JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Optical Cross Sections from Intensity-Density Measurements*

EINAR HINNovt AND HEDWIG KOHNDepartment of Physics, Duke University, Durlam, North Carolina

(Received August 2, 1956)

Optical cross sections corresponding to spectral lines of Li, Na, K, Ca, Sr, Ba, Tl, Cu, Ag, Cr, Mn, Fe,Co, and Ni, emitted by an acetylene-air flame, have been determined. The evaluation of the cross sectionis based on intensity-density graphs, constructed from photoelectric measurements of the total lineintensities as a function of the density of the emitting atoms in the flame.

When the cross section corresponding to the line has been determined, the measured intensity-densitycurves yield the absolute values of the product Nf of the number of atoms in the flame capable of absorbingthe line, and the oscillator strength for the line. If thef value for the line is known, the degree of dissociationof the element in the flame can be found. If the! value for the line is not known, the product Nf allows,in some cases, the evaluation of the absolute f value for the line; in other cases only a lower limit of theabsolute f value can be obtained. The results are compared with those of previous investigators.

INTRODUCTION

ONE of the important factors determining thecontours of a spectral line, and consequently the

self-absorption in the source, is the interaction throughcollisions of the emitting atoms with foreign molecules.The cross section for this type of interaction, resultingin the broadening of the emitted line, is called theoptical cross section. The variation of the emitted lineintensity with the density of the emitting atoms isdetermined by the self-absorption in the source, andtherefore depends on the optical cross section corre-sponding to the line.

In this investigation, the optical cross sections areexperimentally determined for various elements in anacetylene-air flame. The method of evaluation of thecross sections, described in detail elsewhere,' is basedon measurements of the total line intensity. For agiven source the total line intensity is proportional tothe total absorption or "equivalent width" of the lineA (r,a). The variable r is proportional to the opticaldensity Nfl of the source,

20 Nflr=- , (1)

mc APR

and the absorption parameter a is the ratio of thecollision width and the Doppler width of the line:

APR N'VU2a=-(ln2)I= (2)

AVD (8RT/M) 1Ivo/c

If a is experimentally determined for a given spectralline, the optical cross section corresponding to this linecan be calculated from (2). The notation used in (1) and(2) is summarized as follows:

* This work was supported by the Office of Naval Researchunder contracts N6ori-107, T.O.I. and Noiir-1181(05) withDuke University.

t Present address: Department of Physics, University ofMaryland, College Park, Maryland.

' Einar Hinnov, J. Opt. Soc. Am. 47, 151 (1957).

em = the charge and mass of the electronc= velocity of light

N=number of atoms per cm' capable of absorbing the lineunder consideration

f= the oscillator strength for the lineAYv= collision width of the lineAVD= Doppler width of the lineN'= number of perturbing particles per cm'

D= mean speed of the perturbing particles relative to theemitting atom

R= gas constantll= atomic weight of the emitting atomsT= absolute temperature of the sourcevo=frequency at the center of the linea2 the optical cross section.

The relative total line intensities are measured asa function of the number of the emitting atoms in theflame. As an illustration of the procedure, Fig. 1 showsthe resulting logarithmic intensity-density graphs forthe resonance lines of potassium (K7665) and copper(Cu3274). The relative (experimental) scales for thetwo graphs are shown at the top and the right-hand sideof the figure. In the experimental setup, a tungstenribbon lamp is mounted behind the flame, and a lensforms an image of the ribbon at the center of the flame.The optical system is so designed that the bundle ofrays admitted to the monochromator is the same for theradiation from the flame and from the backgroundsource. Two measurements are made of the backgroundintensity concurrently with the line intensity measure-ments: one with, and one without the flame in the pathof the rays. The relative intensities corresponding to theline, the background radiation, and the combined lineand background radiation will be designated byR, B, and RB, respectively. The last two measurementsmust be made at a rather high density of the emittingatoms in the flame, in order to have an appreciabledifference between B and RB.

It has been shown that the total absorption is givenin terms of the measured quantities by'

c D(X)RA=- , (3)

X2 nB

156

VOLUME 47, NUMBE:R 2 FEBRUARY 1957

February 1957 OPTICAL CROSS SECTIONS FROM INTENSITY-DENSITY

FIG. 2. Schematicdiagram of the acety-lene-air burner.

