ch. 1 early historical developments in atomic spectra_ocr

8/8/2019 Ch. 1 Early Historical Developments in Atomic Spectra_OCR

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INTRODUCTIONTO

ATOMIC SPECTRA

BYHARVEY ELLIOTT WHITE, PH.D.

Assistant Professor of Physics, at theUniversit y of Californ ia

McGRAW-HILL BOOK COMPANY, INc.NEW Y ORK AN D LO NDON

1934


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INTRODUCTIONTO A r'f ONIIC SPEcr-rRA

CHAPTER IEARLY HISTORICAL DEVELOPMENTS IN ATOMIC SPECTRASpectroscopy as a field of exper imental and theoretical research hascontributed much to our knowledge concerning the physical nature ofthing s -knowledge not only of our own earth bu t of the sun, of inter

stellar space, and of the distant stars . I t may rightly be said thatspectroscopy had its beginning in the year 1666 with the discovery bySir Isaac Newton t ha t different colored rays of light when allowed topass through a prism were refracted at different angles. T he expe rimentsthat Newton actually carried out are well known to everyone. Sunlightconfined to a sma ll pencil of rays by mea ns of a hole in a diaphragm andthen allowed to pass through a prism was spread out into a beautifulband of color . Although it was known to the ancients t ha t clear crystalswhen placed in direct sunlight gave rise to spectral arrays, it remainedfor Newton to show that t he colors did not originate in t he crystal butwere t he necessary ingredients that go to make up sunlight . With alens in t he optical path the band of colors falling on a screen became aseries of colored images of t he hole in t he diaphragm . T his band Newtoncalled a spectrum.Had Newton used a narrow slit as a secondary source of light andexamined carefully its image in the spectrum , he probably would havediscovered, as did Wollaston 1 and F raunhofer - more than one hu ndredyears later, the da rk absorption lines of the sun's spect rum. Fraunhofertook it upon himself to map out several hundred of t he newly found

lines of t he solar spectrum and labeled eight of t he most prominent onesby the first eight letters of the alphabet (see Fig . 1.1). These lines arenow known as the Fraunhofer lines.1.1. Kirchhoff's Law.- More tha n half a century passed in the historyof spectroscopy before a satisfactory explanation of t he F raunhoferlines was given. Foucault " showed that, when light from a very power-

1 W OLLASTON, W . H ., Phil . Trans. Roy. Soc., II , 365, 1802.2 F RAUNHOFER , J ., Gilbert's, Ann ., 66, 264, 1817.' F OUCAULT, L., Ann . chim . et phys., 68, 476, 1860.

1


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2 INTRODUCTION TO ATOM IC SPECTRA [CHAP. Ifu l arc was first allowed to pass through a sodium flame just in frontof the slit of a spectroscope, two black lines appeared in exactly the sameposition of the spectrum as the two D lines of the sun's spectrum. Notmany years passed before evidence of this kind proved beyond doubtthat many of the elements found on the earth were to be found alsoin the sun . Kirchhoff" was not long in coming forward wit h the theorythat the sun is sur rounded by layers of gases acting as abso rbing screensfor the bright lines emitted from the hot surfaces beneath.

Fraunhof e r Lines

, I000044000 00005 00006 0.0007 Millimeters5000 6000 7000 AngstromsFIG. l . l .-Prominent Fraunhofer lines . Solar spectrum.

In the year 1859 Kirchhoff gave, in papers read before the BerlinAcademy of Sciences , a mathematical and experimental ; proof of thefollowing law : Th e ratio between the powers of emission and the powers ofabsorption f or rays of the same wave-length is constant f or all bodies at thesame temperature. To this law, which goes under Ki rchhoff's name, thefollowing corollaries are to be added : (1) Th e rays emi tted by a substanceexcited in some way or another depend upon the substance and the temperature; and (2) every substance has a power of absorption which is a maximum f or the rays it tends to emit. The impetus Kirchhoff 's work gave to thefield of spectroscopy was soon felt, for it brought many investigatorsint o the field .

