POLYATOMIC MOLECULES 91 



Such a term as this should multiply each term of 23 in ^nj, but since 



k 



^A;max will be only slightly different in each term it will probably be 

 sufficient to write for those j ions which have sufficient energy for a 

 second break 



//^)-(^^ (unstable) = E ,^ P(n) ^^ a,„,, A„ (16) 



„ = „(-) Z^ knj 



i 

 where ^^^^ is the number of terms in the sum over k in knj. It follows 

 immediately that the fraction of stable j ions in this energy range is 



/y(^^-^3) (Stable) = f P(n) ^ «,„,, (1 - A^) (17) 



" = "'"^ Z^ knj 



j 



We can now calculate the amounts of the various breakdown products 

 of the j ion. To do this we require the energy distribution of the j ions 

 formed in the first break. This distribution is given by the terms in 

 An, since each term gives the fractional number of j ions having energy 

 n'. Thus the interesting fact emerges that the distribution function, 

 P{n), once determined, is sufficient to determine also the energy dis- 

 tributions for all secondary and later ions. The expression for the 

 fractional number of j' ions from j ions formed from parent ions in the 

 initial energy range n' to n is 



/,.<^'-«'= E A„.^?^ (18) 



"' = «;* 2^ kn'j' 



J' 



The further calculation of the spectrum is simply a repetition of the 

 calculations indicated before. 



In spite of the simple model employed in the discussion it is obvious 

 that, even if accurate data were available for the dissociation energies 

 and if the values of 7 were known, the calculations would be extremely 

 involved. Such calculations would also be expected to yield answers 

 with only the general outlines of the experimental spectrum. A better 

 approximation would require taking two or three different frequencies 

 for the oscillators, but this would even further complicate the formula- 

 tion. It appears that numerical calculation must await further refine- 

 ment of the theory. 



It remains to consider how much decomposition will occur in a mole- 

 cule in solution when struck by radiation. The well-known formula 



T = e-'-'/^'" (19) 



8pc(7r/c0^ 



