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INTRODUCTION
TO
ATOMIC SPECTRA
BY
HARVEY ELLIOTT WHITE, PH.D .
Assistant Pr ofessor of Physics, at the
University of Californ ia
McGRAW-HILL BOOK COMPANY, INc.
NEW Y ORK
AN D LO NDON
1934
INTRODUCTION
TO Ar'f ONIIC SPEcr-r RA
CHAPTER I
EARLY HISTORICAL DEVELOPMENTS IN ATOMIC SPECTRA
Spectroscopy as a field of experimental and t heoretical research has
cont ributed much to our knowledge conce rni ng t he ph ysical nature of
things-knowledge not only of our own earth bu t of t he sun , of int erstellar space, and of t he distan t stars. It may rightly be said t hat
spectrosco py had its beginning in t he year 1666 wit h t he discovery by
Sir Isaac Newton t ha t different colored rays of light when allowed to
pass t hro ugh a prism were refr acted at different angles. T he expe riments
that Newton actua lly carried out are well kn own to everyone. Sunlight
confined to a sma ll pen cil of rays by mea ns of a hole in a dia phragm and
then allowed to pass t hro ugh a prism was spread out into a bea utiful
band of color . Alt hough it was known to the an cients t ha t clear crystals
when placed in direct sunlight gave rise to spectral arrays, it remained
for Newton to show t hat t he colors did not originate in t he crystal bu t
were t he necessar y ingredients t hat go to make up sunlight. With a
lens in t he optical path t he ba nd of colors fallin g on a screen became a
series of colored images of t he hole in t he dia phragm. T his band Ne wto n
called a spectrum .
Had Newton used a narrow slit as a secondary source of light and
examined carefully its image in t he spectrum , he probabl y would have
discovered , as did Wollaston 1 and F raunhofer - more t han one hu nd red
years later, t he da rk absor ption lines of the sun's spect r um . Fraunhofer
took it up on himself to map out several hundred of t he newly found
lines of t he solar spectrum and lab eled eight of t he most prominent ones
by t he first eight letters of t he alphabet (see Fig. 1.1). These lines are
now kno wn as t he Fraunhofer li nes.
1.1. Kirchhoff's Law. - M ore t ha n half a century passed in t he history
of spectrosco py before a satisfactory explanation of t he F raunhofer
lines was give n . F oucaul t " showe d t hat, whe n light fr om a very powerH ., P hil . T rans. Roy. Soc., II, 365, 1802.
J ., Gilbert's, Ann ., 66, 264, 1817.
L., Ann. chim . et phys., 68, 476, 1860.
1 W OL L AST ON , W.
2
F RAUNHOFER ,
' F OUCAULT,
1
INTRODUCTION TO ATOMIC SPECTRA
2
[CHAP. I
fu l arc was first allowed to pass t hrough a sodium flame just in front
of t he slit of a spectroscope, two black lines appeared in exactly t he same
position of the spect ru m as t he two D lines of t he sun's spectrum. Not
many years passed before evidence of t his kind pr oved beyon d doubt
t hat many of the elements found on the earth were to be foun d also
in the sun . Kirchhoff" was not long in coming forward wit h t he t heory
that the sun is sur rounded by layers of gases acting as abso rb ing scree ns
for the brig ht lines emitted from the hot surfaces beneath .
Fr a unhof e r Lines
,
I
00004
4000
00005
00006
5000
6000
FIG. l.l.-Prominent Fraunhofer lin es.
0.0007 Millimeters
7000 Angstroms
Solar spectru m.
In the year 1859 Kirchhoff gave, in papers read before t he Berlin
Academy of Sciences , a mathematical and experimental; proof of t he
following law : Th e ratio between the powers of emi ssion and the powers of
absorption f or rays of the same wave-length i s constant f or all bodies at the
same tem perature. To this law, which goes under Ki rch hoff's name, t he
following corollaries are to be added : (1) Th e rays emitted by a substance
excited in some way or another depend upon the substance and the temperatur e; 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 t he
field of spectroscopy was soon felt, for it bro ught many investigators
int o the field .
In 1868 Angstrom 2 set abo ut making accurate measurements of t he
solar lines and publi shed an elaborate map of t he sun 's spectrum. Angstrom's map, covering the visible region of t he spectrum, stood for a
number of years as a standard source of wave-lengths . Every line to be
used as standard was given t o ten-millionths of a millimeter.
1.2. A New Era.- The year 1882 marks the beginning of a new era in
the ana lysis of spectra. Realizing that a good grating is essential to
accurate wave-length mea sureme nts, Rowland constructed a ruling
engine and began ru ling good gratings . So successful was Rowland" in
this undertaking that within a few years he pub lished a ph otographic
map of the solar spectrum some fifty feet in lengt h . Reproductions
from two sections of this map ar e given in F ig. 1.2, sho wing the sodium
1 KIRCHHOFF, 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., Up psa la, W. Schultz , 1868.
3 ROWLAND, H. A., John s Hopkins Univ. Cire. 17, 1882; Phil . Mag ., 13,469, 1882;
Natur e, 26, 211, 1882.
3
EARLY HISTORI CAL DEVELOPMENTS
1.21
SEC.
D lines, t heiron E lines, and the ioniz ed calcium H lines. Wi th a wavelength scale above, t he lines, as ca n be seen in the figure, were given to
ten-m illionths of a millimeter, a conv enient unit of leng th in troduced by
o
?
Angstrom and now called t he Ii ngstrorn unit. The Angstrom unit
0
FIG. 1.2 .- Section s of R owl and' s sola r m ap .
is abbrevia ted A, or just A, and, in te rms of t he standard m eter, 1 m
= 10 10 A.
Up t o t he t ime Balmer (1885) discover ed t he law of t he hydrogen
series, many attem pts had been made to discover t he law s govern ing
the distributi on of spectrum lines of a ny eleme nt. It was well kn own
that t he spectra of many elem en t s contained hundreds of lines, wh ereas
the spectra of othe rs containe d relati vely few. In hydrogen , for exa m ple,
half a dozen lines apparently com prised it s entire spectrum . These few
lines formed wh at is now called a series (see Fig. 1.3).
In 1871 St one y;' drawin g an analogy betw een t he harmoni c ov ertones of a fundamental fr equ en cy in sound and t he series of lines in
Blue-Green
1Cd'--"
- -'.J t
--I.
