is sensitive to its methods of preparation and operation. In effect, each resonance lamp requires an independent in-house calibration. Hence, this present study was undertaken to characterize the Lyman-a absorption photometer and, at the same time, to demonstrate that the results are consistent with the theoretical value of the oscillator strength (0,1387 for the weakest multiplet) for the H(2P3jz,1/2) H(,S,I~) tran~iti0n.I~ [HI was determined accurately from a kinetic analysis of data obtained in a discharge-flow apparatus. It should be emphasized that the previous measurement^^^^^^ could not have been made with the presently available precision because the necessary kinetic dataI4-l6 were not available at that time. In this study, the resonance lamp will be characterized, and the curve of growth (ABS vs. [HII, where ABS = In (Zo/I)and I is the optical path length) will be measured. Line absorption calculations with no adjustable parameters will then be made for the conditions of the experiment, and theory and experiment will be compared. Additional line absorption calculations will also be carried out for a variety of conditions for both the resonance lamp and the absorber.
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Experimental Section and Results The characterization of the photometer system required three experimental considerations: (A) the determination of the curve of growth by the discharge-flow technique; (B) the determination
of [HI in the plasma of the resonance lamp; and (C) the determination of the temperature profile in the plasma of the resonance lamp. Experiment A . Determination of the Curve of Growth by the DischargeFlow Technique. The curve of growth was determined by making use of a chemical kinetic technique that has been fully described e l ~ e w h e r e .In ~ ~previous ~ ~ ~ studies this method used several approximations, and, in addition, the rate constants in the kinetic scheme were not known with sufficient accuracy to determine unambiguously the [HI at the detector. At low absorbances, the present method uses the H + NO2 OH NO reaction under second-order conditions to specify [HI at the detector. The experiments were performed in a dischargeflow system of conventional design. A schematic diagram of the apparatus is shown in Figure 1. The techniques of operation have already been d e ~ c r i b e dso ~ ~that ~ , ~only those details specific to the present work will be given. The He flow reactor was operated at P = 2.05 f 0.05 torr and T = 298 K. The flow rates of H2 and NO, were determined from accurately measured pressure drops in calibrated volumes and that of H e from accurate rotameter calibrations. H atoms were generated upstream from the discharge-flow tube in an elec-
+
-
(1) A. C. G. Mitchell and M. W. Zemansky, “Resonance Radiation and Excited States,” Cambridge University Press, Cambridge, England, 1961. (2) A. L. Meyerson, H. M. Thompson, and P. J. Joseph, J . Chem. Phys., 42, 331 (1965); A. L. Meyerson and W. S. Watt, ibid., 49, 425 (1968). (3) J. V. Michael and R. E. Weston, Jr., J . Chem. Phys., 45,3632 (1966). (4) (a) K. P. Lynch, T. C. Schwab, and J. V. Michael, Int. J . Chem. Kine?. 8,651 (1976); (b) J. J. Ahumada and J. V. Michael, J . Phys. Chem., 78,465 (1974), and references therein. ( 5 ) P. Roth and Th. Just, Ber. Bunsenges. Phys. Chem., 79,682 (1975). (6) C.-C. Chiang, A. Lifshitz, G. B. Skinner, and D. R. Wood, J . Chem. Phys., 70, 5614 (1979). (7) W. Braun and M. Lenzi, Discuss. Faraday Soc., 44, 252 (1967). (8) J. V. Michael and J. H. Lee, J . Phys. Chem., 83, 10 (1979), and references therein. (9) J. R. Barker and J. V. Michael, J . Opt. Soc. Am., 58, 1615 (1968). (10) A. Lifshitz. G. B. Skinner, and D. R. Wood. J . Chem. Phvs.. 70, 5607 (1979); Rev. Sei. Instrum., 49, 1322 (1978). (1 1) D. Appel and J. P. Appleton, Symp. (In?.) Combust., [Proc.],15th 1974, 701. (12) 0 atoms: P. Roth and Th. Just, Ber. Bunsenges. Phys. Chem., 81, 572 (1977); K. M. Pamidimukkala, A. Lifshitz, G. B. Skinner, and D. R. Wood,J. Chem. Phys., 75, 1116 (1981). (13) H. Bethe, “Handbuch der Physik, 24/1”, 2nd ed, H. Geiger and K. Scheel, Eds., Julius Springer, Berlin, 1933, p 442. (14) J. V. Michael, D. F. Nava, W. A. Payne, J. H. Lee, and L. J. Stief, J . Phys. Chem., 83, 2818 (1979); H. Gg. Wagner, U. Welzbacher, and R. Zellner, Ber. Bunsenges. Phys. Chem., 80, 1023 (1976); M. A. A. Clyne and P. B. Monkhouse, J . Chem. Soc., Faraday Trans. 2, 73, 298 (1977). (15) D. L. Baulch, R. A. Cox, P. J. Crutzen, R. F. Hampson, Jr., J. A. Ken, J. Troe, and R. T. Watson, J . Phys. Chem. Ref.Data, 11, 327 (1982). (16) N. Cohen and K. Westberg, Aerospace Technical Report ATR-82(7888)-3, Aerospace Corp., El Segundo, CA, July, 1982.
