OCTOBER 15, 193Z PHYSICAL REVIEW VOL UllIIE 4Z

The Spectrum of Potassium Hydride

By G. M. ALMY AND C. D. HAUSE

University of Illinois

(Received August 17, 1932)

The 'Z —+'Z molecular spectrum extending from 4100A to 6600A has been photo-graphed with prism spectrographs with a d.c. potassium arc in hydrogen as source. Inabsorption spectrographs, also attempted, the bands were masked by alkali bandsexcept in a short region, 4600A to 4800A. The spectrum is of the many-lined type.Analysis disclosed 29 bands falling into five v' progressions. Each band consists of Pand R branches only. The rotational and vibrational constants (Table III), whichfall into line with the corresponding values for LiH and NaH, are surprisingly dif-ferent in the two states. B,' and co,' show an anomaly, rising with increasing v' forlow values of v', then decreasing. Extrapolation of the vibrational levels indicatesthat the products of dissociation in the two states di6'er by the energy of the resonancelines of K(1.60 volts). Heats of dissociation of 1.25 and 2.06 volts are obtained forthe excited and ground states, respectively. From potential energy curves a Franck-Condon diagram of intensity is drawn and is in good agreement with observed in-tensities.

~HE molecular spectra of two of the diatomic hydrides have already beenanalyzed and reported; Nakamura' examined the spectrum of LiH as

obtained in absorption while Hori' has made an extensive study of NaH inboth absorption and emission. Most of the LiH spectrum falls between3000A and 4500A, that of NaH between 3500A and 5000A. The two spectra,which are of the many-lined type, are much alike and have been assigned ineach case to a '2—&'Z transition. Extrapolation of the vibrational levels ofthe two states of an alkali hydride indicated as the products of dissociationa normal hydrogen atom and a normal alkali atom from the lower state anda normal hydrogen and an excited 'P alkali atom from the upper state. Inthis paper the analysis of the corresponding 'Z —&'Z system of KH, obtainedin emission and extending from 4100A to 6600A, is discussed.

A point of interest in the alkali hydrides is the anomalous behavior ofe„, the vibrational interval in the upper state. Instead of decreasing steadilywith increasing v in the usual way, it rises, attains a maximum at aboutv'=9, and then falls. This peculiar behavior is found in KH, as well as inLiH and NaH.

EXPERIMENTAL PROCEDURE

The source of the KH spectrum was a d.c. potassium arc operating inhydrogen. The arc was contained in a brass chamber, cooled by water circu-lating in a lead tube coiled about it. The electrodes, also water-cooled, werefixed into the removable top and bottom plates. The lower electrode was ahollow iron cylinder of about 1 cm internal diameter, with an iron cap havinga 4 mm hole in its center. In the cylinder was a piston with a threaded shaft

' G. Nakamura, Zeits. f. Physik 59, 218 (1930);Japanese Journal of Physics '7, 31 (1931).~ T. Hori, Zeits, f. Physik 62, 352 (1930);7'1, 478 (1931).

242

SPEC TR UM OF PO TA SSIUM H YDRIDE 243

such that the piston could be advanced from outside the arc chamber. Thuspotassium, contained in the cylinder, could be gradually extruded throughthe cap to keep a supply in the burning arc. A section of pressure tubing sur-rounded the piston shaft and its sleeve, soldered to the arc chamber, to pre-vent entrance of air. The shaft could be turned in the tubing. The upperelectrode was of nickel or iron. Its shaft also entered the chamber through asleeve, shaft and sleeve being surrounded by a section of tubing. The arc wasstruck by pressing the upper electrode against a coil spring.

Tank hydrogen was supplied continuously through a capillary tube. Apressure of about 20 cm of Hg was maintained, although the pressure didnot seem to be a very critical factor in determining the intensity of the bands.Potential was supplied by a 500-volt d.c. generator and the current in thearc was held to about 3 amperes with series resistance. A single filling ofpotassium (about an ounce) could be made to last 3 or 4 hours. Exposuresup to ten hours were taken.

Most of the analysis was made from photographs taken with an E-1Hilger glass prism spectrograph. When the analysis was nearly completed aprism spectrograph fitted with a glass optical train (Hilger) consisting of a60' prism, a 30' prism, and an achromatic lens of 3 meters focal length, inLittrow mounting, became available. This instrument was used to extendthe spectrum above 5900A where the dispersion of the E-1 was insufhcientto give satisfactory measurements. The larger instrument had a dispersionof 10A per mm at 6600A, equal to the dispersion of the E-1 at 5000A.