FIG. 1. The intensity-density graphs for the K7665 and theCu3274 lines showing both the absolute and the relative (experi-mental) scales. The primed quantities refer to the copper line.C (or C') is the concentration of the metal salt solution sprayedinto the flame, in M/1, and R (or R') is the relative total lineintensity in arbitrary units. Log Co (or log Co') marks the abscissaof the point of intersection of the asymptotes in the experimentalscale. The absolute ordinates for the points of intersection arealso shown. The value of the ordinate of the point of intersectionis equal to log 2a for the line in question.

wheren= R/(B-RB+R). (3a)

Here X is the wavelength of the line, and D(X) theeffective wavelength range (in cm) of the radiationfrom the background source, given as the product ofthe entrance slit width and the linear dispersion of themonochromator at the wavelength X. It can be seenthat the quantity n is the ratio of the black radiationintensities at the temperature of the flame and thebrightness temperature of the background source atthe wavelength X.

The total absorption A obtained from (3) for any oneof the experimental points in the intensity-densitygraph enables the calculation of the absolute ordinatelogEA (ln2)1/AvD] for this point and consequentlyfixes the absolute ordinates for the graph. The absoluteordinate for the point of intersection of the asymptotes,drawn to the experimental curve at very low and veryhigh densities, has been shown to be equal to log 2afor the curve.' This point therefore yields the a valuefor the intensity-density curve, and also serves toestablish the absolute abscissas for the graph, as willbe described in the last section of this paper.: In Fig.1 the ordinate for the point of intersection of the asymp-totes is 0.728 for the potassium line and -0.033 for thecopper line, yielding a= 2.7 and a= 0.46, respectively.The optical cross sections are obtained from thea values according to (2).

The choice of the location of the asymptotes to theexperimental curves is somewhat arbitrary, but usuallywithin quite narrow limits. The error limit of theexperimentally determined a values is estimated tobe not more than i 10% for the following lines:

t See also reference 1.

Acetylene

Li6708, Na5890, K7665, Ca4227, Sr4606, Cu3274,Ag3281-3383; not more than :1 20% for all otherlines reported in this paper. This estimate is based ontrials with other possible locations of the asymptotesto the experimental curves.

The experimental results are discussed in the lasttwo sections after a brief description of the apparatusused. The results are compared with those of otherinvestigators, whenever available.§

EXPERIMENTAL

A short description of the experimental setup hasbeen given in a previous paper'; this section is devotedto supplement the information presented there.

A schematic diagram of the modified Lundegirdh-type burnerI1 together with a more detailed drawing ofthe atomizer, is shown in Fig. 2. The element underinvestigation is introduced in the form of an aqueoussalt solution. Air compressed to about three atmospheresis blown through the narrow nozzle B, which has adiameter of 0.5 mm. The solution is sucked into theatomizer through the opening D, and is shattered bythe air current into a fine spray which moves throughC back into the solution flask. The larger droplets,hitting the rounded end of the solution flask, condenseand return to the solution, while the smaller ones arecarried with the air stream into the burner.

Before entering the flame, the air is mixed withacetylene which is admitted through a narrow nozzle of0.6-mm diameter at a steady pressure of 55 cm ofwater. The mixture thus obtained is slightly richer

§ Part of the experimental material and a more detailed discus-sion are given in the Ph.D. dissertation of Einar Hinnov, DukeUniversity, 1956.

Tables in which the experimental intensity-density values andthe conversion factors for all the spectral lines of this investigationare listed will be included in the Technical Report No. 11 onwork done under contracts N6ori-107, T.O.I. and Nonr-1181 (05).

11 For a description of the Lundegirdh burner see, for example,N. H. Nachtrieb, Spectrochemical Analysis (McGraw-HillBook Company, Inc., New York, 1950), p. 286.

,I

1.4I

157

2 .1. -31 1. -21 110 . log C,

1 .2 ;--- �_,_ a -I

i -

- 0.728 .13 Ii I

0 �-0.033

0 K-cu 0

i

-1

I I I-I log ra

Atomizer

Air

log C..A 7

Vl

.2

E e_

E. HINNOV AND H. KOHN

than stoichiometric, i.e., it contains less oxygen thannecessary for complete combustion into carbon dioxideand water. Entering the flame per second are 126 cm3of air, 11.7 cm3 of acetylene, and 3.4X10-3 g of water(salt solution). The gas volumes are measured bycollecting the gas over water at room temperature,under the same experimental conditions as are used inthe operation of the flame. The amount of water isdetermined by weighing the solution flask, and theburner parts on which the spray may condense, beforeand after the flame has been in operation for about30 min.

