82 CHEMICAL REACTIONS IN THE GAS PHASE 



primary formation of C5 and C3 ions, there is very little formation of 

 heavier fragments. In ethane, the C2H5'^ ion accounts for 10 per cent 

 of the total ionization, but in the butanes the amount of C4H9'^ ions is 

 about 1 per cent and in the octanes the amount of C8H17"*" ions is of the 

 order of 0.01 per cent (23). 



We need to explain why these apparently straightforward assumptions 

 seem to yield answers in contradiction to the data; this interpretation 

 also must explain the relative intensities of those ions whose formation 

 requires the breaking of several bonds in the original molecule, occasion- 

 ally with extensive rearrangements occurring in the process. In small 

 molecules, especially diatomic molecules, the number of electronic states 

 of the ion lying within, say, 50 volts of the molecule ground state will 

 be relatively small. This is not the case in. larger molecules of low 

 symmetry. If we consider the number of states possible for a collection 

 of atoms having n valence electrons, all in their lowest states for widely 

 separated atoms, the number is found to be 2"" (29). Many of these are 

 degenerate; the number of independent eigenvalues for the energy is 



n ' 

 '-^ , but this when evaluated by Stirling's approximation gives 



(n/2!r_ 



V(2/7rn)2", of the same order of magnitude. Thus, even for propane, 

 where n = 20, 2^ = 1.0 X 10^ and V(2/7rn)2'^ = 1.8 X 10^ All these 

 states lie within 100 volts of the ground state, making the average 

 between states about 2 millivolts. We are actually more interested in 

 the states of the ion, but the number of states w4th only one electron 

 less will still be astronomical, especially for larger molecules like the 

 octanes, where n = 50. Moreover, overlapping these states will be an 

 equally large number of other states formed from the lower excited states 

 of the separated atoms. The separation between adjacent states is so 

 small that they approximate a continuum. 



All these states are accessible to the molecule under electron impact. 

 The selection rules that hold for optical spectra where the wave length 

 is long compared to molecular dimensions do not apply here, as the 

 de Broglie wave length associated with a 50-volt electron is 1.8 A, of the 

 order of a bond length. 



With electronic states so dense and with the dependence of potential 

 energy on nuclear configuration different for the different states, inter- 

 section of the potential-energy surfaces in regions accessible to the ion 

 with small amounts of vibrational energy will be very frequent. Radia- 

 tionless transitions, of the type indicated for diatomic molecules by 

 transitions from state V to IV, Fig. 1 (p. 74), will be sufficiently common 

 to permit rapid shifting of the ion between electronic states. This will 