An attempt was made to photograph the KH spectrum in absorption.Potassium was heated, with hydrogen, in a length of iron tube, placed in agas combustion furnace. The absorption spectrum was obtained but it waslargely masked by other spectra. Below 4600A the spectrum of K2 was promi-nent. Above 4800A the blue-green system of Na& (present as an impurity)extended up to the NaK bands falling just below the D lines of Na. Abovethe D lines the red system of Na& appeared. Between 4600A and 4800A,however, the spectrum of KH, corresponding exactly with the emission spec-trum, could be observed.

ANALYSIS OF BAND SYSTEM

The KH spectrum is of the many-lined type; no heads or other regularitiesof structure are apparent on casual inspection. This is due to the fact that theheads of the bands almost coincide with the origins and to the overlappingof the bands. It is, therefore, not possible to make a vibrational analysiswithout first completing the rotational analysis, thus locating the bandorigins.

To carry out a rotational analysis, a beginning was made by picking outa branch of one of the stronger bands using the criterion that the second dif-ferences of the frequencies should be constant. This branch, being a strongone, could be followed through the origin and its character (I' or R), as wellas the rotational quantum numbers, determined. The combination differ-ences,

G. M. ALLY AND C. D. IIA USE

DENT' = R(E") —P(K")DgT" = R(E" —1) —P(K" + 1),

were calculated for this band. Then bands in the same v' progression couldbe identified since they have the same value of A&T", while bands in the samev" progression yielded identical values of 62T'. Once the vibrational intervalswere approximately determined the analysis proceeded rapidly. Often whenthe hunt for the correct combination differences did not give resultspromptly, a new start in the proper region with second differences disclosedthe next band in a progression.

In this way 29 bands were located. The frequencies with quantum as-signments are listed in Table VI at the end of this paper. Since about 85percent of the lines appearing on the plates were assigned and since the re-maining lines were mostly of very low intensity it is quite certain that thebands are of the simple two-branch type originating from a 'Z~'2 transition.The system thus corresponds to the similar systems found for NaH and LiH,assigned to po'2 —+so'2 transitions.

CALcULATIoN QF MoLEcULAR CQNsTANTs

The next step was the calculation of the rotational constants and theband origins. The combination differences were tabulated (Tables IV and V)and mean values taken where more than one value was obtained for a par-ticular pair of rotational levels. Since the rotational energy of a molecule in a'Z state is

T = B„K(K/ 1) y D E'(E y 1)' y F K'(E y 1)'p

the combination differences can be expressed,

dgT = T(K+ 1) —T(E —1)= 48, (E + —',) + 8D„(E + —,')' + 12F„(E'+ -', )' (2)

where terms small in comparison with F„(K+1/2)5 are dropped. B„dependsupon v according to the relation,

B. = B.—~.(~ + k) + v (~ + 2)'

in which B,(=h/ger'I, c) is the extrapolated value corresponding to the non-

vibrating molecule. Theoretically D„and F„also depend on v but the accuracyof the present data did not warrant the calculation of this variation. HenceD, was set equal to D, and F, equal to F,.

A method of successive approximation was used to obtain 8„.First, theD and F terms of Eq. (2), which are relatively small, were neglected andapproximate values of B„obtained, using the measured combination differ-ences from Tables IV and V. Then approximate values of D, and F, werecalculated from the theoretical relations,

D. = —48,'/w, '(4)

F, = (D,'/8, )(2 —n, cu,/68, ') .

co, was approximately known from the separations of corresponding linesin successive bands in a progression. n, was assumed to be zero in this ap-

SPECTRUM OF POTASSIUM HYDRIDE

proximation. These values of D, and F, were then used in Eq. (2) to obtainthe second approximation for 8„, the mean for several values of Z beingtaken. The origins of the bands were then calculated from the equation,

v = vo + (8,' + 8„")M+ (8„' —8„"+ D,' —D,")M2

in which vo is the origin. For the R branch M=X"+1, for the I' branchM = —X".Here the Ii, terms are omitted because they are inappreciable forthe values of M ((15) used. From these calculated origins the vibrationalintervals, co„, were determined and extrapolated to give co,. Then improvedvalues of D, and F, were calculated from Eqs. (4) and the process describedrepeated to give a third approximation. This approximation was found to besuf6cient, considering the accuracy of the data.

TABLE I.BGnd origins with values of co,interPoluted.