The burner tip has a rectangular shape about 1 mmwide and 22 mm long. The flame consists of an innerreaction zone, about 2 mm high, and an outer body ofabout 15 cm in height. At the boundaries of this outerbody, a secondary combustion takes place betweenthe carbon monoxide resulting from the primarycombustion in the inner reaction zone, and the atmo-spheric oxygen.

In order to eliminate the temperature drop at theends of the flame, two auxiliary burner tips are attachedto the main one as shown in Fig. 2. The salt solution isadmitted only to the middle part. The outside Bunsen-type burners ensure an approximately constant temper-ature throughout the region along the line of sight wherethe element under investigation is present. When theentire burner is in operation, the flame forms onecontinuous body, as shown in the diagram; the coloredpart being indicated by the dotted lines.

The approximate composition of the flame gases,after the combustion, has been determined by a methoddescribed in detail by Gaydon and Wolfhard.2 In theregion where the measurements are taken, the partialpressures of the important constituents are (in atmo-spheres):

p(N2)=0.718, p(C02)=0.120,p(CO)=0.048, P(02)=0.0070,p(OH) = 0.0053, p(O) = 0.0012.

p(H20) = 0.104,p(H2) =0.0071,

From this composition of the gases, and the chemicalreactions involved, the theoretical temperature of theflame may be calculated. Numerical data for thiscalculation, and a detailed description of the methodis given by Gaydon and Wolfhard.2 The method consistsof balancing the heat liberated during the reaction atroom temperature against the heat required to raisethe resulting gas mixture to the final temperature and toform the free atoms and radicals in the flame. The finaltemperature is determined by trial and error. Heat lossby radiation is neglected in this calculation. In thepresent case, a final temperature of 2500°K is found bythis method, in good agreement with the temperatureof 2480°K, measured by the line reversal method.

2 A. G. Gaydon and H. G. Wolfhard, Flames (Chapman andHall, Ltd., London, 1953).

The reversal temperatures are evaluated from themeasured values of the quantity n (3a), the brightnesstemperature of the tungsten ribbon, as determined inthe red by means of an optical pyrometer, and theknown values of the tungsten emissivity. The resultingreversal temperatures for all the spectral lines measuredare within 4±200 from the mean, 2480'K. Data, and amore detailed discussion of the reversal temperaturemeasurements will be given in a subsequent paper.

The optics of the monochromator, built for theseexperiments, consists of a spherical aluminized surfacemirror of 72 cm focal length, and a Bausch and Lombreplica grating. The grating has a ruled area of 52X52mm, with 1200 rulings per mm. The dimensions of thelight bundle in the instrument are determined bythe area of the grating. In the first order of the gratingwhere all the present measurements were taken, thelinear dispersion varies from 10.2 A/mm at 8000 Ato 11.4 A/mm at 3000 A. The grating is turned bymeans of a micrometer screw working against an armattached to the turntable on which the grating ismounted. This turning system has practically nobacklash, and allows measurable changes in the wave-length setting in steps of about 0.5 A.

A plano-convex quartz lens inserted directly behindthe exit slit of the monochromator forms an extendedimage of the grating surface onto the cathode of thephotomultiplier tube (RCA P28 or RCA P21).Between this lens and the photomultiplier tube thereis a small plane mirror, capable of being rotated in orout of the path of the rays. This mirror allows viewingthe exit slit without removing the photomultiplierhousing, and simultaneously acts as a shutter.

TABLE I. Optical cross sections.

X,,in Av>R in square

Element angstroms a in sec-I angstroms

Li 6708 0.55 4.OX 109 43Li 3232 0.45 6.8X 109 73Na 5890 0.86 3.9X 109 64Na 3303 2.3 1.9X101c 300K 7665 2.7 7.3X10 135K 4044 2.2 1.1X10 0 203K 4047 2.2 1.1X1010 203Ca 4227 0.46 2.2X 109 41Sr 4606 1.1 3.3X109 69Ba 5535 1.4 2.8X 109 61Cu 3274 0.46 2.3X 109 46Ag 3383 0.96 3.5X 109 75Ag 3281 1.03 3.9X109 83TI 3775 3.0 7.2X109 161Ti 5350 4.3 7.2X 109 161Cr 4254 0.54 2.3X109 44Cr 3579 0.58 2.9X 109 56Mn 4030 0.80 3.5X 109 68Fe 3720 0.53 2.4X 109 48Fe 3737 0,55 2.5 X 109 50Fe 3860 0.62 2.7X109 54Fe 3581 0.59 2.8X 109 56Co 3526 0.78 3.7X 109 73Ni 3524 0.54 2.6X109 51