0022-3654/85/2089-4815$01.50/00 1985 American Chemical Society
4816 The Journal of Physical Chemistry, Vol. 89, No. 22, 1985
n n
He
Maki et al.
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“2
Figure 1. Schematic diagram of apparatus for experiment A: He, helium supply; H2, hydrogen supply; D, microwave discharge; MI, movable
injector, NO2 inlet; PT, pressure tap; RL, resonance lamp; F, atomic filter; P, mechanical pump; A, air filter; PM, photomultiplier; HVPS, high-voltage power supply; E, electrometer; CR, chart recorder. trodeless discharge using microwave power at 2450 MHz (Raytheon Model PGM-10x1). NO, was introduced through a movable injector, and the absorption by H atoms was measured at a fixed position in the flow tube. The photometer system consisted of a Davis-Braun microwave-driven (Raytheon Model PGM-10x1) counter flow lamp” operating at 1.7 f 0.1 torr of research grade H e (MG Industries, 99.9999%), at 16 W of microwave power, and with cooling air from a regulated 40 psi source. There is enough hydrogenous impurities even in this highest quality He to give sufficient Lyman-a radiation. An atomic filter section was placed in front of the resonance lamp. Its operation has already been described,I8 and it has already been adapted for removal of Lyman-a radiation.I9 In essence it is a discharge-flow system operating at 0.2 torr of H,. The pathlength, 1, across the flow tube was 2.67 cm. Spectral isolation of Lyman-a (1 21.6 nm) was accomplished in the usual way with an air filter9 in front of the solar blind photomultiplier (EMR 542G-09-18). The output from the photomultiplier was amplified by an electrometer (Keithley 510B) and was recorded with a potentiometric recorder. Tests of the atom filtering efficiency were routine because H-atom flooding of the main discharge flow reactor yielded the same signal attenuation as that of the atom filter. In this way, the fraction of total photomultiplier signal due to Lyman-a was easily determined before and after each measurement. Hence, inaccuracies in the measurement of absorbance (ABS = In (Zk/Za)) due to long-term lamp drift were effectively eliminated. The relationship between absorbance, ABS, and [HI1 is expected to be nearly linear at low values of absorbance, i.e. Beer’s law holds. This is a known and accepted result from resonance radiation line absorption t h e ~ r y With . ~ ~ this ~ ~assumption, ~ later shown to be valid, the rate constant for wall reaction in the teflon-coated reactor was determined by measuring ABS for various dwell times between the microwave discharge and the detector. The dwell times were changed by varying the flow velocity while holding constant the total pressure, the temperature, [H,], introduced into the flow reactor, and both the lamp and the discharge microwave power. The first-order plot of the data from these experiments is shown in Figure 2 where the logarithmic plot of ABS = K[H]Z is plotted against dwell time. The wall termination constant was found to be k , = 3.4 f 0.5 s-l (one standard deviation) and is listed in Table I. This low value corresponds to a wall recombination coefficient, y, of 3.5 X 10-5.4b The linear relationship between ABS and [HI (at low ABS) was then utilized in the kinetic experiments with the H + NO2 OH NO reaction. The rate constant for this reaction is
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+
(17) D. Davis and W. Braun, Appl. Opt., 7, 2071 (1968). (18) J. H. Lee, J. V. Michael, W. A. Payne, and L. J. Stief, J . Chem. Phys., 69, 3069 (1978). (19) J. C . Miller and R. J. Gordon, J . Chem. Phys., 78, 3713 (1983).