Mean

10

12

13

20527.4 956.9287.8

20815.2 955.8290.5

21105.7 (952.5)291.5

21397.2293.8

21691.0293,0

21984,0292.8

22276. 8291.6

22568.4290.0

22858.4 955.1

19009.9 927.7277.3

19287.2 925.8283.3

19570.5 927.0288.9

19859.4(293.8)

20153.2

21903.3288.0

22191.3284.4

22475. 7281.5

22757. 2

17809.5272. 7

18082.2279.2

18361.4282. 1

18643.5

16386.0 868.3 15517.7259.5 259.5 259.5

16645.5 868.3 15777.2266.5 266.6 266.6

897.5 16912.0 868.2 16043.8271.8 272.2

898.4 17183.8278.2

282.7

288.3

290.5

291.5

293,8

293.0

292.8

291.6

290.0

288.0

284.4

281.5

Mean cv", 955.9 926.8 898.0 868.3

G. 3E. AL3IF AND C. D. &AUSE

In Table I the band origins are listed in square array with assignments ofv' and v". The values of v" are certainly correct but there is some doubtabout v'. The correctness of the assignment of these quantum numbers willbe discussed in the last section of the paper. The values of co„' and co„" alsoappear in Table I. In Fig. 1, co,

' is plotted against v', together with corre-sponding graphs for NaH and LiH, showing the anomalous increase in co„'

with v' for low v'. co„" follows a normal course, decreasing linearly with in-creasing v". The values of co„' have been fitted with a power series in (v+1/2)

Ã0LiM

070

VJO

3 510

HM

250Q ? 4 6 S 10 I2, 14 16

VFig. 1. Anomaious behavior of cv,

' in excited 'Z states of LiH, NaH, and KH.

by a least-squares calculation, with deviations, except one, less than 1 cm '.The result is incorporated in the following equation for the band origins,

v = 19525.2 + [254.51(v' + —',) + 3.26(v' + —')'+ 0.00725(v' + 2)'—0.0105(v' + -,')' + 0.000273(v' + —',)'] —[984.3(v" + —',)—14.5(v" + -')'].

The calculated values of B,' and B,"are listed in Table II. B,' parallelsve, ' in its anomalous behavior. It increases until v'=6 and then decreases.

TABLE IE,

BII B', Bll Bf/

1.3591.3851.4051.4221.4321.438

3.3733.2923.2093.1223.041

67

89

1011

1.4371,4321.4311.4161.4051.391

1213141516

1.3/61.3601.3341.3231.307

SPECTRUM OF POTASSIUM HYDRIDE

8," decreases linearly with increasing v".- The rotational and vibrationalconstants together with those of LiH and NaH, obtained respectively fromNakamura's and Hori's papers, are collected in Table III.

TABLE III. Principal rotation and vibration constants.

Constant LiH NaH

B11

l1e

D I /

Fl1

IIe

II IIX or e

3 ~ 'TX10 4'

1.6 X 10-s

7.38

1395

22. 7

5.65X10 "1 ' 88 X10 s

4.896

0.13—3.3X10 4

1 3X10 s

1170.818.9

8.10X10 "(gcm')

2.24X10 '(cm)3.4150.083

—1.65X10 4

1.5X10 s

984.314.5

r e

B'.

F'.I

Or e

I ISore

9.3 X10-4o

2.5X10-s3.00

272—9.61

14.66X10 4'

3.03X10 '1.887

—0.028—1.85X10 4

~0 8X10 s

335.24

—. 4.416

20 6 X 10 4' (g cm')

3.58X10 ' (cm)

1.344—0.030—1 44X10 4

3 8X10 s

254.5—3.26

Heat of D'dissoc. D"

1.142.56

1.472.24

1.25 (volts)2.06 (volts)

A satisfactory explanation of the peculiar behavior of the upper state hasnot been given. Following Nakamura's account of it in LiH, Weizel at-tempted to explain the anomaly as due to an uncoupling, as the rotationincreases, of the orbital angular momentum l of the pa electron of the excitedmolecule. Such an effect would result in a calculated value of 8„less than the"true" 8, the depression being greater for slower vibrations. Such an ex-planation is inadequate to account for the behavior of cu„'. The positions ofthe origins should be independent of rotational uncoupling effects. It might beargued that since the origins were calculated from rotational data, the calcu-lated positions of the origins does depend upon the uncoupling. If, however,one uses for co, ' the frequency intervals between corresponding lines of suc-cessivebands —lines for which X" is so small, say 2, that the rotation couldscarcely affect it—one obtains a series of values of co, inappreciably differentfrom those obtained from the calculated origins. That is to say, the anomaly,at least for m„', seems to be iridependent of any rotational uncoupling thatmay be present.

s W. Weizel, Zeits. f. Physik 60, 599 (1930).