In 1868 Angstrom 2 set about making accurate measurements of thesolar lines and publi shed an elaborate map of t he sun's spectrum . Angs trom's map, covering the visible region of the spectrum, stood for anumber of years as a standard source of wave-lengths. Every line to beused as standard was given to ten-millionths of a millimeter .1.2. A New Era.- The year 1882 marks the beginning of a new era inthe analysis of spectra. Realizing that a good grating is essential toaccurate wave-length measurements, Rowland constructed a rulingengine and began ru ling good gratings. So successful was Rowland" inthis undertaking that within a few years he published a photographicmap of the solar spectrum some fifty feet in length. Reproductionsfrom two sections of this map ar e given in Fig. 1.2, showing the sodium

1 K IRCHHOFF , G., Monaisber, Berl. ..l kad. lVi ss., 1859, p . 662; Pogg. Ann ., 109,148,275,1860; Ann. ehirn. et phys., 58, 254, 1860 ; 59, 124, 1860.

2 ANGSTROM , A. .1., Uppsala, W. Schultz, 1868.3 ROWLAND, H. A., John s Hopkins Univ. Cire. 17, 1882; Phil . Mag ., 13,469, 1882;

Natur e, 26, 211, 1882.


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SEC. 1.21 EARLY HISTORICAL DEVELOPMENTS 3D lines, t he iron E lines, and the ionized calcium H lines. Wi th a wavelength scale above , t he lines, as can be seen in the figure, were given toten-millionths of a millimeter , a convenient unit of leng th in troduced byo ? 0Angstrom and now called the Iingstrorn unit. The Angstrom unit

FIG. 1.2 .- Section s of Rowl and' s sola r m ap .is abbrevia ted A, or just A, and , in te rms of t he standard meter, 1 m= 1010 A.Up to the t ime Balmer (1885) discovered the law of t he hydrogenseries, many attempts had been made to discover t he laws governingthe distribution of spectrum lines of any element . I t was well knownthat t he spectra of many elements contained hundreds of lines, whereasthe spectra of others contained relatively few. In hydrogen, for example,half a dozen lines apparently comprised its entire spectrum. These fewlines formed what is now called a series (see Fig. 1.3).

In 1871 Stoney;' drawin g an analogy between the harmonic overtones of a fundamental fr equency in sound and t he series of lines in

Blue-Green1Cd'--" --I. ---.J'tHydrogen

0.00044000 0.00055000 0.00066000 Millimeter sA ngstromsFIG. 1.3 .- T he Balmer series of hydrogen.

hydrogen, pointed out that the first, second, and fourth lines were t hetwentieth, twenty-seventh, and thirty-second harmonics of a fundamen talvibration whose wave-length in vacuo is 131, 274,14 A. Ten years laterSchuster- discredited this hypothesis by showing that such a coincidenceis no more than would be expected by chance.

I STONEY, G. J ., Phil. Mag., 41, 2!H, 1871.SCHUSTER, A., Proc. Roy. Soc. London, 3 1 , 337, 1881.


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4 INTRODUCTION TO A TOMIC SPECTRA [CHAP. I

I , !

Liveing and Dewar, 1 in a st udy of the absorption of spectrum lines,made the outst anding discovery that most of the lines of sodium andpotassium could be arranged into series of groups of lines. A reproduction of their diagram is given in Fig. 1.4. Excluding the D lines ofsodium, each successive group of four lines becomes fain ter and morediffuse as it approaches the violet end of the spectrum. Liveing and0 Ill I[5 d 5 d s d L-______ d D'--- - -

K [ [D] r - - - - - - - ; [ I I J L - - _s d s d s d s d 5 d 5 dI I !4500 5000 5500

FIG. 1.4.- Schema tic representation of the sodium and potassium ser ies.and Dewar.)

6000 Angstroms(After Livein g

Dewar say that while the wave-lengths of the fifth, seventh, and eleventhdoublet s of sodium were very nearly as } 5 :}rr :} f' t he whole series cannotbe represented as harmonics of one fundamental. Somewhat similarharmonic relations were found in potassium bu t again no more than wouldbe expected by chance. ' .