Hydrogen
0.0 004
4000
0.0005
0.0006
5000
6000
FIG. 1.3 .- T he Balmer ser ies of hydrog en .
Millimeter s
A ng stroms
hydrogen, pointed ou t that the first, second , and fourth line s were t he
twentieth, twenty-seventh, and t hirty-second harmonics of a fundamen tal
vibration who se wave-length in vacuo is 131, 274,14 A. Ten ye ars la te r
Schust er- di scredited this hypothesis by sho wing t hat such a coinc idence
is no more than would be expected by chance .
I
STONEY,
G. J ., Phil. Ma g., 41, 2!H, 1871.
A., Proc. Roy. Soc. London, 3 1 , 337, 1881.
~ S CH U STER,
4
[C HAP. I
I NTROD UCTIO N TO A TOM IC SP EC T RA
Liveing and Dewar, 1 in a st udy of t he absorp tion of spectrum lines,
made the outst anding discovery t hat most of t he lines of sodium and
potassium could be arranged in to series of groups of lines. A reproduction of their dia gram is given in Fig. 1.4. E xcluding t he D lines of
sodium, each successive group of four lines becomes fain ter and more
diffuse as it approaches t he violet end of t he spectrum . Liveing and
~
d 5 d 5
d
0
s
L-______
d
[[D]
K
sd
sd
sd
~
Iil
d
D'---
-
-
I[
~r-------;[IIJL--_
sd
5
d
5
I
I
!
4 500
5000
5500
d
I
,
!
6000 Angstroms
- A~
FIG. 1.4 .- S ch ema ti c representation of t he sodium and potassium series .
and D ewar. )
(After Livein g
Dewar say t hat while t he wave -lengths of t he fifth, sevent h, an d eleventh
doublet s of sodium were very nearl y as } 5 :}rr :} f' t he whole series cannot
be repr esented as har monics of one fundam ental. Somewhat similar
harm oni c relati ons were found in pot assium bu t again no more t han would
be expe ct ed by cha nce.
'
.
Four years later H ar tl ey ? discovered t hat t he components of a
doublet or t riplet series have t he same separations when measured
in t erms of frequ en cies instead of wave-lengths. This is now known as
Hartley' s law. This same year Liv eing and Dewar " announced t heir
discovery of series in thallium, zinc, and aluminum. 4
1.3. Balmer's Law.-By 1885 t he hydrogen series, as observed in the
spectra of cert ain types of stars, had been extended to 14 lines. Photographs of t he hydrogen spectrum are given in Fi g. 1.5. This year is
significant in the history of spectrum ana lysis for at t his early da te
Balmer announced t he law of t he entire hydrogen series. He showed
t hat, within t he limit s of experimental errol', each line of t he series is
given by t he simple relation
A= h
2
n2
n§ -
,
ni
(1.1)
where h = 3645.6 A and n l and n2 are sma ll inte gers. The best agreemen t for the whole series was obtained by making n l = 2 t hroughout
G. D . , and J . D E W AR , Proc. Roy. Soc. London, 29,398, 1879.
W. N., J our. Chem. Soc., 43, 390, 1883.
3 L IVEIN G, G. D. , and J . D E WAR , Phil. T rans. Roy. Soc., 174, 187, 1883.
, 4 A more com plete an d gene ra l acco unt of the ea rly history of spectrosco py is to
be found in Kayser, " H anclbuch cler Spe ktroscopie, Vol. I, pp . 3-128, 1900.
1 LIVEING,
2 HARTLEY,
5
EA RL Y HISTORIC AL DEVELOPMENTS
SEC. 1.4]
and n2 = 3, 4,5,6 . . . for t he first, second, t hird, fourth,
members
of t he ser ies. The agreem ent betw een t he calcul ated and observed
values of t he first four lines is shown in t he following table :
TABLE l. l.-
B ALIIIE R'S L AW FO R T Il E HYDROGEN S E RI E S
Cal culated wave-len gths
H a = l h = 6562 .08
HfJ = Hh = 4860.80
H.., = Hh = 4340.00
H~ = Hh = 4101.30
A
Angstrom 's
obse rve d va lues
6562. 10
4860 .74
4340 . 10
4101 .20
A
D ifferen ce
+
+
-
0 .02
0 .06
0 . 10
0 .10
A
Whil e t he differen ces bet ween calculated and observe d wav e-lengths
for t he next 10 lines are in some cases as large as 4 A, t he agreement is as
good as could be expected from t he exist ing measurements. The
He<
Balmer Senes
of
HYDROGEN
Stella r a nd Solar Spectra
.lJXK i
...
"'~-"'-~~--------";'_
.........
- ....-- ---.....
en!:
. ». . . . .
.._ • ..J x Pegasi
ex Lyr
Solar
~==~~:;:~=,:=:;::=:~~===~========!!
Eclipse
-.::::to o co
'0"'......0.
lJ)
N)
~~~I:ti f55
0..
0
N
0
~
~
~
'<t
"<t
~
co......
<:>;:)l;
~
FIG. 1.5.- Stella r and solar spe ctrograms sho wing t he Balm er se ries of hydrogen.
accuracy wit h which lines were t hen know n is seen from t he following
measur ements of five differe nt investi gators for t he first member of t he
hydrogen series:
TABLE 1.2.-EARLY M E ASU RE S OF THE H YDROGE N LINE
6565 . 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6562 .10
6561 . 62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
6560 .7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6559 . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Ha
Van der Willigen
Angstrom
Menden ha ll
Mascart
Di t scheiner
1.4. Rydberg's Contributions.-Rydb erg's ea rly contributions to
atomic spectra consisted not only in findin g t he laws of a number of
series bu t also in showing t hat H ar tley's law of constant frequ ency
differences was applica ble in cases where t he doublet or t ri plet components were very far apa rt. For exa mple, he showe d t hat t he first
member of t he prin cipal series of t ha llium is a doublet with the enormous
6
[C HAP. I
INTROD UCTIO N TO ATOMI C SPECTRA
sepa ration of 1574 A, one line lyin g in t he green at >"5350 and t he ot her
in t he nea r ult ra-violet at >"3776. T his discovery proved to be of considerable importance, as it suggested the possibility that a ll series arising
from t he same element were in some simp le way connected wit h each
ot her.