O - 1 50
0
IO0
I50
t /ms
Figure 2. Determination of wall termination rate constant. ABS =
K[H]I is plotted against dwell time. Points represent experimental data; solid line represents least-squares fit, slope = 3.4 f 0.5 s-’, intercept = 0.41 i 0.01, where the error is taken at one standard deviation. TABLE I: Chemical Kinetics for Experiment A at 298 K
reaction A. Upstream from Probe Tip ( 6 ) H “ a “ 1/2H2 k , = 3.4 f 0.5 s-I
ref a
B. Downstream from Probe Tip (1) H + N O , - O H + N O k , = 1.4 X 10-10cm3 14 molecule-’ s-I (2) OH + OH 4 H20 0 k , = 1.8 X cm3 15
-
(3) 0 + NO2 (4)
(5)
+
+ NO 0 + OH 0 2 + H OH + NO + M HNO, + M
( 6 ) HE?.
0 2
1/2H2
-
moiecule-I SKI X cm3 15 molecule-’ s-I k4 = 4.0 X lo-’’ cm3 16 molecule-I s-I k , = 6.5 X cm6 15 molecuk2 s-’ k3 = 9.3
a
Present work known to within f10% (one standard deviation) at room temperature14and is listed in Table I along with those of other possible secondary processes.15J6 If we know the initial [NO,] and [HI, and the rate constants shown in Table I, the [HI, measured at the detector, is uniquely specified at any probe distance. ABS was then measured as a function of dwell distance (or time) for constant values of [NO,], and [H,],. The results of four experiments are shown in Figure 3. The kinetic behavior was simulated by numerical integration of the chemical equations shown in Table I. [N021qwas measured and [HIoD,the hydrogen atom concentration entering the flow tube from the discharge at d = 43.5 cm, was varied parametrically. Upstream from the probe tip the kinetics are specified only by wall reaction, whereas downstream, both the wall and the H + NO2 reactions contribute. At the low absorbance levels shown in Figure 3, secondary processes (reactions 2-5), though included in the numerical simulation, are negligible. It should be noted that a complete simulation for each probe distance is required since [HIoT,the hydrogen atom concentration at the probe tip, increases with increasing distance from the detector. Furthermore, the fact that [H2], is constant for experiments (a) and (b) and for (c) and (d) in Figure 3 requires that [HIoDbe constant for the same experiments in the kinetic
The Journal of Physical Chemistry, Vol. 89, No. 22, 1985 4817
Lyman-a Photometry 0.51
I
I
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TABLE II: Absorbance at 121.6 nm of Low and High Hydrogen Atom Concentrations A. Low Concentrations’
1
I
I
5
IO
15
t/ms
Figure 3. Chemical kinetic simulations with the reactions of Table I. ABS = In ([,/I) = K[H]I is plotted against time for kinetic runs with T = 299 K, p = 2.06 torr, distance from discharge to detector = 48.5 cm, u = 2143 cm s-l, and: (a) [HIoD= 1.065 X lo1, atoms ~ m - [NO,], ~, = 4.71 X 10” molecules ~ m -K~ = , 1.82 X cm2 atom-’; (b) [HIoD = 1.065 X 10I2 atoms ~ m - [NO,], ~, = 1.18 X lo1, molecules ~ m -K~ =, 1.59 X IO-” cm2 atom-’; (c) [HIoD= 1.278 X 10” atoms cm-3, [NO,]; = 1.16 X lo1, molecules ~ m - K~ = , 1.73 X lo-” cm2atom-’; (d) [HI, = 1.278 X lo’, atoms ~ m - [NO,], ~, = 1.86 X 10” molecules ~ m - K~ = , 1.49 X lo-” cm2 atom-’. Points represent experimental values, whereas solid lines represent