468 BELL SYSTEM TECHNICAL JOURNAL 



ever attain, are capable of causing false conclusions. The third sig- 

 nificant figure in the \alue of an ionizing-potential is many times harder 

 to attain than the first two; and it is not surprising that many experi- 

 menters ha\e chosen to mix some standard gas such as helium into the 

 gases with which they experimented, and to determine the difference 

 between the ionizing-potentiais of the standard gas and the other gases, 

 rather than any of them absolutely. 



Before bringing out the numerical values of ionizing-potentials, I 

 must allude to the fact that the quantity measured in these experi- 

 ments is the kinetic energy possessed by the electrons when they are 

 just able to ionize the atoms, w'hich might not be the same thing as the 

 energy actually transferred to the atoms. A particle of mass m moving 

 wnth speed ii has not only kinetic energy K = '}/2niii~ but also momen- 

 tum mu. If it impinges against a previously-stationary particle of mass 

 AI, and momentum is conser\ed in the impact, then the particles must 

 be in motion after the impact, and some of the initial kinetic energy 

 of the striking particle must be saved, so to speak, to provide for this 

 motion. What is left over is available for ionization or other purposes. 

 Without involving ourselves in the general case, we may note that the 

 most favourable conceivable case for having a large proportion of en- 

 ergy left over, when the striking particle is less massive than the struck 

 one, is that in which the more massive particle has all the momentum 

 after the impact. Suppose therefore that after the impact the striking 

 electron and the liberated electron are both stationary, and the ion of 

 mass M is moving with speed V. Conservation of momentum is ex- 

 pressed by writing: 



imc = MV. (3) 



The energy- T available for ionization or other purposes is given by: 



K = imn:' = ^MV-'}-T. (4) 



so that 



T = K(l-m/M). (5) 



Since the masses of atoms range from 1845 to nearly half a million 

 times the mass of an electron, an electron might spend over 999 pro- 

 mille of its energy in ionizing an atom; and therefore there is no essen- 

 tial impossibility in supposing that the energ>' possessed by an electron 

 just able to ionize is actually equal, within the uncertainty of measure- 

 ment, to the ionizing-energy of the atom. This supposition is con- 

 firmed by the agreements between observed ionizing-potentials and 

 the theoretical values deduced from spectra by using Bohr's method of 

 interpretation. 



