cp2 Table 611 



NORMAL SERIES RELATIONS IN ATOMIC SPECTRA 



(From manuscript by Henry Norris Russell, 1932.) 



Every spectral line is believed to be emitted (or absorbed) in connection with the 

 transition of an atom between two definite (quantized) states, of different energy-content — 

 the frequency of the emitted or absorbed radiation being exactly proportional to the change 

 of energy. The wave number (or frequency) of the line may therefore be expressed as the 

 difference of two spectroscopic terms which measure, in suitable units, the energies of the 

 initial and final states. It is customary to use in place of true frequency (sec." 1 ) the wave 

 number (cm" 1 ), i. e., the number of waves in one centimeter in a vacuum. All quantities 

 of the nature of frequency or energy are most conveniently expressed in cm" 1 units. The 

 multiplication of such values by c (= 2.99796 X io 10 cm. sec." 1 ) gives the true frequency 

 in sec." 1 and by he ( = 1.9658 X io" 16 ergcm) gives the true energy in ergs. Combinations 

 between these terms occur according to definite laws, which enable us to classify them 

 into systems, each containing a number of series of terms, which are usually multiple. The 

 energy is often measured in " electron volts," one of which = 8106 cm" 1 . 



Terms, and the corresponding energies, may be measured either upward from the lowest 

 energy state of the atom (in a given degree of ionization), or downward from a series 

 limit (see below). 



Series of terms are found in many spectra which satisfy the relation 



Here y is the term-value, measured downward from the appropriate limit; 5= 1, 2, 3 



for neutral, singly, doubly, ionized atoms ; R is the Rydberg constant, and n a " running " 

 integer, which changes by 1 from one member of the series to the next. The " residual " x 

 is often nearly constant (Rydberg's formula). Ritz's formula x= fi + o-y (/*. a, constants) 

 is usually a good approximation though not rigorous. 



In the simplest spectra (e. g., Na, Ca + ) all the series have the same limit (corresponding 

 to an isolated lowest energy state of the atom in its next higher degree of ionization) and 

 long series of terms are known. But in most spectra there are many limits, corresponding 

 to different states of the more highly ionized atom : few members of any given series are 

 observed, and these perturb one another so that the Ritz formula no longer holds good. 1 

 The interpretation of these spectra depends upon the combination relations, formulated 

 mainly by Sommerfeld and Lande, and the relations between electron configurations and 

 term structure which have been put into definitive form by Hund. 2 These relations may be 

 summarized as follows : 



(a) The terms (or energy levels) of any given atom fall into two main groups of 

 different parity (odd and even). Transitions producing spectral lines normally occur only 

 between an odd and an even term. Those between terms of the same parity are "for- 

 bidden" but may occur under exceptional circumstances (as in gaseous nebulae). 



(b) Terms of the same parity fall into systems — singlets, doublets, triplets, etc., char- 

 acterized by the multiplicity R — the maximum number of components which a term may 

 possess. 



(c) In each system are found terms of various types denoted by the letters S, P, D, F, 



G, H, I The number of components increases along the series 1, 3, 5, but stops 



short at the maximum R (whether odd or even) characteristic of the system. The suc- 

 cessive terms of a given series are always of the same multiplicity, type, and parity : but 

 other terms of the same sort may be interpolated among them. 



1 Compare Shenstone and Russell, Phys. Rev., 39, 415, 1932. 



2 Linienspektren der Elemente, 1927. 



Smithsonian Tables 



