84 



RADIATION BIOLOGY 



Oscillator strengths are of more theoretical significance than extinction 

 coefficients. They are related to the intrinsic time constants as follows: 



and 



/t = 1.5/ v^ for fluorescence 

 « 2 X 10-9 sec near 3500 A; 



/t = 4.5/j'2 for phosphorescence 

 « 10-» sec near 5000 A. 



These formulas were derived from one given by Lewis and Kasha (1945) 

 (neglecting some questionable terms due to the refractive index of the 

 solvent) and from Eq. (2-10). A chart summarizing the known time con- 



SINGLET-SINGLET 

 logfimox tog/ logr TT-TRANSITIONS 



Fig. 2-8. Approximate molar extinctions, oscillator strengths for absorption from 

 ground, and luminescence lifetimes for different types of upper states. {Compiled 

 with the help of M. Kasha.) Nonbonding triplets are not well known and have been 

 omitted (Reid, 1953). 



stants, together with the related peak intensities and oscillator strengths 

 for a number of types of transition in condensed-ring systems, is given in 

 Fig. 2-8 and fits these formulas quite well. The '5 states of such sys- 

 tems are similar to those of polyenes in their properties. 



But photon emission must compete with other processes. One such 

 process is radiationless transition between excited singlets, the result of 

 the crossing of their potential curves, Avhich we have not discussed here 

 (Franck and Sponer, 1948). Such transitions are indicated by dashed 

 lines in Fig. 2-7. In these a vibrational distortion of the molecule may 

 permit it to go from one excited state by easy stages into another in times 

 of the order of a few vibration periods, say, 10-''-10~'* sec. To go from 

 singlet to triplet by this process is more difficult, since one of the electron 

 spins must reverse itself at the same time. The time for this process in a 

 hydrocarbon is more like 10~'^ sec. 