kinetic simulations with indicated cross sections, K. simulations. The simulated profiles were then compared with experimental data by a normalizing procedure using (ABS)t,lcd = K[H],l, where [HI, is the simulated concentration and K (the experimental cross section) is a derived proportionality constant that minimizes (ABS)‘,,,, - (ABS)t,,lc,+ Best fits of curves of against time for the determined [HIoDare compared with the (ABS)‘,,,, data in Figure 3. The conditions and results for each experiment are given in the figure caption. In this simulation and comparison procedure, changes of f10% in [HIoD from the best fit value are easily seen to be unacceptable: Le., the shapes of the fits are worse. The experimental cross sections from Figure 3 can then be used to generate an [HI for each point in Figure 3. These, when multiplied by the path length, 1 = 2.67 cm, give the values listed in Table 11. These p i n t s are then plotted as in the inset in Figure 4, to give the curve of growth. With the line constrained through zero, the linear least-squares fit (Le., the slope of the low absorbance data in Figure 4) gives the cross section cm2 atom-’, where the random error value, (1.73 f 0.05)X is taken at two standard deviations. At higher absorbances additional points on the curve of growth were measured as follows. At a chosen fixed distance of 30 cm, [H,],, and hence ABS, was set at some large value. [NO,], was then increased until ABS decreased to some low but measurable value; Le., [HId, the H-atom concentration at the detector, was decreased by NO, reaction to a low but measurable value. This procedure ”under titrates” [HIoTwith NOz, but since the ABS against [HI function is known at low ABS (Figure 4), the specific value of [HId in the under titration is known. The system of differential equations specified by the reactions in Table I was
[H]/1O1I atom cm-3 1.60 2.02 2.30 2.77 2.94 3.32 3.33 3.53 3.88 4.08 4.30 4.33 4.52 4.87 5.04 5.07 5.52 5.62 5.84 6.35 6.42 6.59 6.77 7.12 7.14 7.18 7.18 7.43 8.08 8.48 8.72
[H]I/10” atom 4.3 5.4 6.1 7.4 7.9 8.9 8.9 9.4 10.4 10.9 11.5 11.6 12.1 13.0 13.5 13.5 14.7 15.0 15.6 17.0 17.1 17.6 18.1 19.0 19.1 19.2 19.2 19.8 21.6 22.6 23.3
ABS 0.064 0.081 0.092 0.1 10 0.125 0.132 0.142 0.150 0.165 0.188 0.171 0.184 0.209 0.225 0.233 0.2 16 0.220 0.259 0.248 0.293 0.312 0.320 0.328 0.328 0.285 0.305 0.349 0.361 0.392 0.391 0.423
B. High Concentrations [NO,],/ 10l2 [H]oT/ 10”
molecules cni3
atoms cm-3
sb
2.96 3.95 4.74 6.15 8.68 7.71 9.62 12.73 14.34 17.64 21.99 18.99 25.26 44.78
1.69 2.34 3.24 3.68 4.10 5.05 5.80 7.30 8.02 9.62 10.6 10.7 12.7 19.4
1.75 1.69 1.46 1.67 2.11 1.53 1.66 1.74 1.79 1.83 2.07 1.77 1.99 2.31
[HIC/10”
[HI// 10l2
atoms
atoms
1.61 2.23 3.09 3.50 3.90 4.81 5.52 6.95 7.63 9.16 10.1 10.2 12.1 18.5
4.30 5.95 8.25 9.35 10.41 12.84 14.74 18.56 20.34 24.46 27.0 27.2 32.3 49.4
ABS 0.83 1.11 1.40 1.30 1.55 1.79 1.97 2.26 2.43 2.62 2.74 2.76 3.03 3.47
a Linear least-squares analysis, 95% confidence (two standard deviations), zero constrained; slope = (1.73 f 0.05) X IO-” cm? atom-’. b~ is defined as the ratio [N02]o/[H]oT.c [HIo* values corrected for wall loss, d = 30.0 cm.
