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QUANTUM THEORY 
(3, 
1 ), 
(4, 
1 ), 
(5, 1), 
( 6 , 1 ), 
(7, 1) 
(3, 
2 ), 
(4, 
2 ), 
(5, 2 ), 
( 6 , 2 ), 
(7, 2 ) 
(3, 
3), 
(4, 
3), 
(5, 3), 
( 6 , 3), 
(7, 3) 
(4, 
4), 
(5, 4), 
( 6 , 4), 
(7, 4) 
(5, 5), 
( 6 , 5), 
(7, 5) 
S series 
P series 
D series 
F series 
The possible transitions between these orbits are governed by the 
selection principle, to which reference has already been made, viz. that 
n' must change by + 1 or — 1 . It follows that there can be no transitions 
between orbits in the same series; the electron must pass to an orbit in 
the line next above or below. 
In practical investigations we study primarily emission spectra. When 
through electrical bombardment the electron finds itself in one of the 
excited orbits enumerated above, it will usually prefer to fall to the lowest 
possible energy level consistent with the selection principle. Evidently 
(3, 1 ) is the lowest level reachable from the P series; (3, 2 ) is reachable 
from the S and D series, and (3, 3) from the F series. Although other 
lines ( combination lines) due to a fall to an energy level which is not the 
lowest permissible may occur, the strongest lines have as their terminal 
orbits (3, 1), (3, 2), (3, 3), etc. 
Atoms in their normal unexcited state can absorb only the P series 
(principal series) since the only permissible transition from (3, 1) is into 
an orbit in the line below. 
The frequency of the radiation absorbed or emitted on account of a 
transition is given by the fundamental quantum relation (36T). But 
except for a nucleus attended by only one electron (H and He + ) the energies 
of the orbits cannot yet be calculated theoretically. The manner in which 
the classical perturbations of the electrons on one another are modified 
by quantisation has not yet been made out. We must still resort to the 
clumsy expedient of observing the spectra. 
When the quantum number is very large the excited electron is 
throughout most of its orbit remote from the rest of the atom, which then 
behaves approximately as a point charge of strength + e for a neutral 
atom, + 2e for a singly ionised atom, + 3e for a doubly ionised atom, etc. 
The energy then converges towards the values given by (42-62) with 
Z = 1 , 2 , 3 , ..., or to X n, ±Xn, 9x», , where is the energy of the nth 
orbit in the hydrogen atom. When a few lines of a series have been 
observed it is generally easy to see whether the difference of frequency of 
successive lines is converging towards once, 4 times, or 9 times the corre 
sponding frequency difference in the hydrogen series, and the series can 
be assigned to the appropriate ion. 
The common nomenclature* of the lines of the spectrum is based on 
* I follow the nomenclature in A. Fowler’s Report on Series in Line Spectra, p. 87.