214 RADIATION BIOLOGY 



3-2c. The Franck-Condon Principle. This principle, a useful guide in 

 the determination of the most probable process among all possibilities 

 established on the grounds of energy conservation alone, is essentially a 

 consequence of the application of the law of conservation of momentum 

 with the additional recognition of the vastly smaller mass of an electron 

 compared to the mass of any atomic nucleus (Herzberg, 1950). It has a 

 variety of applications to atomic and molecular processes, both those 

 involving emission and absorption of radiation, and those occurring in 

 impacts. 



The principle states that, because of the smallness of the mass of an 

 electron relative to that of any atomic nucleus, readjustments of electronic 

 shells of atoms and molecules in electronic transitions (whether radiative 

 or collisional) take place so quickly that little alteration in either the 

 positions or the momenta of any atomic nuclei involved can occur. This 

 often provides a criterion for selecting, among a great number of possible 

 transitions, those which have significant probability. It should be noted 

 that the very existence, or more properly the physical validity, of the 

 concept of a potential curve rests on the same physical basis as the 

 Franck-Condon principle. 



As an elementary application of the principle, the absorption of light 

 by Br2 is now considered. The molecules of bromine vapor, if not at an 

 elevated temperature, will be predominantly in the lowest {v = 0) vibra- 

 tional level of the ground (^S^) electronic state, and the separation 

 between the two Br atoms must therefore be just r^ (2.28 A), with a slight 

 fluctuation about that value because of the zero-point vibration. If, 

 now, a Br2 molecule absorbs a photon and undergoes a transition to an 

 excited electronic state, the interatomic separation of the excited Br2, at 

 the first instant after its formation, must still be about 2.28 A. The 

 excited state commonly formed in light absorption is the ^no» (cf. Fig. 3-4) ; 

 it has a '' stable " type of potential curve with, however, the comparatively 

 great Ve of 2.66 A. Thus direct transition to the lowest (?' = 0) vibra- 

 tional level of this electronic state is cjuite impossible, for the heavy Br 

 nuclei cannot move apart the necessary 0.38 A in the very short time (of 

 order of magnitude 10^^ second) available. Instead, the excited Br2 is 

 formed at that locality of its potential curve where r = 2.28 A, and, as 

 will be seen from Fig. 3-4, this point lies energetically above the dissocia- 

 tion level of the excited Br2. Thus the excited molecule will fly apart in a 

 time of approximately one vibrational period, namely, ^-^10"^^ second. 

 Moreover, since for energies in a given electronic state above the dissocia- 

 tion energy there can be no vibrational levels — the energy levels there are 

 continuous — the absorption spectrum must be continuous. These two 

 predictions of the Franck-Condon principle, namely, continuous absorp- 

 tion and formation of atomic bromine thereby, are acciuately verified by 

 experiment. Exactly the same reasoning, and conclusions, apply to the 



