90 CHEMICAL REACTIONS IN THE GAS PHASE 



different for different ranges of n, since knj is zero for molecules having 

 n < Uj*. The fraction fj given by expression 12 does not represent the 

 number of species j ions which will be found in the mass spectrum. For 

 values of n sufficient to break two or more bonds in the molecule the 

 chance exists that the initial break will leave the rij ion with enough 

 energy to break a second time. The resulting fragment may also de- 

 compose further. 



In order to simplify the discussion it will be convenient to break the 

 energy distribution into a number of more or less arbitrary ranges. We 

 shall suppose that there is some definite range Ei = E'-^^ to Ei = E^^^ 

 within which the energy is sufficient to break only one bond in the 

 parent ion. A second range E^^^ to E^^^ is defined such that the products 

 of the first dissociation of the parent ion will have between them enough 

 energy to cause one more dissociation but not enough for two. Higher 

 ranges can be similarly defined. Now the fraction of parent ions which 

 do not dissociate at all is 



h = Z ^^;^^ (13) 



and the fractional amount of a product j resulting from parent ions 

 having energies in the first range is 



//■>-<^'= V P(«)^ (14) 



3 



A similar expression can be written for the j ion produced in the second 

 energy range, but now the situation becomes more complicated. For 

 each j ion produced in this range we must consider the chance that at 

 the time of the initial break enough of the energy not concentrated in 

 the breaking bond will be in the charged product of this break to cause 

 subsequent dissociation of this fragment. That is, if the j ion which is 

 formed by the initial break has q oscillators, then we must calculate the 

 chance that these q oscillators will, at the instant of the first break, 

 contain a number of quanta rij*' or more, where 7ij*' is the minimum 

 energy necessary for the j ion to decompose to give a fragment /. This 

 chance is given by 



{n - Uj* - n' + s - g - 2) ! {n' + g - 1) ! 



^ in - Uj* - n')\{s - q - 2)\ 7i'\{q - l)\ 

 A„ = E ^ — — (15) 



n' = nj*' {n — llj* + 8 — 2)! 



{n - ny*)!(s - 2)! 



