POLYATOMIC MOLECULES 89 



summation over rik except for the term where Uk = Uk^ . The rate 

 then finally becomes 



rr^^^ ~ ^^mnx " K"* - 1) + S - 3]! ^ 



k [n- m^,^ - {nj* - l)]!(s - 3)! "^^ ' ''°^'" ^ ' ^' ^ 



(10) 

 In order to evaluate knj it will be necessary to find a value for 7. As- 

 suming V = 10^^ (approximately the vibration frequency of one of the 

 oscillators), one term of knj would be of the order of 10^ to 10^^ if 7 = 1. 

 The half life of an ion in the mass spectrometer is of the order of 10~^ 

 sec, so that 7 can be no smaller than about 10~^ to 10~^. These values 

 for 7 seem reasonable when we consider that it is the probability of 

 transferring energy from an oscillator having lower energy than the one 

 which is to receive the energy. 



It is now possible to discuss the general nature of the mass spectrum 

 of a molecule. In a molecular ion with a given amount of vibrational 

 energy a number of different reactions may be possible. Moreover, if 

 the energy is sufficient the products of the initial dissociation of the 

 ionized molecule may undergo one or more successive breaks. The 

 probability that a given molecule will break at two points simultaneously 

 is small. We shall therefore consider that the mass spectrum results 

 from a number of successive decompositions and that the problem of 

 calculating the spectrum can be discussed in terms of a set of competing 

 reactions which have reached a steady state. For a given molecule the 

 fraction fnj of products of decomposition which will be formed by initial 

 break of the parent ion will be 



fnJ = P{E,) -^ (11) 



} 



where X) is the summation over all possible single decompositions of the 



j 

 parent ion. (We shall ignore the uncharged fragments here, although 

 their number and energy distribution could also be calculated.) The 

 fraction fnj represents the fractional number of ions of species j resulting 

 from the break of a parent ion with energy nhv = Ei. The total fraction 

 of all parent ions which yield this species will be 



L- = i:fnj = j:p(n)^;^ (12) 



n , n / y Kif^j 



J 



where now P{n) has been written for P{Ei) and the summation extends 

 from the minimum energy necessary to produce species j to the maximum 

 energy of the impacting electrons. The sum over j will, in general, be 