Using Liveing and Dewar's data on the sodium and potassium
series, Rydberg made for the first time the distinctio n between what is
called a sharp seri es and a dt":ffuse series . T he Na and K series given in
Fig. 1.4 were each shown to be in realit y two series, one a series of sharp
doub lets (designated by s) and t he ot her a series of diffuse doublets (designated by d).
A t hird type of series found in many spectra is the so-called principal
series, involving as its first member the resonance or persistence line of t he
entire spectrum . Resonan ce or persistence lines are t hose relatively
st rong lines most easily excited. Such lines usually appear st rong in a
Bunsen flame. The yellow D lines are a good exam ple of t his.
Still a fourth type of series was discovered by Bergmann. T his type
of series is usually observed in the near infra-red region and' is sometimes
called t he B ergmann series. Since Bergmann did not discover all such
series, H icks called t hem the fundam ental seri es. Although t his name is
per ha ps less app ropriate t ha n t he ot her and is rea lly misleading , it has
afte r 20 years become attached to t he series. New series were discovered so ra pidly abo ut t his t ime t hat ma ny different nam es and
systems of notation arose. Three of t hese systems commonly used are
given in t he following table.
TABLE 1.3.-8ERIE S NOTATION U SED BY D I F F E R E N T INVESTIGATORS
Foote and Mohler
Second subord ina te
Principal
First subo rd inate
Bergm ann
.
.
.
Paschen
Rydberg
II. Nebenserie
Hauptserie
1. Neb enserie
Bergm ann
Sharp
P rincipal
Diffu se
Fundam ental
In searching for a genera l series formu la Rydberg discove red t hat
if t he wave-lengths X or t he frequ en cies 1J of a series be plot ted aga inst
consecutive whole numbers, a smooth curve which is approximately a
displaced rectangular hyperbola is t he result.' For a curve such as t he
one shown in Fig . 1.6 he attempted a solution of t he form
1 It is convenient in practice to express v numerically not as the actual frequency
but as the fr equ ency divided by the velocity of light. Such quantities are called
wave number8 and, since c = VA, they a re given by the reciprocal of the wave-length
measu red in centimeters. In this way a spect ru m line is described by t he nu m ber of
waves per centimeter in vacuo. Wa ve numbers, therefore, are units with the dimensions of reciprocal cent imete rs, abbreviated em- I.
EARLY HISTORICAL DEVELOPMENTS
SEC. 1.4)
Vn =
V oo -
-
C
--,
n + J.I.
n = 2, 3, 4, 5, . . .
7
(1.2)
00 ,
where 1'" is t he wave number of t he give n line n , and 1' .. , C, a nd J.I. are
constants. In t his eq uation, 1'" approaches 1' .. as a limi t, as n a pproaches
infinity. While t his formula did not give t he desir ed acc uracy for an
entire series, R ydberg was of t he opinion t hat t he for m of t he eq uation
could no t be far fr om correct.
The nex t eq uation in vesti ga ted by R ydber g was of t he form
1'"
=
1' ..
-
(n
N
+ J.I. )2'
n = 2, 3, 4, 5, . . .
(1.3)
00 ,
where, as befor e, Nand J.I. are constants, 1' .. is t he limi t of t he series, and
n is t he ordina l number of t he lin e in t he series. This formula proved
1~1410,00l I
I
o
30.000 cm-
20,000
f
_ .,.,8
' - - Pn
5
--I
-'- EI
- :....
vn
25
~ Voo -
R
(n ')1 )2
Principol S eries
LIT HIUM
FIG . l. 6.- F r eq u en cy plot of th e principal series of lithium.
to be so successful wh en applied to m any series t hat R ydberg ado pted
it in all of his succe eding work. The impor t ant fa ct a bout t he formula
is that N takes t he sa me value in a ll series in all elem en t s. It is interesting to obse rve t hat, by pl acin g J.I. = 0, t he eq uation reduces to Balmer's
formul a for hydrogen (see Sec . 1.8). Since n t ak es on in t egral values
only, t he hydrogen series affords a direct m eans of ca lculating t his
universal constant N, now known as t he Rydb erg constant R . Rydberg's
equation is now wri tten
1'"
=
1' .. -
(n
+R J.I.)2'
n = 2, 3, 4, 5, . . .
00 .
(1.4)
If we now let I'~, I'~, I'~, and I'~ represent 1'" for t he shar p, principal,
diffuse, and fundamental series, resp ecti vel y , t he n t he four genera l
series m ay be represented by
Sharp series:
R
• • • 00.
(1.5)
(n
8)2' where n = 2, 3, 4,
+
8
I NTROD UCTION TO A TOMIC S PEC T RA
[CHAP. I
Principal series :
v~ =
v~
-
(n
+R P )2' where n
=
••
00 .
(1.6)
(n
+R D )2' where n
= 2,3,4, .. .
00.
(1.7)
+R F )2' where n
=
3, 4,5, . . .
00 .
(1.8)
1, 2, 3,
•
Diffuse series :
v~
=
v~
Fundament al series :
v;
=
vI, - (n
HereS,P, D, and F represen t t he values of j.I., and v:', v ~ , v ~, and v ~ t he
limits of the different series. In a pplying t he ab ove equations t o t he
t hree chief series of lithium , R ydberg obtained t he following express ions :
v~
=
28601.6 - (n
109721.6
0.5951) 2
(1.9)
v~
=
43487.7 - (n
109721.6
0.9596i
+
(1.10)
28598 5
109721.6
0.9974 ) 2'
(1.11)
d
Vn
=
.
-
(n
+
+
These eq uations show a re lation t hat migh t have been anticipated
fr om an examination of t he shar p and diffu se series of Na and K in Fig.
lA , viz., t hat t he limi t s of t he Sand D series are prob ably t he sa me,
i .e., v:, = v ~ . It is t o be no ted t hat the first member of t he sharp series,
E q . (1.9), st art s with n = 2. Wi th n = 1 t his formula gives t he first
member of t he princip al series wit h a negative value .
1.5. The Rydberg-Schuster Law.-Rydberg obse rve d t hat if n is
pla ced equal to uni ty in t he shar p-series formul a, Eq . (1.9), t he righthand term became a pproximately t he limi t of t he princip al-seri es formula,
Eq. (1.10) .
(1
109721.6
_ 43123 7 "" p
0.5951 ) 2 .
v
+
=
00 '
(1.12)
Simil arl y, if n is placed eq ual to un it y in t he principal-series formula,
t he righ t-h and te rm becom es a pproximately t he limi t of t he sharp
series :
(1
109721.6
0.9596 )2 = 28573.1 = v :'.
