IONISATION, DIFFUSION, ROTATION 
253 
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Table 30 gives the energy levels, as far as possible, for every fourth 
element. The columns K, L x , M x , N x * are observed values obtained either 
from measurements of the absorption edges or from the terms of the spectral 
series; in a few cases where the element itself has not been measured the 
value given is an interpolation between the elements next before and after. 
These values are considered to give the energy of removal of the first electron 
of the group, though there may be an appreciable difference between the 
energy of removal from a complete atom and from an ion with the outer 
groups missing. The columns K', L’ , M' are the theoretical energies of 
removal of the last electron of the group calculated from (42-62). For 
calculation of L' the two K electrons are considered to coincide with the 
nucleus; and for calculating M ' the ten inner electrons are considered to 
coincide with the nucleus. For reference the intermediate elements are 
named in the last column; and values for them can readily be interpolated. 
175. We denote the values of ijj and A which correspond to x = 0-5 by 
ifj x and X x . When there is not too much overlapping of the different stages 
of ionisation we may take the atoms to be all ionised down to the energy 
level i/r x . Even if there is overlapping this is generally the best average 
level to adopt. But it is quite possible for ifj x to be negative, that is to say, 
no ionisation is as much as half completed; nevertheless if T is large a 
great number of successive ionisations may be partially accomplished so 
that there is on the whole a fair amount of ionisation. 
The cleanness of the ionisation depends on ifjfiRT. If this is large a 
small percentage change of ifj will make a big change in x. It is when the 
conditions are such that iftfiRT is less than 2 or 3 that we may expect 
most trouble from overlapping. Moreover, when ifjfiRT is large, excited 
atoms are rare and our neglect of them in this discussion is justifiable. 
To excite a K or L electron to a higher orbit more than half the energy of 
ionisation is required, so that by Boltzmann’s Law the proportion of 
excited systems is of the order e~ i4, l RT . If ifj < ift x the excitation is fore 
stalled by ionisation; and if ifj > i/j x the proportion of excited atoms is 
small provided that ifjfiRT is large. 
176. We now examine what value of the molecular weight corresponds 
to the ionisation found at the centre of Capella. Roughly, the elements 
up to Z = 22 retain no electrons, from 30-50 they retain 2 electrons and 
from 50-70 from 2 to 10 electrons. This gives the following results for 
typical elements— 
Element 
c 
O 
A1 
Ti 
Fe 
As 
Zr 
Ag 
Ba 
Sm 
Ta 
Pb 
Z 
6 
8 
13 
22 
26 
33 
40 
47 
56 
62 
73 
82 
1-7 
1-8 
1-9 
21 
2-2 
2-3 
2-3 
2-3 
2-6 
2-7 
2-9 
2-9 
* The suffix 1 indicates the uppermost level of a group—corresponding to 
greatest A.