158 Vol. 47

February 1957 OPTICAL CROSS SECTIONS

The entrance slit widths used in these measurementsrange from 200 microns to 700 microns, dependingon the width of the line under investigation. Theseslit widths were selected individually for each line, soas to be large enough for total intensity measurements,and yet small enough to allow temperature measure-ments by the line reversal method.

OPTICAL CROSS SECTIONS

The collision widths and the corresponding opticalcross sections are presented in Table I for the spectrallines identified in the first two columns. These quantitiesare determined from the measured a values accordingto (2). The appropriate mean relative speeds, and thedensity of the perturbing molecules have been obtainedfrom the ideal gas law, corresponding to the pressure(1 atmos) and the temperature (2480'K) in the flame.Since nitrogen constitutes more than seventy percentof the flame gases, the optical cross sections thusobtained are essentially the probabilities of broadeningcollisions between the excited atoms and the normalnitrogen molecules.

Although the data obtained up to the present timeare still rather fragmentary, as far as information aboutthe different groups in the periodic table is concerned,several interesting qualitative relationships can beobserved among the measured optical cross sections.For the same atom, the cross section depends on thestate of excitation. Generally, a line arising from a stateof higher excitation corresponds to a larger crosssection. This is particularly apparent in case of thealkali metal atoms, where the cross sections correspond-ing to the second members of the principal series areconsiderably larger than those of the first members.In case of silver, there is a measurable difference evenin the cross sections associated with the two componentsof the first member of the principal series. The qualita-tive conclusion may be drawn that the valenceelectron in the higher state of excitation being moreloosely bound, is more easily perturbed by the collidingparticles. It may also be concluded that the higherstate of a given transition is considerably more import-ant than the lower level in determining the correspond-ing cross section. However, the irregularities in themagnitudes of comparable cross sections, particularlyapparent in the alkali metals, show that no simplerelation exists between the cross sections and excitationenergies corresponding to a given spectral line.

Certain regularities also appear within the samegroup of elements. Thus the cross sections for the copperand silver resonance lines are proportional to theiratomic number (or atomic weight), i.e., the ratio ofa-2/at. wt is the same for both elements. The samerelation holds approximately for Ca and Sr, and forthe second members of the principal series of Li and Na.However, the next elements in the groups-Ba and K,respectively-not only deviate from this relation, but

TABLE II. Comparison of measured optical cross sections. Thecross sections are given in square angstroms.

,,2

Author Li Na K Rb Cs Ca TI

Sobolev et al. 53 85 132 115James and Sugden 22 68 125 180 164Present Work 43 64 135 41 161

display cross sections which are actually smaller thanthose of the preceding elements, Sr and Na, respectively.A similar behavior has been reported by James andSugden3 for the cross sections corresponding to thefirst members of the principal series of the alkalimetals. The results of these authors indicate that thecross section for cesium is lower than that for rubidium.Thus, it seems that within the same group of elements,the cross sections for corresponding lines first increasemore or less linearly with increasing atomic weight(or at. number), pass through a maximum, and finallydecrease in some manner not yet determined.

Comparison of elements in different groups is moredifficult because, due to the difference in the energystates, it is not certain just what quantities should becompared. Nevertheless, a few general features maybe noted. The cross sections for the lines of the metalsfrom chromium to nickel show that the elements withan odd number of electrons seem to display somewhatlarger cross sections than those with an even numberof electrons. The copper group may be an exception tothis rule, but this cannot be ascertained until thecross sections for zinc or cadmium are also measured.On the other hand, the cross sections for the alkalimetals are considerably larger than those for theadjoining elements. Thus, the cross section for thepotassium resonance line is about three times as largeas that of calcium. It can be predicted with reasonableassurance that similar relations hold between sodiumand magnesium, and between lithium and beryllium.