+
(1.13)
Rydberg came t o the con clusion t hat t he calculat ed differences were
due to experimental errors and that t he sharp- and diffu se-series limits
were identi cal. He t herefore could writ e E qs. (1.9), (1.10), a nd (1.11)
in t he follo wing form:
SEC.
1.5]
EARLY HISTORICAL DEVELOPMENTS
v~
=
R
(1
+ P) 2 -
9
R
(n
+ S) 2'
R
R
(1.14)
v~ = (1
+ S)2
(n
+ P)2'
(1.15)
=
+R P )2
(n
+R D) 2
(116 )
.
vd
n
(1
It was not until 1896 t hat Rydberg! discovered, as did Schust er " in
the same year, t hat t he first line of t he principal series in t he alkalies
is also t he first member of t he sha r p series when taken with negati ve sign.
If n is placed equa l to uni ty in E qs . (1.9) and (1.10), t hen vi = -lIl ' In
exactly t his same way it was found t hat t he difference betw een t he limit
of the principal series and t he common limit of t he sha rp and diffuse
series is equal t o t he first memb er of t he principal series :
v~
-
1I ~
= III = -1I 1.
(1.17)
These import an t relations are now kn own as t he Rydberg-Schu ster law.
Immediat ely upon t he discovery by Bergmann, 12 year s lat er , of t he
fundamental series, Runge an nounce d t hat t he difference bet ween t he
limits of t he diffuse and fundam ent al series is equa l to t he first line of
the diffuse series :
(1.18)
lIj - li to = 1I~ .
Hence, fro m E qs . (1.7) and (1.18), Eq. 1.8 can be written
1 _
li n
-
(2
R
+ D )2
_
(n
R
,
+ F )2
()
1.18a
and this equ ati on added to t he group (1.14), (1.15), and (1.16) shows
that the fre qu en cy limit of everyone of t he four series has now been
expressed in te rms of t he constants of some other series. F or t he diffuse
series, n usually starts wit h two in place of uni ty.
The Rydberg-Schu ster law as well as t he R unge law is shown in
Fig. 1.7 by plot tin g t he spectral frequ en cies, in wave nu mb ers v, against
the order number n, for t he four chief series of sodium. T o prevent
confusion amo ng t he lines belonging to t he different series eac h one is
plotted separately. In order to show t hat t he first membe r of t he
principal series becomes t he first member of t he sharp series, whe n taken
with negati ve value, t he scale has been extended to negative wave
number s. Un fortunately t he freq uency scale is to o small to sho w t he
doublet nature of each line. The R ydberg-Schu ster law is indicat ed
by th e intervals Xl of t he figure and t he Runge law by t he int er vals X 2•
A st udy of t he singlet and triplet series discovered in a number of
elements shows t hat similar laws ar e to be found. This may be illus1 RYDBERG,
2
S CH U STER,
J.
R . , Astrophys. J our. , 4, 91, 1896.
A., Nature, 66, 180, 200, 223, 1896.
10
i NTROD UCTIO N TO ATOMiC S P EC T RA
[C HAP. I
trated by t he calcium series shown schematically in Fig. 1.8. T he
upper four series represent the t riplets and t he lower four t he singlets.
Interva ls between certain series limit s, shown at t he bot tom of t he figure,
3QOOO
1
c
IQoaa
2QOOO
-JQOOO
I
I
I
1
I
_ _ _
I
Sharp
I
_
_ _ _ _ _ _ _ -1._
Dif fuse
1
Radiated f requencies
I
I
I
I
1
Pr inc.p e !
1
Fundamental
I
SODIUM
",\ .
XI
, I'
x., - . J
F IG. 1.7. - Sch em a ti c p lo t of t he four ch ief series of so d iu m dou bl ets s ho wing t he R ydbergS ch uster and Runge law s.
are observed to be t he same as t he freq uen cies of certain radiated lines.
Fi gur es such as t hese reveal many imp or tant rela ti ons and, as we shall
see later , facilit ate the form ati on of what are called energy level diagrams.
50.000 ern"! 40,000
-
-
-
-
-
"'---
20,000
30,000
,----
-
---,-
-
10,000
-L;".1.L.1---'----'--
o
-20,000
-1 0,000
--j _ _
L
~rin;:ip~l
Shorp
Diffuse
Fund orn entol
Principa l
_ _ __
-'-_ _----,.-1
_ __ _ _ _---'--"'-l..1-..l--'
1_
~~~p
Diffuse
Fun dornentcd
>---7"=-- X, - --+--- X,
-
-
-oi
CALC IUM
X
X4
1--#--4 I: 1 X'I
Limit s
FIG. l.8.-Sch ematic p lot of the ch ief triplet an d sin glet series o f calciu m sho wing t h e
Rydber g-S chuster and Runge law s.
1.6. Series Notation.- A somewhat abbreviated notatio n for Rydberg's formul as was em ployed by R itz . This ab brev iated not ation,
which follows dire ctly from Eqs. (1.14) , (1.15), (1.16), and (1.18a) , for
t he four chief types of series is written as follows :
SEC. 1.7]
E ARL Y HIST ORICA L DE VEL OP MEN TS
v~
= IP - nS,
v~ =
IS - nP,
v~,
v~
= IP - nD .
= 2D - nF .
11
(1.19)
In order t o distinguish betwe en singlet-, doublet-, and triplet-series
systems, va rious schemes have been pro posed by different investi gat ors.
Fowler;' for example, used capital let ters S, P , D, et c., for singlets, Greek
lett ers a, 11" , 0, etc ., for doub lets, and small let ters s, p , d, etc ., for triplets.
Paschen and Gotz e" on t he ot her hand ado pted t he scheme of small
letter s s, p, d for both doublets and t riplets, an d capitals S, P , D for
singlet s.
A more recen t scheme of spect ra not ati on , published by Russell, Shenstone, and Turner," has been accepted intern ationally by ma ny investigators. In t his new system capital let ters are used for all series and small
superscrip ts in fron t of each let ter give t he multiplicity (see Table 1.4).