Four years later Hartley? discovered that t he components of adoublet or triplet series have the same separations when measuredin terms of frequencies instead of wave-lengths. This is now known asHartley's law. This same year Liveing and Dewar" announced theirdiscovery of series in thallium, zinc, and aluminum. 41.3. Balmer's Law.-B y 1885 the hydrogen series, as observed in thespectra of certain types of stars , had been extended to 14 lines. Photographs of t he hydrogen spectrum are given in Fi g. 1.5. This year issignificant in the history of spectrum analysis for at this early da teBalmer announced the law of the entire hydrogen series. He showedthat, within the limits of experimental errol', each line of t he series isgiven by t he simple relation

2A = h n2 , (1.1 )n - niwhere h = 3645.6 Aand n l and n2 are small integers. The best agreement for the whole series was obtained by making nl = 2 throughout

1 LIVEING, G. D . , and J . D EWAR, Proc. Roy. Soc. London, 29,398, 1879.2 HARTLEY, W. N., J our. Chem. Soc., 43, 390, 1883.3 L IVEING, G. D. , and J . D EWAR, Phil. T rans. Roy. Soc., 174, 187, 1883.

, 4 A more complete an d gene ra l acco unt of the ea rly history of spectroscopy is tobe found in Kayser, " Hanclbuch cler Spektroscopie, Vol. I, pp . 3-128, 1900.


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SEC. 1.4] EA RLY HISTORICAL DEVELOPMENTS 5and n2 = 3, 4,5,6 . . . for the first, second, t hird, four th,of t he ser ies. The agreement betw een the calcul ated andvalues of the first four lines is shown in the following table:

membersobservedTABLE l . l . - B ALIIIER'S L AW FOR T Il E HYDROGEN S ERIES

Calculated wave-lengths Angstrom'sobse rved va lues Difference

Ha = l h = 6562 .08 AHfJ = Hh = 4860.80H.., = Hh = 4340.00H = Hh = 4101.30

6562. 10 A4860 .744340.104101 .20+ 0 .02 A- 0 .06+ 0 . 10- 0 .10

While t he differences between calculated and observed wave-lengthsfor t he next 10 lines are in some cases as large as 4A, the agreement is asgood as could be expected from the exist ing measurements. The

ex Lyr

He---7"=-- X,---+---X, - - -o iCALC IUM

X X41--#--4 I:1 X'I Limit sFIG. l.8. - S ch emat ic p lo t of t he chief trip le t and sin gle t ser ies of calcium sho wing t heR y d ber g-S ch us ter and R unge law s.

1.6. Series Notation.- A somewhat abbreviated no tatio n for Rydberg's formul as was employed by Ritz. This abbrev iated notation,which follows dire ctly from Eqs. (1.14) , (1.15), (1.16), and (1.18a), forthe four chief types of series is written as follows :


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SEC. 1.7] EARLY HISTORICAL DEVELOPMEN TS 11= IP - nS,= IS - nP, = IP - nD.v = 2D - nF. (1.19)

In order to distinguish between singlet-, doublet-, and triplet-seriessystems, various schemes have been proposed by different investigators.Fowler;' for example, used capita l letters S, P,D, et c., for singlets, Greekletters a, 11" , 0, etc ., for doublets, and small let ters s, p , d, etc ., for triplets.Paschen and Gotze" on the other hand adopted the scheme of smallletters s, p, d for both doublets and t riplets, and capitals S, P, D forsinglets.A more recent scheme of spect ra notation, published by Russell, Shenstone, and Turner," has been accepted intern ationally by many investigators. In t his new system capital let ters are used for all series and smallsuperscripts in fron t of each let ter give the multiplicity (see Table 1.4).

TAllLE 1.4.- SERIES NOTATIONSeries Fow ler Paschen Adopted

Singlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S P D F S P D F IS Ip ID IFDoublet .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . U 7r 0


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12 INTRODUCTION TO ATOMIC SPECT RA [CHAP. ISimilar relations are found to exist among the t riplet series of t healkaline earths. The first four members of t he four chief series of

calcium are shown schematically in Fig. 1.10. From the diagram it isseen, first, that t he common limit of sharp and diffuse series is a triple

11Limts 4th. 3rd. 2nd. lsi.

FIG. 1.9.-F requ en cy plo t of t he double t fine structu re in t he chief ser ies of-caesium.limit with separations equal to t he first member of t he principal series;second, that t he limit of t he fundament al series is a t riple limit wit hseparations equal to the separations of t he strongest line and satellitesof the first member of t he diffuse series; and third, that the principalseries has a single limit. I t is to be noted in the doublet series (Figs.