then numerically integrated over the fixed distance, i.e., the fixed dwell time. For each experimentally determined [NO,],, [HIoT was parametrically varied until [HId was equal to the value measured experimentally in the under titration. As expected, the [HId left at the detector for a given high value of [NO,], was a sensitive function of [HIoT. Changes of about f2-4% in [HIoT typically resulted in about k6-40% changes in [HId at the detector so that the determination is accurate to within about a 10% variation in [HIoT. The ABS value at the detector with no added NO, refers to the wall attenuated value of [HIoT,and therefore the [HI associated with a measured ABS is slightly decreased due to the wall reaction even with the low value of k, = 3.4 s-’. The values for the H-atom concentration so derived are shown in Table I1 along with other experimental quantities. It should be noted that the overall stoichiometry, s, usually does not reach l.O[H] to 1.5[NOz] as assumed in previous Lyman-a line absorption
4818
Maki et al.
The Journal of Physical Chemistry, Vol. 89, No. 22, 1985
4.01
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TABLE III: Measured Absorbances in Exwriment B" PH,/torr ABS PRe/torr ABS PH,/torr 1.37 0.84 0.290 0.44 0.232 1.51 0.47 0.176 0.88 0.219 1.76 1.00 0.294 0.64 0.228 1.92 0.64 0.171 1.09 0.389 1.16 0.263 ~~
3.0-
~~~
ABS 0.304 0.456 0.419 0.360
a Linear least-squares analysis, 95% confidence (two standard deviations), zero constrained; slope = 0.24 f 0.04 torr-'. For T = 298 K and I = 14.0 cm the experimental cross section, K = 1.73 X lo-" cm2 atom-!, combined with this slope, gives (3.1 f 0.5) X lod for the Hatom mole fraction in the delivered research grade He.
[HI
atoms cm-2
Figure 4. Curve of growth for hydrogen with a 410 K Doppler source. ABS is plotted vs. [HI/ using the 16-W discharge source. Data are from Table 11. Points represent experimental data with indicated errors (one standard deviation) decreasing with decreasing [HI/. The solid line represents the calculated curve of growth (eq VIII). Inset: ABS is plotted vs. [H]f for low concentrations. Points represent experimental results (Table 11), solid line represents the theoretically calculated curve of growth (eq VIII), and the dashed line represents the linear leastsquares fit to the low concentration experimental data, slope = (1.73 f 0.05 X IO-" cm2 atom-' (zero constrained), where the error is taken at two standard deviations. This line is replotted in the main figure for comparison.
PT
A
l l PM
HELIUM SUPPLY
Figure 5. Schematic diagram of apparatus for experiment B: N, needle valve; D, microwave discharge; RL, resonance lamp; PT, pressure tap; P, mechanical pump; F, atomic filter; A, air filter; PM, photomultiplier; HVPS, high-voltage power supply; E, electrometer; CR, chart recorder.
