580 



TABLE 621.— L VALUES AND SPECTRAL TERMS RESULTING FROM 

 TWO ELECTRONS (concluded) 



A third contribution to the total energy of an atom or ion conies from the rotation of 

 each electron about its own axis. This axial angular momentum is the same for all elec- 

 trons ; it is represented by the spin quantum number j = l /z. When two or more electrons 



are present the individual spin vectors Sx, Si, combine with each other to yield a 



resultant S, but (like L) the resultant spin 5' can take only certain discrete values, the 

 maximum being obtained when all the individual spins are parallel, and the minimum 

 being either one-half or zero according as the number of electrons is odd or even. Electron 

 spins account for the splitting of most spectral terms into two or more components (called 

 levels) and give a physical meaning to the subscripts attached to these levels. These sub- 

 scripts are called inner quantum numbers ; they are symbolized by J to represent the 

 vector sum of L and 5. The largest and smallest values of / result from simple addition 

 and subtraction of L and 5" and all intermediate values of J that differ by integral amounts 

 are allowed : 



J=(L + S), (L + S-l), 



when L >6* the number of permitted / values is 2S + 1, which fixes the term multiplicity 

 R and underlies the alternation law, since the maximum multiplicity will be even or odd 

 according as the number of electrons is odd or even. The 5 values and spectral-term 

 multiplicities associated with numbers of optical electrons are displayed in Table 613. 



Because s = l4 for each electron the total angular momentum J of an atom or ion will 

 have integral values for levels belonging to odd multiplicities, and half-integral values for 

 levels if the term multiplicities are even, as shown in Table 615. 



TABLE 622.— TERMS FROM EQUIVALENT ELECTRONS 



Electrons Terms (omitting / values) 



S* \S" 



p* \y, 1 d, *p 



p* 2 P, 2 D, *S 



d 3 \S\ X D, >G, *P, *F 



d* *P, 2 D, 2 D, "F, *G, 2 H, *P, *F 



f l S, X D, *G, 7, a P, a F, *H 

 etc. 



The actual types and multiplicities of terms arising from various configurations of 

 optical electrons depend on whether the electrons are equivalent or nonequivalent, that is, 

 have the same or different values of n and /. In any atom the maximum number of equiva- 

 lent electrons is 2(2/+ 1), and no shell can contain more than two J electrons (s 2 ), six p 

 electrons (/>*), ten d electrons (d 10 ) or fourteen / electrons (/"). In simple cases the 

 spectral terms arising from nonequivalent electrons may be obtained from the L values 

 of Table 621 and the 5" values of Table 613, as shown in Table 616. 



When the optical electrons are equivalent, the Pauli exclusion principle introduces sim- 

 plifications, some of which are evident by comparing Tables 616 and 622. 



An important consequence of the Pauli principle is that closed shells, in which the maxi- 

 mum number of equivalent electrons is present, have L = and i" = O and therefore 

 may be ignored in deriving the terms given by any electron configuration. Furthermore, 

 any subgroup that lacks one or more electrons to fill the group behaves spectroscopically 

 as if the lacking electrons were present, except that the terms are, in general, regular 

 (smallest / level has least energy) when the group is less than half filled but inverted when 

 more than half filled. 



Each configuration (excluding single electrons and closed shells) yields many energy 

 states, and the object of spectrum analysis is to determine (1) the numerical values of the 

 energy levels, (2) the quantum numbers that characterize them, and (3) the electron con- 

 figurations from which they arise. The wave number of each observed spectral line meas- 

 ures the energy difference between two quantized states of an atom or ion, but, because 

 the same level can in general combine with many others, the number of levels is usually 

 much smaller than the number of classified lines. The combining properties of atomic 

 energy levels are governed by simple rules. Thus all terms or levels of a given atom fall 

 into two groups of different parity called even and odd according as the arithmetical sum 

 of the / values of the optical electrons is even or odd (distinguished by the sign ° and by 



SMITHSONIAN PHYSICAL TABLES 