Except for the measurements of pressure broadeningof the sodium D lines which are quoted in a previouspaper,' there have been, to the authors' knowledge, onlytwo attempts to measure the optical cross sections foratoms in a medium of predominantly nitrogen. One isthe previously quoted work of James and Sugden3 whohave measured the cross sections for the resonancelines of alkali metals in a hydrogen-air flame by amethod to a certain degree analogous to the procedureused in this work. The other is a paper by Sobolev,Mezhericher, and Rodin4 who have determined thecross sections for the resonance lines of Li, Na, Ca,and the green line of thallium from interferometricmeasurements of the line contours emitted by anacetylene-air flame. The results are compared inTable II. There is a fair agreement between the results

3 C. G. James and T. M. Sugden, Nature 171, 428 (1953).4 Sobolev, Mezhericher, and Rodin, Zhur. Eksptl. i Teort. Fiz.

21, 350 (1951).

159FROM INTENSITY-DENSITY

E. HINNOV AND H. KOHN

of the present work and those of James and Sugden,except for lithium. The cross sections measured bySobolev et al., on the other hand, are clearly incompat-ible with the results of this paper, particularly in caseof calcium resonance line. No explanation for thesediscrepancies can be offered at present.

Numerous theories of the pressure broadening ofspectral lines have been proposed, notably by Weis-skopf,5 Margenau and Watson,' and Lindholm.7According to most of these theories the line broadeningat not too high pressures arises from the interactionof the London forces between the colliding particles.There seems to be a fair agreement between thetheoretical predictions and the few available experi-mental results, if the perturbing particles are idealgas atoms, i.e., if they possess spherical symmetry.Calculations of the cross sections presume the knowledgeof the strengths of the transitions (f values) betweenthe energy levels of both the perturbed and the perturb-ing particles, which are usually not sufficiently wellknown. Nevertheless, it can be seen that the Weisskopf-Lindholm theory, if it were applied in the present caseof perturbing nitrogen molecules, would fail to accountfor such large differences in the cross sections ofrelated atoms, as are observed, for example, in case ofsodium and potassium. From this result it might beconcluded that the nonspherical charge distributionand internal structure of the perturbing nitrogenmolecules exert an influence on the collision interactiontoo large to be neglected. The available data are stilltoo meager to allow more definite conclusions. Moreexperimental work is necessary, involving not onlymore elements, but also the same elements in differentsurroundings, before even empirical relationships,capable of predicting the values of optical cross sectionsfor any two colliding particles, can be developed.

DEGREES OF DISSOCIATION AND f VALUES

The intersection of the asymptotes of an intensity-density curve has been shown' to occur at r= 4 /r. Ifthe concentration of the salt solution at this point isC0 , the proportionality factor between the abscissasof the absolute and the experimental intensity-densitycurves is given by

Q= 4a/7rCo. (4)

The value of log Co for any particular element isobtained directly from the corresponding experimentalintensity-density curve, as shown in Fig. 1. At anyconcentration C of the solution, the concentration ofthe atoms in the flame capable of absorbing the lineunder consideration is therefore

N= mcLPRQC/2e2fla (5)

6 V. Weisskopf, Physik. Z. 34, 1 (1933).I H. Margenau and W. W. Watson, Revs. Modern Phys. 8, 22

(1936).7 E. Lindhiolnm, dissertation, Uppsala, 1942.

according to (1). This number, representing the popula-tion of one particular energy level, makes possible thecalculation of the total number of free atoms of theelement, according to Boltzmann's distribution law.

If the element in question is completely dissociatedin the flame, the concentration of the free atoms isidentical with the total concentration of this elementin the flame. In the following discussion it has beenassumed that the total concentration of the element inthe flame, corresponding to a concentration of thesalt solution C, is the same for all elements, i.e., thatthe total amount of solution brought into the flamedoes not change from element to element. This totalconcentration, as measured for sodium under thepresent experimental conditions, is given by'

NtOtai = 6.2X 10' 4C atoms/cm3 . (6)

Either chlorides or nitrates are used for the saltsolution, because of the high solubility of these saltsin water. In the flame the concentration of Cl, orNO3, is very low, and therefore the original salts arepresumably completely dissociated. From the composi-tion of the flame gases it follows that the existingcompounds of the metals must be predominantlyeither oxides or hydroxides, or both. If the compoundis known to be the oxide of the metal, the degree ofdissociation obtained from (5) and (6), in conjunctionwith the calculated concentration of the free oxygenin the flame, enables the determination of the dissocia-tion energy for the oxide. This method of finding thedissociation energies of metal oxides, except for themanner of determining the degree of dissociation in theflame, has been used by Huldt8 and Lagerqvist andHuldt.0