determination^.^*^,^ The ratio is almost always larger than 1.5 to 1.O simply because not enough time is available for complete reaction at the [NO,], and [HI, used in these experiments. The final "undertitrated" value of [HId is determined by the excess amount of added [NO,],. The resulting [HI corresponding to ABS for the N02-free measurement, after multiplication by the path length, is plotted on the curve of growth, Figure 4. Experiment B. Determination of [HI in the Resonance Lamp Plasma. The [HI in the resonance lamp plasma was estimated in separate experiments. A schematic diagram of the apparatus is shown in Figure 5. A fast flow of the same research grade He was used in both the same resonance lamp as used in experiment A and a 14.0-cm optical length discharge-flow system in the configuration shown in the figure. The only loss process
for the atoms flowing out of the plasma region into the flow system is wall reaction and, to test the severity of this process, ABS was measured with the microwave discharge located at various positions along the entrance tube. The flow rates used were so high that little difference was noted with changes in the discharge position. Therefore, the wall reaction is negligible. ABS, through the long optical path, 1 = 14.0 cm, was then measured by using the same conditions in the resonance lamp as those employed in the curve of growth experiments ( P = 1.7 h 0.1 torr of He, 16 W of microwave power). Several pressures were used in the flow system, and its microwave generator was operated at a constant 60-W power level. The results are given in Table I11 where it can be seen that the mole fraction of H atoms resulting from the delivered He is (3.1 f 0.5) X lo4. At 1.7 torr and 298 K, this translates to an [HI of 1.7 X 10" atoms ~ m - ~It .should be noted that this value refers to the dischargeflow system where the microwave power employed was 60 W instead of the 16-W power level used in the resonance lamp. A decrease of microwave power from 60 to 16 W causes about a factor of 2 change in ABS so that a good estimate of the atom concentration in the plasma is -(5-10) X 10'O atoms ~ m - ~ . Experiment C. Determination of the Resonance Lamp Plasma Temperature. In order to carry out the necessary line absorption calculations, the temperature of the resonance lamp was measured as a function of microwave power with a thermocouple placed in a movable thin-walled sealed quartz probe. Microwave absorption in the glass only resulted in a 2 OC rise in its temperature even at a high microwave power level (100 W). When the discharge was initiated, the thermwuple probe showed that the temperature in the flowing gas peaked at the cavity center and then progressively decreased on both sides toward the ends. The results are shown in Figure 6. In all earlier work the temperature of the plasma has been assumed to be high and constant throughout. Furthermore, even though the electronic temperature is high, it has always been assumed that line broadening in these low-pressure He lamps is translationally equilibrated due to the predominance of thermalized electron excitation rather than metastable state energy transfer or ion collision mechanisms, i.e., the emission profiles are Doppler broadened, and the Doppler temperature is the translational temperature. In general, this temperature has been determined either from line absorption data2-3.9or from actual optical profile measurements.'0*20 Also, in most previous work, a reversal layerz1 has been included in front of the plasma region to account for The purpose of the absorption within the lamp itself.3,4,6,9,10v20 present temperature profile determinations was to eliminate temperature as an adjustable parameter in the subsequent description. The results described in Figure 6 show that temperature decreases monotonically on either side of the cavity center, and thus, the steady-state condition of heat flow is analogous to one-dimensional linear heat flow through a rod where the ends are at fixed temperatures. In this case the peak temperature is fixed by the energy input (microwave power)-energy output (cooling (20) W. Braun, A. M. Bass, and D. D. Davis, J . Opr. Soc. Am., 60, 166 (1970). (21) W. Braun and T. Carrington, J. Quant. Spectrosc. Radial. Transfer, 9, 1133 (1969).
The Journal of Physical Chemistry, Vol. 89, No. 22, 1985 4819 900 7
0I
I
I
0
I
I
-
I
where n designates the regions 1 and 2 as well as 3, the external absorber.
0I
uOn= (f/6,)?r-'/'ire2/mc 500 -
.. /
-*
300
e and m are the charge and mass of the electron, andf = 0.1387 for the weakest component.13 Also
\
/
/
(111)
\
6, = ( U ~ / C ) ( ~ R T , , / M ) ' ~ ~
(IV)
where c, R , M , and T, are the speed of light, gas constant, atomic weight of the absorber, and temperature in the region n, respectively, and where vo is the center line frequency for the weakest transition ('P112 *S1/2). Region 3 refers to the absorber which is external to the resonance lamp and, in the present case, this absorber is [HI in the flow tube at T3 = 298 K. A y is the displacement of 2Sl/2)from the weak the center of the strong component ('P3l2 component and is, specifically 0.5988, since the splitting between components, in frequency units, is 1.094 X 1O1Os-'. With y defined in eq V, the quantity a is simply &,/a3 = (T1/T3)Il2.In eq I, the temperature of the reversal layer is taken to be the same as the external absorber, T3. Lastly, in eq I the multiplet statistical factors are already included in the exponential arguments. From the results of experiment B, eq I can be immediately simplified. Firstly, the product, uol[H],I1,with [HI, = (5-10) X 1O'O atoms is so low,