T AllLE 1.4.- SERIES NOTATION
Series
Fow ler
Singlet . . . . .. . ... . . . .. . . . . . . . . . . . . . . . . . S P D F
Doublet .. . . . . ... . .. . . .. . ... .. .. ... . . . . U 7r 0 <P
Triplet .. . . . . . .. . . ... . .. . . . . . . . . . . . . . . . s p d f
P aschen
Ado pted
S P D F
S
P d f
s p d f
IS Ip ID IF
2S 2p 2D 2F
3S 3p 3D 3F
1.7. Satellites and Fine Structure.-The appearance of faint lines,
or satellites, in some series was discovered by Rydberg an d also by
Kayser and Runge. At first t he satellites, which usually appea r on t he
long wave-length side of t he diffuse series, were considered as a secondary
diffuse series until it was discovered t ha t H artl ey 's law of constant.
frequency separations applied to t he separation of t he satellite an d on,'
of the st rong lines of t he doublet. In most diffuse doublets the strongest
line lies between t he satellite and t he weaker line of t he doubl et .
Thi s is illustrated in F ig. 1.9, where t he first four mem bers of t he four
chief series of caesium are plot t ed schematically. Pl ot ted to a frequency
scale it is seen t hat t he outside separation of each member of t he sharp
and diffuse series an d t he first mem ber of the principal series is exactly
the same. It should also be noted t hat t he first memb er of the principal
series is, when inverted, t he first memb er of t he sha rp series. This member is shown dotted.
Unlike ot her 2F series, to be studied later , t he st rongest line in each
F-doublet in caesium lies on the low-frequency side of t he respective
satellit es. Like all 2F series, however, each doublet has one interval in
common with t he first mem ber of t he diffuse series.
FOWLER, A., "Report on Series in Line Spect ra ," Fleetway Press, 1922.
PASCHEN, F ., and R . GOTZE, " Seriengese tze der Lini ensp ektren ," Julius
Springer , 1922.
3 R USSELL, H . N. , A. G. SHENSTONE, an d L. A. TURNER, Ph ys. Rev., 33, 900, 1929.
I
2
12
[CHAP. I
I NTROD UCTION TO A T OM IC S PEC T RA
Similar relations are found to exist am ong t he t riplet series of t he
alkaline earths. The first four members of t he four chief series of
calcium are shown schematically in Fig. 1.10. From the diagram it is
seen , first, t hat t he common limit of sha rp and diffuse series is a triple
11
Limits
4th.
3rd.
2nd.
lsi.
FIG. 1.9.- Frequen cy plot of t he dou blet fine str uctu re in t he chief series of -caesiu m.
limit with sepa rations equa l to t he first member of t he principal series;
second, t hat t he limit of t he fundament al series is a t riple limit wit h
sepa rations eq ua l to t he separations of t he strongest line and satellites
of t he first member of t he diffuse series; and t hird, t hat t he principal
series has a single limit. It is to be noted in t he doubl et series (F igs.
~~~
.
I
l
LL~~indpal
:
.
~-LLlkh,p
11
III
Limits
--1.......l.-L
I
I
I
I
I
I
I
I
I
•
JlllLl
---l!L -llL -L
4th
3rd.
2nd.
:.1 :1:
~use
Gom,Oo'
1st.
F IG. 1.I D.- Frequen cy plot of the t ri p let fin e st ru cture in t he ch ief se ries of ca lciu m .
1.9 and 1.7) t ha t, while t he first principal doublet becomes the first
sha r p doublet when inverted , t he rever se is t rue for t he t riplet series of
calcium . By inverting the first sharp-series member (F ig. 1.10), t he
lines fall in with t he principal series in order of sepa rations and intensities.
SEC.
13
E ARLY HISTORICAL DE VEWPMENTS
1.7]
In t he development of Rydberg's formula, each member of a series
was assumed to be a single line. In t he case of a series where each
member is made up of two or more components, t he constants v .. and J.I
of Eq . (1.4) mu st be calculat ed for each component. Rydberg's formulas
for the sharp series of triplets, for example, would be written, in the
accepted notation,
v"n
R
R
= (1 + 3P - (n + 3S = 13P 2 - n 3S I,
2)2
1)2
R
+ 3P 1)2 R
(1 + 3P O)2
v"n =
v"n
(1
=
R
13P 1 - n 3S 1,
+ 3S1)2 =
R
(n + 3S1)2 =
(n
(1.20)
3
3
1 P o - n S 1,
where 3S 1, 3P O, 3P 1, 3P 2 , occurring in t he denominators, are small con
stants . Symbolically 13P2 stands for the term R I (1 + ap 2)2 which is
one of the t hree limits of t he sharp series. The subscrip ts 0, 1, and 2
used here to distinguish between limit s, are in accord with, and are par t
of, t he internationally adopted not ati on and are of importance in t he
theory of atomic structure.
A spectral line is seen to be given by t he difference bet ween t wo
terms and a series of lines by t he difference betw een one fixed term and a
series of running terms. The va rious components of t he diffuse-triplet
series wit h t hree main lines and t hree satellites are designated
13P2 - n 3D 3, first st rong line ;
13P 1 - n 3 D 2 , second st rong line.
3
13P2 - n D 2 , sa t ellite ;
13P 1 - n 3D 1 , satellite.
(1.21
3
13P o - n 3D 1, third st rong line .
13P2 - n D 1, sa t ellite ;
The general abbreviated notation of series te rms is give n in t he
following table along with t he early schemes used by F owler and Pasch en
T AB LE
1.5.-NoTATION
OF SER IES T ERMS
Paschen
Internation ally
adopted
Singlet .... . . . . . . . . . . . . . . . . ... . . . . . S P D F
S P D F
ISo IP I lD 2 IF.
Doublet .. . . . . . . . . . . . . . . . . .. . . . . . . . a "'2 0
'P
8
0'
<p'
P2 d2 t,
PI d l /I
2S! 2P i 2Di 2Fi
2P i 2D1 2Ft.
PI d l f l
'SI ' P 2 3D. ·F.
' P I ' D2 'Fa
Series
Fow ler
"' 1
Triplet .. . . . . . . . . . . . .. .... . . . .. . .. .
8
PI d
f
P2 ti' f'
p. d" f"
8
P2 d 2 12
pa d. f a
' P o ' D I ' F2
While t he ne w not ation is somewhat complicated by t he use of
superscripts and especially by half-integral subscripts, it, will be seen
INTRODUCTION TO ATOMIC SPECTRA
14
[CHAP. I
later that each letter and number has a definite meaning, in the light of
present-day theories of atomic structure.