The density of the free atoms can be obtained from(5) only in case the f value for the line in question isknown. If the f value is not known, but the element istotally dissociated in the flame then N is given by (6),and (5) can be used for calculating the f value for theline under consideration. In case the element is nottotally dissociated, this method yields only a lowerlimit for the f value. In principle, N could also bedetermined if the dissociation energy for the compoundor compounds of the element formed in the flamewere known; but the dissociation energies are usuallynot known in sufficient accuracy to make this procedurefeasible.

In the following discussion the information obtainedfrom the present experiments is treated separately foreach element. The results are too diverse to be expressedin a more concise form. The f values taken fromLandoldt-Bbrnstein0 are identified by (L-B) after thenumerical value.

8 L. Huldt, dissertation, Stockholm, 1948.9 L. Huldt and A. Lagerqvist, Arkiv Fysik 2, 333 (1950).'0Landoldt-Bornstein, Zailenwerte und Funktionen (Springer-

Verlag, Berlin, 1950), 1 Teil, 6th edition, p. 260.

160 Vol. 47

February 1957 OPTICAL CROSS SECTIONS FROM INTENSITY-DENSITY

Li6707, f=0.71 (L-B). Degree of dissociation 21%.This degree of dissociation yields f= 0.0048 for theLi3232 line, as compared with 1= 0.009 (L-B).

Comments on the dissociation energy are giventogether with those for potassium.

Na5890, f= 0.67 (L-B). Completely dissociated. Forthe Na3303 line, there results f=0.011, as comparedwith 1=0.014 (L-B).

K7665, f=0.70 (L-B). Degree of dissociation 43%.According to the work of James and Sugden,"1 thecompounds of lithium and potassium in the flame arethe hydroxides. The vibrational and rotational con-stants are not known for these molecules; thus thedissociation energies can only be roughly estimated tobe about 4.5 ev, with the dissociation energy of LiOHabout 0.2 ev higher than that of KOH.

For the second member of the principal series,the results are f(4044)=0.0137 and f(4077)=0.0067.The first value, f(4044), is given in three significantfigures to show thef ratio of the two components inproper accuracy. The sum of the two f values is givenas 0.014 by (L-B).

Ca4227, f= 2.27 (L-B). Degree of dissociation 4.7%.Comments on the dissociation energy are given

together with those for barium.

Sr4606, A= 1.20 (L-B). Degree of dissociation 11%.Comments on the dissociation energy are given

together with those for barium.

Ba5535, f= 2.21 (L-B). Degree of dissociation 0.21%.The strong bands emitted by the flame when calcium,strontium, or barium are present, appear to be due tothe oxides of these metals. However, several of thosebands have not been positively identified, and some ofthem may be emitted by the molecules or radicals ofthe hydroxide of the metal.'2 Assuming that thecompounds are exclusively oxides, Lagerqvist andHuldt9' 3 have determined the dissociation energies ofthese compounds on the basis of line intensity measure-ments in a flame. Their results are in fair agreementwith thermochemical calculations by Brewer'4 andDrummond and Barrow.' 5 Gaydon'6 has given "recom-mended" values for these dissociation energies, basedon all available data. The results of the present experi-

11 C. G. James and T. M. Sugden, Proc. Roy. Soc. (London)227, 312 (1955).

12 A. Lagerqvist and L. Huldt, Naturwissenschaften 42, 365(1955).

1 A. Lagerqvist and L. Huldt, Z. Naturforsch. 9a, 991 (1954).14 L. Brewer, Chem. Revs. 52, 1 (1953).15 G. Drummond and R. F. Barrow, Trans. Faraday Soc. 47,

1275 (1951).16 A. G. Gaydon, Dissociation Energies and Spectra of Diatomic

Molecules (Chapman and Hall, Ltd., London, 1953), 2nd edition.

ments are compared with these recommended valuesin the following table:

GaydonPresent work

CaO SrO4.7-t0.5 ev 4.64+0.5 ev4.5 ev 4.3 ev

BaO5.4+0.5 ev5.4 ev

Cu3274, 1=0.32 (L-B). Degree of dissociation 82%.If the undissociated copper exists in the form of CuO,

as the green bands emitted by the flame in presence ofcopper indicate, the dissociation energy for CuO wouldbe 3.8 ev. Gaydon'6 gives the dissociation energy ofCuO tentatively as 4.9 ev. This figure is definitely toohigh, as it would correspond to a degree of dissociationof about 2%.