:.1 :1:11III

.~ l L L ~ ~ d p a l. :~ - L L l k hI I I I I I I I I

--1.......l.-L Jl l lLl---l!L -llL -L Gom,o'

Limits 4th 3rd. 2nd. 1st.F IG. 1.ID.- Frequen cy plo t of th e t ri p le t fine st ructure in t he chief se ries of ca lcium.1.9 and 1.7) that, while the first principal doublet becomes the firstsha rp doublet when inver ted, t he reverse is t rue for the triplet series ofcalcium . By inver ting the first sharp-series member (Fig. 1.10), thelines fall in with t he principal series in order of sepa rations and intensities.


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S EC. 1.7] EARLY HISTORICAL DEVEWPMENTS 13In the development of Rydberg's formula, each member of a serieswas assumed to be a single line. In t he case of a series where eachmember is made up of two or more components, t he constants v .. and J.I

ofEq . (1.4) must be calculated for each component. Rydberg's formulasfor the sharp series of triplets, for example, would be written, in theaccepted notation,R R 13P 2 - n3S I," = (1 + 3P 2)2 - (n + 3S 1)2 =

v" = R R 13P 1 - n3S 1, (1.20)(1 + 3P 1)2 - (n + 3S1)2 =R Rv" = (1 + 3P O)2 - (n + 3S1)2 = 13P o - n3S 1,

where 3S 1, 3P O, 3P 1, 3P 2, occurring in the denominators, are small constants . Symbolically 13P2 stands for the term R I (1 + ap 2)2 which isone of the t hree limits of the sharp series. The subscripts 0, 1, and 2used here to distinguish between limits, are in accord with, and are par tof, the internationally adopted notati on and are of importance in thetheory of atomic s tructure.A spectral line is seen to be given by t he difference between twoterms and a series of lines by the difference between one fixed term and aseries of running terms. The various components of the diffuse-tripletseries with three main lines and three satellites are designated13P2 - n3D 3, first st rong line ;13P2 - n3D 2, satellite;13P2 - n3D 1, satellite;

13P 1 - n 3D 2, second st rong line.13P 1 - n 3D 1, satellite. (1.2113Po - n3D1, third st rong line.

The general abbrevia ted not ation of series terms is give n in thefollowing table along with t he early schemes used by Fowler and Paschen

T ABLE 1.5. - N o T ATION OF S ER IE S T ER MSSeries Fowler Paschen Internationallyadopted

Singlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . S P D F S P D F ISo IP I lD2 IF.Doublet .. . . . . . . . . . . . . . . . . . . . . . . . . . a "'2 0 'P 8 P2 d2 t, 2S! 2P i 2Di 2Fi

" '1 0'


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14 INTRODUCTION TO ATOMIC SPECTRA [CHAP. Ilater that each letter and number has a definite meaning, in the l ight ofpresent-day theories of atomic structure.1.8. The Lyman, Balmer, Paschen, Brackett, and Pfund Series ofHydrogen.-It is readily shown that Balmer's formula given by Eq. (1.1)is obtained directly from Rydberg's more general formula

R RP - -n - (nl + J.Ll) 2 (n2 + J.L2)2by placing J.Ll = 0, J.L2 = 0, n l = 2, and n2 = 3, 4, 5,Eq. (1.1),

(1.22)Inverting

1 1 1 ni>.: = a- an = Pn ,

where a = 3645.6 A. Writing R = ni/a,P = R _ R = R ( _ ~ ) n ni ni n

. (1.23)

(1.24)

(1.29)

(1.26)

(1.28)

(1.25)

(1.27)

This is the well-known form of the hydrogen-series formula".It was Ri tz, as well as Rydberg, who made the suggestion that n2

might take running values just as well as nl. This predicts an entirelydifferent series for each value assigned to nl. For example, with nl = 1,2,3 , 4, and 5, the following formulas are obtained:

Lyman series:Pn = R(ii - ~ where n2 = 2, 3, 4,

Balmer series:

(1 1) .n = R ,22 - n , where n2 = 3, 4, 5,Paschen series:P = R(;2 - ~ ~ where n2 = 4, 5, 6,

Brackett series:Pn = R(i2 - ~ ~ where n2 = 5,6,7,

Pfund series:Pn = R (;2 - ~ ~ where n2 = 6,7,8,

Knowing the value of R from the well-known Balmer series the positionsof the lines in the other series are predicted with considerable accuracy.The first series was discovered by Lyman in the extreme ultra-violetregion of the spectrum. This series has therefore become known as theLyman series. The third, fourth, and fifth series have been discovered