1.8. The Lyman, Balmer, Paschen, Brackett, and Pfund Series of
Hydrogen.-It is readily shown that Balmer's formula given by Eq. (1.1)
is obtained directly from Rydberg's more general formula
P
by placing
Eq. (1.1),
J.Ll
R
-
n
(nl
-
= 0, J.L2 = 0,
nl
1
>.: =
where a
=
3645.6
A.
+ J.Ll) 2
1 ni
1
a- an~
R _ R
=
ni
n
R
(n2
+ J.L2)2
= 2, and n2 = 3, 4, 5,
Writing R
P
-
ni/a,
=
n~
Inverting
. (1.23)
Pn ,
=
(1.22)
=
R(~
ni
_
~).
n~
(1.24)
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 entirely
different series for each value assigned to nl. For example, with nl = 1,
2,3, 4, and 5, the following formulas are obtained:
Lyman series:
R(ii - ~~} where n2 2, 3, 4,
Balmer series:
= R (1 1) , where.n2 = 3, 4, 5,
Pn
=
=
,2 2
Pn
-
n~
(1.25)
(1.26)
Paschen series:
Pn
=
R(;2 -
~~} where n2 =
4, 5, 6,
(1.27)
R(i2 -
~~} where n2 =
5,6,7,
(1.28)
~~} where n2 = 6,7,8,
(1.29)
Brackett series:
Pn
=
Pfund series:
Pn
= R(;2 -
Knowing the value of R from the well-known Balmer series the positions
of the lines in the other series are predicted with considerable accuracy.
The first series was discovered by Lyman in the extreme ultra-violet
region of the spectrum. This series has therefore become known as the
Lyman series. The third, fourth, and fifth series have been discovered
SEC .
1.9}
15
EARLY HISTOR ICAL DEVELOPMENTS
where t hey were pr edicted in t he infra-red region of the spect rum by
Paschen , Bracket t , and Pfund, res pectively. The first line of these five
series ap pears at Al215, ;\6563, ;\18751, M05 00, and ;\74000 A, respectively. It is to be seen from the formulas that t he fixed terms of the
second, third, four th, and fifth equ a tions are t he first, second, t hird, and
fourth running terms of t he Lyman series . Similarly, t he fixed terms of
the t hird, fourth, and fifth equ ations are t he first, second, and t hird
runni ng terms of t he Balmer ser ies; etc. This is known as the Ritz
combination principle as it applies to hydrogen .
1.9. The Ritz Combination Principle.- P redictions by the Ritz
combination principle of new series in elements other than hydrogen
have been verified in many spectra. If t he sha rp and principal series of
the alkali metals are represented, in t he abbreviated notation , by
Sharp:
Principal :
P"
P"
= 12P - n 2S , where n = 2,3,4,
= 12S - n 2p , where n = 2,3,4,
,
,
(1.30)
ihe series predicted by Ritz are obtained by changing the fixed te rms
12P and 12S to 2 2P, 3 2P and 2 2S , 3 2S , et c. The resultant formulas are
of the following form:
Combina tion sharp series:
22P - n 2S , where n
3 2P - n 2S , where n
etc .
=
=
3, 4, 5,
4, 5, 6,
(1.31)
Comb ination principal series :
2 2S - n 2p , where n = 3, 4, 5,
3 2S - n 2p , where n = 4, 5, 6,
etc.
(1.32)
In a similar fashion new diffuse and fundamental series are predicted
by cha nging the fixed 2p term of the diffu se series and the fixed 2D term
of the fundamental series.
Since all fixed terms occurring in Eqs. (1.31) and (1.32) are included
in the running terms of Eqs. (1.30), t he pr edicted series are simply combinations, or differences, between terms of t he chief series. Such series
have t herefore been called combination series. Ex tensive investigations
of the infra-red spectrum of many elements, by Paschen, have led to t he
identificati on of many of the combination lines and series.
In t he spectra of the alkaline earth element s t here are not only the
four chief series of triplets 3S , 3p , 3D, and 3F but also four chief series of
singlets lS, lp, lD, and IF. Series and lines have been found not only
for triplet-triplet and singlet-singlet combinations but also triplet-singlet
and singlet-triplet combinations . These latter are called intercombination
lines or series.
16
INTRODUCTION TO ATOMIC SPECTRA
[CHAP. I
1.10. The Ritz Formula.- The work of Ritz on spectral series is
of considerable importance since it marks the development of a series
formula still employed by many investigators. Assuming that R ydberg's
fo rmula for hydrogen was correct in form
Vn
=
R(~
p2
- 1),
q2
(1.33)
and realizing that p and q must be funct ions involv ing the order number
n, Ritz obtained, from t heoretical considerations, p and q in the form of
infinite series:
(1.34)
Using only the first two terms of p and q, Ritz's equation becomes
identical with Rydberg's general form ula which is now to be considered
only a close approximation. In some cases, the first three terms of the
expansion for p and q are sufficient to represent a series of spectrum lines
to within the limits of experimental error.
1.11. The Hicks Formula.- T he admirable work of Hicks! in developing an accurate formula to represent spectral series is worthy of mention
at this point. Like Ritz, Hicks starts with the assumption that Rydberg's form ula is fundamental in that it not only represents each series
separately but also gives the relations exist ing between t he different
series. Quite independent of Ritz, Hicks expanded the denominator of
Rydberg's Eq. (1.3) into a series of,terms
n
abc
+ p. + n + n2 + n3 +
(1.35)
The final formula becomes
JJ n
=
V ao
R
b
C
( n+p.+-+-+-+
n
n2 n 3
a
(1.36)
This formula, like Ritz's, reduces to Rydberg's formula when only
the first two members in the denominator are used.
1.12. Series Formulas Applied to the Alkali Metals.- T he extension
of 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, and
caesium, to the twenty-third, twenty-fourth, and twentieth members,
1 HICKS, 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.
SEC.
17
EARLY HISTORICAL DEVELOPMENTS
1.121
respectively by Bevan 1 furnishes the necessary data for testing the
accuracy of proposed series formulas. A careful investigation of these
series was carried out by Birge" who found that the Ritz formula was to
be preferred and that with three undetermined constants it would
represent the series of the alkali metals of lower atomic weight with fair
accuracy. Birge shows that the number of terms that need be used in
Principal Series of Soolium
IIlIlIllII I'1 1 I
I
Series Limit
'- i;;;l ,= :::r-::::::::::y.:::::=;.,::;::::r.= =
64 75 2490
12
43
2593
->-.- -
FIG. 1.11.-Principal series of sodium in absorption.
