266 Robert Platzman and James Franck 



energy released in such an attachment process is small, apart from the contribu- 

 tion from polarization, and may be positive or negative, since the energy evolved 

 in negative-ion formation (electron affinity) must, if it is substantial, compensate 

 for the energy required to rupture a chemical bond. (This is a consequence of 

 the fact that electron affinities of molecules always are small; the only large 

 electron aflinities are those of certain atoms and radicals, which by their nature 

 must be present in bound states.) Thus the effect on the medium will be very 

 much like that for the positive ion. 



III. PHYSICAL CONSEQUENCES OF IONIZATION IN PROTEINS 



The ejection of an electron in an ionization act by even a fairly slow secon- 

 dary electron is an exceedingly quick process and may be considered to have 

 duration of at most 10~^^ sec. The response of a highly polar medium to such 

 an event has been analyzed qualitatively above. After subtraction of the 

 electronic polarization, equation (1) shows that a total amount of energy 

 approximately equal to e^flrfiR will be dissipated during the several subsequent 

 stages of polarization ; here R denotes a distance of the order of magnitude of 

 the mean separation of polar molecular groups, and for proteins must be only 

 slightly greater than atomic dimensions. A value of R of about 2 A thus 

 corresponds to an energy dissipation of 60 kcal/mole. If all of this energy were 

 expended in dissociating secondary bonds, which may be considered to have 

 dissociation energies of approximately 5 kcal/mole, on the average, a rupture 

 of some twelve secondary bonds would be expected. A more detailed analysis 

 for the particular case of proteins, which leads to the same conclusion, will 

 now be presented. Although it is again based upon the Born formula, which 

 applies strictly only to a continuous dielectric, the error caused by neglect of 

 molecular inhomogeneity will not alter the result in order of magnitude. 



The development of polarization ensuant to electric charge localization in 

 the medium may be divided into four stages. These stages, although distinct in 

 character, are by no means without mutual effects, but such interactions can 

 be disregarded in the present analysis, which is only semi-quantitative. 



1. Electronic Polarization — This effect, in contrast to the others, is strongly 

 coupled to the physical processes which lead to localization of the charge, and 

 indeed to the initial ionization act itself (8). Its inffiience on the secondary-bond 

 structure probably is negligible. 



2. 'Infrared', or True Vibrational Polarization — The polarization resulting 

 from degrees of freedom corresponding to the characteristic infrared oscillations 

 is developed during a period corresponding to the longest wavelength of such 

 oscillations, or about 3 X 10"^^ sec. With a plausible value of 1.7 for the 

 dielectric constant after this stage of polarization, equation (1) yields an energy 

 dissipation of 1 1 kcal/mole. Thus at most two secondary bonds can be broken, 

 and more probably none are. - 



3. Secondary- Bond Polarization— li has already been emphasized that pro- 

 teins and similar substances must possess regions of intense dielectric absorp- 

 tion at frequencies between the accessible infrared and the radiofrequency 

 or even microwave regions. Part, or the whole of this absorption, which 

 has yet to be investigated experimentally, stems from the highly polar 