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SEC . 1.9} EARLY HISTORICAL DEVELOPMENTS 15

(1.30)

(1.31)

(1.32)

where they were predicted in the infra-red region of the spectrum byPaschen, Bracket t , and Pfund, res pectively. The first line of these fiveseries appears at Al215, ;\6563, ;\18751, M0500, and ;\74000 A, respectively. I t is to be seen from the formulas that the fixed terms of thesecond, third, four th, and fifth equa tions are t he first, second, t hird, andfourth running terms of the Lyman series. Similarly, t he fixed terms ofthe third, fourth , and fifth equ at ions are t he first, second, and thirdrunni ng terms of the Balmer series; etc. This is known as the Ritzcombination principle as it applies to hydrogen.1.9. The Ritz Combination Principle.- Predictions by the Ritzcombination principle of new series in elements other than hydrogenhave been verified in many spectra. I f the sharp and principal series ofthe alkali metals are represented, in the abbreviated nota tion, bySharp: P" = 12P - n 2S, where n = 2,3 ,4 , ,Principal: P" = 12S - n 2p , where n = 2,3,4, ,ihe series predicted by Ritz are obtained by changing the fixed te rms12P and 12S to 22 P , 32P and 22 S , 3 2 S , et c. The resultant formulas areof the following form:

Combina tion sharp series:22 P - n 2S , where n = 3, 4, 5,32P - n 2S , where n = 4, 5, 6,etc .

Comb ination principal series:22S - n 2p , where n = 3, 4, 5,32 S - n 2p , where n = 4, 5, 6,etc.

In a similar fashion new diffuse and fundamental series are predictedby changing the fixed 2p term of the diffuse series and the fixed 2D termof the fundamental series.Since all fixed terms occurring in Eqs. (1.31) and (1.32) are includedin the running terms of Eqs. (1.30), the predicted series are simply combinations, or differences, between terms of the chief series. Such serieshave therefore been called combination series. Ex tensive investigationsof the infra-red spectrum of many elements, by Paschen, have led to theidentificati on of many of the combination lines and series.In the spectra of the alkaline earth element s there are not only thefour chief series of triplets 3S , 3p , 3D, and 3F but also four chief series ofsinglets lS, lp, lD, and IF. Series and lines have been found not onlyfor triplet-triplet and singlet-singlet combinations but also triplet-singletand singlet-triplet combinations. These latter are called in tercombinationlines or series.


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16 INTRODUCTION TO ATOMIC SPECTRA [CHAP. I1.10. The Ritz Formula.- The work of Ritz on spectral series isof considerable importance since it marks the development of a series

formula still employed by many investigators. Assuming that Rydberg'sfo rmula for hydrogen was correct in form

Vn = ( -1), (1.33)p2 q2an d realizing that p and q must be funct ions involving the order numbern, Ritz obtained, from theoretical considerations, p and q in the form ofinfinite series:

(1.34)

(1.35)

Using only the first two terms of p and q, Ritz's equation becomesidentical with Rydberg's general formula which is now to be consideredonly a close approximation. In some cases, the first three terms of theexpansion for p an d q are sufficient to represent a series of spectrum linesto within the limits of experimental error.1.11. The Hicks Formula.- The admirable work of Hicks! in developing an accurate formula to represent spectral series is worthy of mentionat this point. Like Ritz, Hicks starts with the assumption that Rydberg's formula is fundamental in that it not only represents each seriesseparately but also gives the relations existing between the differentseries. Quite independent of Ritz, Hicks expanded the denominator ofRydberg's Eq. (1.3) into a series of,terms

abcn + p. +n+ n2+ n3 +The final formula becomes

JJn = V aoR

( a b Cn+p.+-+-+-+n n2 n3(1.36)

This formula, like Ritz's, reduces to Rydberg's formula when onlythe first two members in the denominator are used.

1.12. Series Formulas Applied to the Alkali Metals.- The extensionof the principal series of sodium to the for ty-seventh member by Wood"(see Fig . 1. 11) and of the principal series of potassium, rubidium, andcaesium, to the twenty-third, twenty-fourth, and twentieth members,1 H I C K S , W. M., Phil. Trans. Roy. Soc., A, 210, 57, 1910; 212, 33, 1912; 213, 323,1914; 217, 361,1917; 220, 335 ,1919.