2680 A
(A fter Wood.)
the denominator depends directly on the size of the coefficients of the
several terms, and that these coefficients increase with atomic weight.
This increase is shown in the following table:
TABLE l.6.-SERIES COEFFICIENTS
(A f ter Birge)'
Elem ent
H
He
Li
Na
K
Rb
Os
I BIRGE.
Atomic weigh t
a
b
1
4
7
23
39
85
133
0
0 .0111
0.047
0 .144
0 .287
0 .345
0.412
0
0 .0047
0 .026
0.113
0 .221
0.266
0.333
R . T oo A str ophy• . J our.• 32, 112 . 1910.
To illustrate the accuracy with which the Ritz formula represents
series in some cases, the principal series of sodium is given in the table
shown on page 18.
The Rydberg constant as calculated by Birge from t he first five
members of the Balmer series of hydrogen and used by him for all series
formulas is R = 109678.6. It is to be noted that the maximum error
throughout the table is only O.lA.
This work greatly strengthened the idea that the Rydberg constant
was a universal constant and that it was of fundamental importance in
series relations. The Ritz equation has therefore been adopted by many
investigators as the most accurate formula, with the fewest constants,
for use in spectral series. A modified but equally satisfactory form of
the Ritz formula will be discussed in Sec. 1.14.
'BEVAN,
• BIRGE,
P. V., Phil. Mag., 19, 195, 1910.
R. T., Aslrophlls. Jour., 32, 112, 1910.
18
I NTROD UCTIO N TO ATOMIC SPECTRA
[C HA P.
I
TABLE 1.7.-THE RITZ FORMUL A ApPLIED TO THE SODIUM SERIES OBSERVED BY WOO D
(Calculations aft er Birge) 1
R
v" = A - (
n
b)2'
+a +n
2
where A = 41,450.083 cm r ", R = 109,678.6 cm" ', a = 0.144335, and b = -0. 1130286 ·
n
Av a c obs .
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
5897 .563
3303 .895
2853 .63
2681.17
2594 . 67
2544.49
2512 .90
249 1 .36
76 .26
65 .1 8
56 .67
50 .11
44 .89
40 .71
37 .35
34 .50
1 BIRG E,
Calc.
diff .
n
0.00
0 .00
-0 .04
+ 0 .09
+0 .09
-0 .05
+ 0. 07
- 0 .0 4
+0 .03
+0 .10
+ 0. 05
+ 0 .04
-0 .03
+ 0 .01
+0.06
+0.04
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Av a c obs.
Cal c.
diff.
n
Av a c obs .
Ca lc .
di ff.
-0 .0 1
-0 .02
-0 .01
+ 0 .02
+0 . 03
+ 0 . 01
0 .00
0 .00
+0 .02
+ 0 .01
+0. 04
+0.07
+ 0. 06
- 0 .05
0 .00
- 0 .01
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
2418 .03
17 . 75
17 .4 5
17 . 21
16 .9 8
16.76
16.54
16 .35
16 . 17
16.02
15 .86 ..
15.71
15 .59
15 .43
15 .29
15 .15
+0 . 01
+0 .02
0 .00
+ 0 .03
+ 0 . 04
+ 0 . 03
+0 . 02
+ 0 .03
+ 0 .02
+ 0 .03
+ 0 .04
+ 0. 03
+ 0. 05
+ 0. 01
- 0. 01
- 0 .04
-
2432 .08
30 .07
28 .3 7
26 .93
25.65
24 .53
23 .55
22 .6 9
21.93
21 .25
20 .6 7
20 .15
19 .65
19 . 09
18 .74
18 .36
R. T. A s/roph y s. J our ., 32 , 11 2,1 910.
1.13. Neon with 130 Series.- T he first successful ana lysis of a really
complex spe ctrum was made by P aschen I in t he case of neon . Althou gh
the neon spectrum was foun d to contain a great many lines, P aschen was
able to arrange them into 130 different ser ies. T hese series, classified
as 30 principal series, 30 sharp series, and 70 diffuse ser ies, were found to
be combi nations between 4 series of S te rms, 81, 82, 83 , and 84 ; 10 ser ies of
P terms, PI, P2, Pa, . . . ,PI0; and 12 series of D te rms, di, d 2 , d a, •.. ,
d 12 • P aschen showed t hat, while ma ny of t he series were regular and
followed a R itz formula, others were irr egular and could not be fit ted to
any form ula. T hese ab normal ser ies will be discussed in t he following
section.
1.14. Normal and Abnormal Series.- Occasionally it is found t hat
certain members of a well-established serie s do not follow t he ordinary
Rydberg or R itz formula to within t he limits of experime ntal error.
Well-known series of t his kind were point ed out by Saunde rs in the
singlet series of Ca, Sr, and Ba, an d by P aschen in certain neon series.
A convenient method, employe d by P aschen and ot hers, for illustrating
deviations from a normal series is to plot f.L , t he residual constant in t he
Rydberg denomi nator, of each te rm aga inst n, t he order number of the
1
P ASCHE N.
F. , Ann. d. Phys., 60, 405, 1919; 63, 201, 1920.
S E C.
E ARLY HISTORICAL DEVELOP11JEN T S
1.14]
19
term. Several of the diffuse series of terms of neon as given by Paschen
are reproduced in Fig. 1.12. A normal ser ies should show re siduals t hat
follow a smooth curve like the first nine members of the d 4 series. The
curves for the d 1 , d 3, and d 5 terms sho w no such smoot hness, m aking it
very difficult to represent t he series by a ny t y pe of series formula .
A series following a Rydberg formula is represented on suc h a graph
by a horizontal line, i .e., JL constant. With a normal series like d 4 of
0.035
......
0.030
~
'%
0.025
t
a 020
1°.
015
/
. /~
..
~
.-2/
;;;.-- ~
.--
<,
/'
-,
<, 1/
0010
d ·.s-:" ~
0 005
Neon
0000
3
4
6
7
8
10
II
- n ~
F IG. 1.1 2.- Four di ffu se ser ies in n eon sho wing no rmal and abnormal progression of t he
residual J.L. (Aft er P a schen .)
neon, a Ritz formula with at least one ad de d term is necessary to adequately represent the series. If T'; represen t s t he running term of a
Ritz formula, and T 1 t he fixed t er m, .