G. 3f. AI.MF' AND C. D. IIA USE

POTENTIAL ENERGY CURVES AND HEAT OF DISSOCIATION

Potential energy curves, based on the Kratzer form, are shown in Fig. 2.In the form used, the potential energy does not involve coeKcients in thevibrational energy beyond the second (xcu, ) nor coefficients in the expressionfor B„(Eq.(3)) beyond n, . Though ordinarily positive xv, and a, are negativein the upper state of KH. This change tends to steepen the potential energycurve for r &r, and fiatten it for r(r, . For the ground state the potentialenergy curve was obtained from the Kratzer expression for r near r„while inthe neighborhood of dissociation the Morse form was used.

The heat of dissociation of the lower state was calculated from the ex-pression D =co, /(4xco, ) since the vibrational energy in this state is accuratelyrepresented by T'= is, (s+ —',) —@co,(s+-', )' with co, =984.3 and nv. = 14.5. D isthus 2.06 volts.

30000 K('P) one HPS)

V

20000

L2V volte

IA 0volts

K(Q) and H( 3„/\

10000

2,06 volt~

0'.0 2 4 6 8 f0 12

Internuclear distance (cm x lo')

Fig. 2. Potential energy of normal and excited states of KH.

On account of the peculiar behavior of co„' the heat of dissociation of theupper state was determined by making use of the energy of the dissociatedproducts. Rough extrapolation of the vibrational levels of the upper stateindicated a heat of dissociation of about 1.5 volts. This requires that theatomic energy of the products of dissociation in the upper state be i.8 voltsgreater than that of the products of the ground state. The resonance linesof potassium correspond to an excitation of 1.60 volts. Hence the productsof dissociation in the upper state are normal hydrogen and potassium in thefirst excited state ('P). This atomic energy was added to D" (2.06) volts)and the electronic energy of the excited molecular state (i 0) subtracted fromthe sum to give 1.25 volts for D', the heat of dissociation in the upper state.

From the potential energy curves the Franck-Condon intensity diagramin Fig. 3 was drawn, using the improved form suggested by Loomis andNusbaum. 4 The theoretical locus of maximum intensity is shown by the

SPECTRUM OIi POTASSIUM HFDRIDZ 249

curve, the observed bands by sma11 circles. The discrepancy at high frequen-cies is not surprising since the steep, uncertain, part of the energy curve ofthe upper state is involved.

ASSIGNMENT OF V AND V . ISOTOPE EFFECT

The assignment of v" is certainly correct since a thorough search onemission and, more important, on absorption photographs disclosed no bandsof a lower progression than the one for which v" was set equal to zero. Asto the upper state we suggested in a preliminary report' that the bands nowmarked v'=4 belonged to the state for which v'=0. Improvements in tech-nique enabled us to extend the spectrum to the red four vibrational intervalsof the upper state. In the progression for which we now put v'=0, there areonly two bands, (0, 3) and (0, 4). The evidence for the present assignment is

I90002.000

IlT' (cm-'08000 6000 SOOO 10000

0 0er

glaoO;JY 0

(])

g&000'

o

8

25000

g resonance tines &

$7000L

Fig. 3. Intensity diagram for KH. Circles are observed band origins.Curve is theoretical locus of maximum intensity.

first, that no bands assignable to a lower n' could be found even though thebands in this region (6100A—6500A) were well developed in the long expo-sures and, second, that the assignment fits well with the Franck-Condoncurve, which is most reliable in this region. Additional evidence was soughtthrough the isotope e6ect. The heavier isotope of potassium, of mass 41, ispresent in the ratio of about 1 to 20. No lines of K4'H could be found in theemission photographs. In the absorption photographs, limited to the region4600—4800A, faint lines accompanied the intense lines in about the estimatedpositions. Measurements of the isotope shifts (about 1—2 cm ') made on twoplates, were not suKciently accurate to fix with certainty the v' assignment.Averages of calculated and measured values indicate that the assignment isabout right, but may still be too high by one. Such a change would makelittle difference in any of the molecular constants listed.

4 F. W. Loomis and R. E. Nusbaum, Phys. Rev. 38, 1447 (1931).' G. M. Almy and C. D. Hause, Phys. Rev. 39, 178 (1932).

G. 3f. AL, MV AND C. D. IIA USE

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SPECTRUM OF POTASSIUM IIYDRIDE

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G. M. AI.MF AND C. D. IIA USE

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SPECTRUM OF POTASSIUM HYDRIDE 253

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