2 WOOD , R. W., Astrophys. Jour. , 29, 97, 19011.


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SEC. 1.121 EARLY HISTORICAL DEVELOPMENTS 17respectively by Bevan 1 furnishes the necessary data for testing theaccuracy of proposed series formulas. A careful investigation of theseseries was carried out by Birge" who found that the Ritz formula was tobe preferred and that with three undetermined constants it wouldrepresent the series of the alkali metals of lower atomic weight with fairaccuracy. Birge shows that the number of terms that need be used in

Principal Series of Soolium

IIlIlIllII I' 1 1 I I '- i;;;l ,= :::r-::::::::::y.:::::=;.,::;::::r.= =Series Limit 64 75 2490 12 43 2593 ->-.-- 2680 A

FIG. 1.11.-Principal series of sodium in absorption. (After Wood .)the denominator depends directly on the size of the coefficients of theseveral terms, and that these coefficients increase with atomic weight.This increase is shown in the following table:

TABLE l . 6 . - SER IES COEFFICIENTS(Af ter Birge)'

Elemen t Atomic weight a bH 1 0 0He 4 0 .0111 0 .0047Li 7 0.047 0 .026Na 23 0 .144 0.113K 39 0 .287 0 .221Rb 85 0 .345 0.266Os 133 0.412 0.333

I BIRGE . R . T oo A str ophy . J our . 32, 112. 1910.To illustrate the accuracy with which the Ritz formula representsseries in some cases, the principal series of sodium is given in the tableshown on page 18.The Rydberg constant as calculated by Birge from the first fivemembers of the Balmer series of hydrogen and used by him for all seriesformulas is R = 109678.6. I t is to be noted that the maximum errorthroughout the table is only O.lA.This work greatly strengthened the idea that the Rydberg constantwas a universal constant and that it was of fundamental importance in

seriesrelations. The Ritz equation has therefore been adopted by manyinvestigators as the most accurate formula, with the fewest constants,for use in spectral series. A modified but equally satisfactory form ofthe Ritz formula will be discussed in Sec. 1.14.'BEVAN, P. V., Phil. Mag., 19, 195, 1910. BIRGE, R. T., Aslrophlls. Jour ., 32, 112, 1910.


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18 INTRODUCTION TO ATOMIC SPECTRA [C HAP. I

v" = A - ( b)2n + a + n 2where A = 41,450.083 cmr ", R = 109,678.6 cm"', a = 0.144335, and b = -0 . 1130286TABLE 1.7.-THE RITZ FORMULA ApPLIED TO THE SODIUM SERIES OBSERVED BY WOOD(Calculations aft er Birge) 1R

A ac obs . Calc. A ac obs. Calc. A ac obs . Ca lc.n diff . n diff. n di ff.-2 5897 .563 0.00 18 2432 .08 - 0 .0 1 34 2418 .03 +0 .013 3303 .895 0 .00 19 30 .07 - 0 .02 35 17 .75 +0 .024 2853 .63 - 0 .04 20 28 .37 - 0 .01 36 17 .45 0 .005 2681.17 + 0 .09 21 26 .93 + 0.02 37 17 .21 + 0 .036 2594 .67 +0 .09 22 25.65 +0 .03 38 16.98 + 0 .047 2544.49 - 0 .05 23 24 .53 + 0 .01 39 16.76 + 0 .038 2512 .90 + 0. 07 24 23 .55 0 .00 40 16.54 +0 .029 2491 .36 - 0 .04 25 22 .69 0 .00 41 16 .35 + 0 .0310 76 .26 +0 .03 26 21.93 +0 .02 42 16 . 17 + 0 .0211 65 .18 +0 .10 27 21 .25 + 0 .01 43 16.02 + 0 .0312 56 .67 + 0. 05 28 20 .67 +0. 04 44 15 .86 .. + 0.0413 50 .11 + 0 .04 29 20 .15 +0.07 45 15.71 + 0. 0314 44 .89 - 0 .03 30 19 .65 + 0. 06 46 15 .59 + 0. 0515 40 .71 + 0 .01 31 19 .09 - 0 .05 47 15 .43 + 0. 0116 37 .35 +0.06 32 18 .74 0 .00 48 15 .29 - 0. 0117 34 .50 +0.04 33 18 .36 - 0 .01 49 15 .15 - 0 .041 B IRGE , R. T. A s/rophys. J our ., 32 , 112,1 910.1.13. Neon with 130 Series.- T he first successful analysis of a reallycomplex spectrum was made by Paschen I in the case of neon. Although

