Resonance and Ionization Potentials. 



65 



It has been shown that the resonance potentials may be 

 calculated from the quantum relation 



hv=eV, 



where v is the frequency of the radiation excited at the 

 potential V. It is interesting to note that it is possible from 

 the experimentally observed values o£ V and v to calculate 

 the order of magnitude of the diameter of the sphere of 

 interaction between the electron and the gas molecule, 

 assuming that the time of interaction is simply related to 

 the period of vibration of the light emitted. Taking mercury 

 as a typical case, it is observed that one of the principal 

 resonance potentials, exciting the line 2537 A (period (t) 

 = 8*46 x 10" 16 ), is 4*90 volts. Assuming that the electron 

 is completely stopped by the encounter, and that during the 



__ i r~ e 



encounter it travels with an average velocity v= ~\f 2— -V, 



where V = 4*90 volts, we find that in a time equal to t/4 it 

 will have travelled a distance a = 1*4 x 10~ 8 cm., a value 

 comparable with the diameter of the molecule as calculated 

 from other data. It should also be noted that, if we assume 

 as an experimental fact the validity of the relation hv = eV, 

 we must conclude that <r is not constant but is given by an 

 expression of the form 



- i / h 

 4z V 2mv 



and we are led to the conclusion that there are, for the 

 different characteristic frequencies of vibration in the atom, 

 differing spheres of interaction with the moving electron, a 

 conception which might be regarded as pointing to an atomic 

 structure such as Bohr's. 



The experimental values of the ionization potentials are 

 found also to satisfy a relation of the form /iv = eV y except 

 that in this case v is the limiting frequency of the series of 

 lines excited ut the potential V. Conversely, it may be con- 

 cluded that this frequency is also the long wave-length limit 

 of the photo-sensibility of the gas, and experiments are now 

 in progress which, it is hoped, will determine whether or not 

 this is true. Unfortunately the data on the photo-sensibility 

 of gases and metallic vapours are rather unreliable on 

 account of possible surface effects, and it is obviously not 

 permissible to apply the results obtained on metallic surfaces 

 to the metal in the form of vapour. 



Phil. Mag. S. 6. Vol. 36. No. 211. July 1918. F 



