74 
QUANTUM THEORY 
the empirical series relations, and is not directly connected with the 
quantum interpretation in terms of n and n'. The letters 8, P, D, F are 
used for n' = 1, 2 , 3, 4, and the orbits are thus denoted by mS, mP, mD, 
mF, where m is an integer. The lowest orbits are denoted by IS, IP, 2 D 
respectively, so that the four chief series are— 
An exception however arises in the following way. Consider, for example, 
ionised calcium Ca + ; the normal orbit 1 $ has the quantum specification 
(4, 1 ); and as usual the (4, 2 ) orbit is denoted by IP, and the (4, 3) orbit 
by 2D. It must be understood that in these complex systems the principal 
quantum number is only a vague indicator of the energy of the system, 
and there is no close correspondence of the energies in (4, 3) and (4, 1) 
orbits. In the elements immediately following calcium an extension of 
the M group of electrons (3-quantum orbits) begins; and the coming event 
casts a shadow before in so much that a (3, 3) orbit although still of energy 
greater than a (4, 1 ) orbit has less energy than a (4, 3) orbit*. Hence the 
orbit of lowest energy in the D series is a (3, 3) orbit denoted by ID] the 
fundamental series is accordingly mF -> ID. 
In the above case the ID orbit is metastable, that is to say, the electron 
cannot (ordinarily) get out of it without first absorbing a quantum. By the 
selection principle it can only go from ID to an orbit in the P or F series, 
and the lowest orbits in these series, (4, 2) and (4, 4), have greater energy. 
A third quantum number n" (known as the inner quantum number) 
also plays an important part in optical spectra. The energy depends on it 
to only a slight extent, so that two orbits differing only in n" give a pair 
of lines close together—a doublet. The quantum theory of doublets is, we 
believe, undergoing a fundamental revision at the time of writing, and we 
shall not here pursue the subject of doublet and multiplet structure. 
52. It is not possible for a solitary electron to absorb a quantum of 
radiation and add the energy to its own kinetic energy. This is made clear 
by the theory of relativity. We cannot say whether the kinetic energy of a 
particle has increased or decreased until we have decided on our axes of 
reference; but we can say whether a quantum of radiation has disappeared 
independently of frames of reference. Hence there can be no association 
* An element often builds a new group of electrons not because there is “no room ” 
in the lower group but because by so doing it obtains a configuration of less energy. 
Thus normal calcium contains (4, 1) orbits although there are still ten 3-quantum 
orbits available; the valency electrons can pass into these by excitation. 
Sharp Series 
Principal Series 
Diffuse Series 
Fundamental (or Bergmann) Series 
mS -> IP. 
mP -> IS. 
mD -> IP. 
mF -> 2D. 
Scattering of X Rays by Electrons.