the neon spectrum was found to contain a great many lines, Paschen wasable to arrange them into 130 different ser ies. These series, classifiedas 30 principal series, 30 sharp series, and 70 diffuse series, were found tobe combinations between 4 series of S te rms, 81, 82 , 83 , and 84 ; 10 series ofP terms, PI, P2, Pa, . . . ,P I0; and 12 series of D te rms, di, d2 , da, .. ,d12 Paschen showed that, while many of t he series were regular andfollowed a Ritz formula, others were irregular and could not be fit ted toany formula. These abnormal series will be discussed in the followingsection.1.14. Normal and Abnormal Series.- Occasionally it is found thatcertain members of a well-established serie s do not follow the ordinaryRydberg or Ritz formula to within the limits of experimental error.Well-known series of this kind were point ed out by Saunders in thesinglet series of Ca, Sr, and Ba, and by Paschen in certain neon series.A convenient method, employed by Paschen and others , for illustratingdeviations from a normal series is to plot f.L, t he residual constant in theRydberg denominator, of each term against n, t he order number of the

1 P ASCHEN. F. , Ann. d. Phys., 60, 405, 1919; 63, 201, 1920.


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S EC. 1.14] EARLY HISTORICAL DEVELOP11JENTS 19

II0

....../ .-- < ,

'%

. / / '.. ;;;.-- < ,1/ -,.-2/d .s-:"

Neon00050000

0.030

ta0201.150010

0.025

term. Several of the diffuse series of terms of neon as given by Paschenare reproduced in Fig. 1.12. A normal series should show residuals thatfollow a smooth curve like the first nine members of the d4 series. Thecurves for the d1, d3, and d5 terms show no such smoot hness, making itvery difficult to represent t he series by any type of series formula .

A series following a Rydberg formula is represented on such a graphby a horizontal line, i .e., JL constant. With a normal ser ies like d 4 of

0.035

FIG. 1.12.-Four di ffuse ser ies in neon showing no rmal and abno rmal progression of t heresidual J.L. (Aft er P aschen .)

neon, a Ritz formula with at least one added term is necessary to adequately represent the series. I f T'; represen ts the running term of aRitz formula, and T 1 the fixed term, .

RPn = T 1 - Tn = T 1 - 2' (1.37)(n+a+ 2 Another useful form of the Ri tz formula is obtained by inserting therunning term itself as a correctio n in the denominator:

RT'; = en + a + bTn )2' (1.38)This term being large at the beginning of a series, the correction iscorrespondingly large. Formulas represen ting abnormal ser ies liked1, d3, and d5 in Fig. 1.12 will be t rea ted in Chap. XIX.

Other anomalies that frequently occur in spectral series are theirregular spacings of t he fine st ruc ture in certain members of the series.A good example of this type of anomaly is to be found in the diffusetriplet series of calcium. In Fig. 1.13 a normal diffuse series, as isobserved in cadmium, is shown in con trast with the abnormal calciumseries. The t hree chief lines of each t riplet are designated a, b, and d,and the three satellites c, e, and f. Experimentally it is the interval


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20 I NTRODUCTION TO A TOM IC SPECT RA [CHAP. Ibetween the two satellites f and c and the in terval between the satellitec and the chief line a that follows Hartley's law of equal separations inboth series . In cadmium it is seen that the main lines and satellitesconverge toward t he three series limits very early in the series. Incalcium, on the other hand, the lines first converge in a normal fashion,then spread out anomalously and converge a second time toward thethree series limits. These irregulari ties now have a very beautifulexplanation which will be given in detail in Chap. XIX .