Ag3281-3383. The f values for the silver resonancelines are not known, but silver must be nearly com-pletely dissociated in the flame. The silver compoundshave generally low binding energies. No bands in thevisible spectrum appear in the flame when silver isintroduced, while the resonance lines are emittedstrongly even at rather low concentrations. Assumingcomplete dissociation, the resultingf values are f(3281)= 0.39, f(3383) = 0.22.

T13775-5350. The statements given for silver applyalso for thallium except thatf= 0.096 has been measuredby Kuhn'7 for the ultraviolet line. Assuming completedissociation, the present experiments yield f=0.17for the ultraviolet line, and 1=0.28 for the green line.The result for the green line has been obtained bycalculating the population of the lower energy state,62P, from Boltzmann's distribution law.

Cr4254; 3579. Chromium is not totally dissociatedin the flame. Evaluation of (5) yields 1>0.011 for the4254 line. The absolute f value for this line has beenmeasured by Lagerqvist and Huldt' 8 who obtainf=0.00097, and by Estabrook' 9 who finds f=0.084.The present result obviously supports Estabrook'svalue. According to this f value, the degree of dissocia-tion for chromium would be 13%. If the chromiumcompound in the flame is CrO, this degree of dissociationwould correspond to a dissociation energy of about4.4 ev, in agreement with the result of Lagerqvist andHuldt.'0

For the ratio f(3579)/f(4254) the value 3.6 followsfrom the present data, as compared with 2.9 given byLagerqvist and Huldt'8 and 3.3 by King and Hill.2 '

Mn4030. From (5), the lower limit of the f value forthis line is found to be 0.052. This is in fair agreement

17 W. Kuhn, Naturwissenschaften 13, 724 (1925).18 L. Huldt and A. Lagerqvist, Arkiv Fysik 5, 91 (1952);

J. Opt. Soc. Am. 42, 142 (1952).19 F. B. Estabrook, Astrophys. J. 115, 571 (1952).20 L. Huldt and A. Lagerqvist, Arkiv Fysik 3, 525 (1951).21 A. J. Hill and R. B. King, J. Opt. Soc. Am. 41, 315 (1951).

161

E. HINNOV AND H. KOHN

with the results of Lagerqvist and Huldt2 0 who obtainf=0.062 in conjunction with the dissociation energyof 4.0 ev for the MnO.

Fe. For Fe3720 we obtain f>0.046. King2 2 hasmeasured f= 0.013, and Kopfermann and Wessel23

find f = 0.043 for this line. The agreement is not good,although the latter value could be within the combinederror limits of the present work, and the measurementof Kopfermann and Wessel.

Investigations of other Fe lines yielded the followingrelative values: f (3737)/f (3720) = 1.02; f (3860)/f (3720)-0.53; and f(3581)/f (3720) = 4.9.

Co3526,f> 0.028. No values are given in the literaturefor comparison.

Ni.3524 f>0.187. For this line, Estabrook2 4 givesf=0.0183.

The absolute f values measured by Kuhn, King, and

22 R. B. King, Astrophys. J. 95, 78 (1942).23 H. Kopfermann and G. Wessel, Z. Physik 130, 100 (1951).24 F. B. Estabrook, Astrophys. J. 113, 684 (1951).

Estabrook depend on the vapor pressure data of theelement. All thesef values are considerably smaller thanthose determined from the present experiments, withthe exception of the f value of Cr4254 measured byEstabrook. The agreement with experimental resultsnot depending on vapor pressure data is considerablybetter, again with the exception of thef value of Cr4254as measured by Lagerqvist and Huldt. The greatdifferences in the measured absolute f values partic-ularly for the chromium, iron, and nickel lines, asdetermined by different investigators under variousexperimental conditions, reflect the difficulties ofaccurate measurements of the absolute intensities ofspectral lines. They also show that many of the meas-ured f values are not necessarily well established, andstress the necessity of further experimental work inthis matter.

ACKNOWLEDGMENTS

We wish to express our indebtedness to Dr. H. Sponerand to Dr. W. M. Nielsen for their continued interestin this work.

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