P
n = T1
-
Tn = T 1
R
-
(n+ a+ ~2)
2'
(1.37)
Another useful form of t he Ri tz formula is obtained by inserting t he
running term itself as a correction in t he denominator:
R
T'; =
en + a + bT )2'
(1.38)
n
This term being large at the beginning of a series, the correction is
correspondingly large. Formulas represen ting abnorm al ser ies like
d1, d3 , and d5 in Fig. 1.12 will be t rea ted in Cha p. XIX.
Other anomalies that frequently occur in spect ral series are the
irregular spacings of t he fine st ruc t ur e in cert ain members of the series.
A good exam ple of this type of anomaly is to be found in the diffu se
triplet series of cal cium. In Fig. 1.13 a normal diffu se series, as is
observed in cadmium, is sho wn in con trast with t he abnor mal calcium
series. The t hree chief lines of each t riplet are designated a, b, and d,
and the three satellit es c, e, and f. Experimentally it is t he interval
20
[C HAP. I
I N TROD UCTIO N TO A T OM I C S PE CT RA
between the t wo satellit es f and c and the in terval between the satellite
c and the chief line a that follows Hartley's law of equal separations in
both series . In cadmium it is seen that the main lines and satellites
converge toward t he t hree series limits very early in the series. In
calcium, on t he other hand, t he lines first converge in a normal fashion,
t hen spread out anoma lously and conve rge a second time toward t he
three series limits. These irregulari ties now have a ve ry beautiful
explanation which will be given in detail in Chap. XIX.
c
b
0
d
I
f
I
,
a
lLIL
3
~
IL
h
I,
I
I
d
e f
I
I ,
1.1....-
4
I.
It
I.
11
e
I,
IL
II,
6
1\
7
~
2
I
IL
l
9
10
I
I I.
II,
1
~
1
•
11
Limit s
l
Triplets
II,
1
I.
Abnorrmt Series of Co1cium
I
8
"
Lim its
b c
--L-I I
L
II
I
e
00
-A.-
Normol Ser ies of Cadmium
Tr iplets
F IG. 1.1 3 .-Diffuse se ries of triplets in cadm iu m and ca lci u m .
1.16. Hydrogen and the Pickering Series.- In the hands of Balmer
and Rydberg the historical hydrogen series was well accounted for when
Pi ckering, in 1897, discovered in t he spect rum of t he star r-Puppis a
series of lines whose wav e-lengt hs are closely rela ted t o the Balmer serie s
of hydrogen. Rydberg was t he first to show t hat t his new series could
be represented by allowing n2 in Balmer's formula t o t ake both half and
whole integral va lues. Balmer's formula for the Pickering series may
therefore be written
Pn
=
R(;2- ~~),
where
n2
= 2.5, 3, 3.5, 4, 4.5, .. ' .
(1.39)
The Balmer and Pi ckering series are both shown schematically in Fig.
1.14. So good was the agreement between calculated and observed
wave-lengths that the Pickering series was soon attributed to some new
form of hydrogen found in the stars but not on the earth.
21
EARLY HISTOUICAL DEVELOPMENTS
1.161
SEC .
Since n2 was allowed to take on half -in tegral values, Rydberg predicted
new series of lines by allowing n l to take half-integral values. One series ,
for example, could be written
~n = RC.~2 - ~~),
where n2 = 2, 2.5, 3, . . . .
(1.40)
All of the lines of this predicted series, except t he first , are in t he ultraviolet region of t he spectrum. With the appearance of a line in the
spectrum of r-Puppis at M688, t he position of the first line of t he predicted series, Rydberg's assumption was verified and the existence of a
new form of hydrogen was (erroneously) established.
r
t
JIIJIIIJ
[
JJill1tJ~
Balme-r-Se-r-les------------J
Picker ing Series
I
,
,
,
,!
!
"
I
,
,
,
,
I
J '
,,
!,
I
"
"
I
,
,
,
3.500
4,000
4,500
5,000
~500
6,000
4500 A
FIG. 1.14.- C omparison of t he B almer ser ies of h ydrog en a n d the Pickerin g ser ies.
Fowler in his experiments on helium brought out, with a tube containing helium and hydrogen, not only t he first t wo members of the
Pickering series strongly but also a number of other lines obser ved by
Pickering in the st ars. While all of t hese lines seemed to be in some way
connected with the Balmer formula for hydrogen, they did not seem to
be in any way connected with t he known chief series of helium. The
whole mat ter was finally cleared up by Bohr! in the extension of his
theory of the hydrogen atom to ionized helium. This is the subject taken
up in Chap. II.
l.16. Enhanced Lines.- Spectral lines which on pas sing from arc to
spark conditions become brighter, or more int ense, were early defined
by Lockyer as enhanced lines. In the discovery of series relations
among t he enhanced lines of the alkaline earths, Fowler " made the distinction between t hree classes of enhanced lines; (1) lines that are strong
in the arc but strengthened in the spark, (2) lines that are weak in the
arc but strengthened in the spark, and (3) lines that do not appear in t he
arc at all but are brought out strongly in the spark.
Fowler discovered, in the enhanced spectra of Mg, Ca, and Sr, series
of doublet lines corresponding in type to the principal, sharp, and diffuse
N. , Phil. Mag ., 26, 476, 1913.
A., Phil. Trans. Roy. Soc., A, 214, 225 , 1914.
1
BOHR,
2
FOWLER ,
22
INTRODUCTION TO ATOMIC SPECTRA
[CHAP. I
doublets of the alkali metals. In an attempt to represent these series
by some sort of Rydberg or Ritz formula, it was found that n2, the order
number ofthe series, must take on half-integral as well as integral values.
The situation so resembled that of the Pickering series and the hydrogen
series that Fowler, knowing the conditions under which the enhanced
lines were produced, associated correctly the enhanced doublet series of
Mg, Ca, and Sr with the ionized atoms of the respective elements. For
such 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 formula
becomes
Un
= 4R{
(nl
1
+ J.Ll)2
_
(n2
1
+ J.L2)2
},
(1.41)
where n2 is integral valued only .
Problem
With the frequ en cies of the four chi ef series of spec trum line s as given for ionized
calcium by Fowl er , "Series in Lin e Spect ra ," construct a diagram similar to the one
shown in Fig. 1.7. Indicate clearl y th e intervals illustrating the Rydberg-Schu ster
and Runge laws.