0 b c d e f a b c d e fI I , --L-I I I I ,II lL- 2 I I. 11....-L IL 3 It II,

IL 4 I. ILh 11 e I, ILI, II, 6 1I I I I 7" I I. 8 lI. II, 9 11 10 I1

11

Lim its l Lim i t s0 0Abnorrmt Ser ies of Co1c ium -A.- Normol Ser ies of CadmiumTr iplets Tr iplets

F IG. 1.13 .-D iffuse se ries of triplets in cadmium and ca lcium.1.16. Hydrogen and the Pickering Series.- In the hands of Balmerand Rydberg the historical hydrogen series was well accounted for whenPickering, in 1897, discovered in the spectrum of t he star r-Puppis aseries of lines whose wave-lengths are closely rela ted t o the Balmer serie sof hydrogen. Rydberg was the first to show that t his new series couldbe represented by allowing n2 in Balmer's formula to t ake both half andwhole integral va lues. Balmer's formula for the Pickering series may

therefore be writtenPn = R(;2- ~ ) where n2 = 2.5, 3, 3.5, 4, 4.5, .. ' . (1.39)

The Balmer and Pickering series are both shown schematically in Fig .1.14. So good was the agreement between calculated and observedwave-lengths that the Pickering series was soon attributed to some newform of hydrogen found in the stars but not on the earth.


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SEC. 1.161 EARLY HISTOUICAL DEVELOPMENTS 21Since n2was allowed to take on half -in tegral values, Rydberg predictednew series of lines by allowing n l to take half-integral values. One series,for example, could be written

(1.40)here n2 = 2, 2.5, 3, . .. .= R C . ~ 2 - ) All of the lines of this predicted series, except the first , are in the ultraviolet region of the spec trum . With the appearance of a line in thespectrum of r-Puppis at M688, the position of the first line of t he predicted series, Rydberg's assumption was verified and the existence of anew form of hydrogen was (erroneously) established.

J J i l l 1 t J ~ r talme-r-Se--le-s- - - - - - - - - - - -JJIIJIIIJ [Picker ing Series

I , , , ,! ! " I , , , , I J' ,, !, I " " I , , ,3.500 4,000 4,500 5000 5 0 6,000 4500 AFIG. 1.14.- Comparison of the Balmer series of hydrog en and the Pickering ser ies.Fowler in his experiments on helium brought out, with a tube containing helium and hydrogen, not only the first two members of thePickering series strongly but also a number of other lines observed byPickering in the st ars. While all of t hese lines seemed to be in some wayconnected with the Balmer formula for hydrogen, they did not seem tobe in any way connected with the known chief series of helium. The

whole mat ter was finally cleared up by Bohr! in the extension of histheory of the hydrogen atom to ionized helium. This is the subject takenup in Chap. II.l.16. Enhanced Lines.- Spectra l lines which on passing from arc tospark conditions become brighter, or more int ense, were early definedby Lockyer as enhanced lines. In the discovery of series re lationsamong the enhanced lines of the alkaline earths, Fowler" made the distinction between three classes of enhanced lines; (1) lines that are strongin the arc but strengthened in the spark, (2) lines that are weak in thearc but strengthened in the spark, and (3) lines that do not appear in thearc at all but are brought out strongly in the spark.Fowler discovered, in the enhanced spectra of Mg, Ca, and Sr, seriesof doublet lines corresponding in type to the principal, sharp, and diffuse1 BOHR, N. , Phil. Mag ., 26, 476, 1913.2 FOWLER , A., Phil. Trans. Roy. Soc., A, 214, 225, 1914.


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22 INTRODUCTION TO ATOMIC SPECTRA [CHAP. Idoublets of the alkali metals. In an attempt to represent these seriesby some sort of Rydberg or Ritz formula, it was found that n2, the ordernumber of the series, must take on half-integral as well as integral values.The situation so resembled that of the Pickering series and the hydrogenseries that Fowler, knowing the conditions under which the enhancedlines were produced, associated correctly the enhanced doublet series ofMg, Ca, and Sr with the ionized atoms of the respective elements. Forsuch series we shall see in the next two chapters that t he Rydberg constant R is to be replaced by 4R so that the enhanced series formulabecomes

Un = 4R{ 1 _ 1 },(nl + J.Ll)2 (n2 + J.L2)2where n2 is integral valued only .

(1.41)

ProblemWith the frequ encies of the four chief series of spectr um line s as given for ionizedcalcium by Fowl er , "Series in Line Spect ra ," construct a diagram similar to the oneshown in Fig. 1.7. Indicate clearl y th e in tervals illustrating the Rydberg-Schu ster

and Runge laws.

ch. 1 early historical developments in atomic spectra_ocr

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