\ RADIATION BIOLOGY 



priiuiplt', I hut the range of probable transitions (starting from the ground 

 state) Hes between the vertical arrows a and c. Transitions whose arrows 

 lie between arrows b and c are similar to those discussed in connecti(jn with 

 Fig. 1-1 a. Transitions arising from points to the left of arrow 6 result in 

 the formation of an excited molecule whose vibrational energy is greater 

 than that required to dissociate it into atoms, one normal and one excited. 

 Accordingly, direct optical dissociation is a probable event. If the gas is 

 irradiated with photons of energy greater than that indicated by the 

 length of arrow h and less than that of arrow a, the radiation will be 

 strongly absorl)ed. For each such absorption act, a molecule will be dis- 

 sociated (within the half period of a single vibration), and there will be no 

 fluorescent emission. Since the end state is not quantized, the absorption 

 spectrum will be contiiuious in this region. 



HALP^ LIFE OF THJ: KXCITED STATE 



If no chemical process, such as optical dissociation, can take place, the 

 half life (ti,,,) of the excited state of a molecule is greater than 10~^ sec, and 

 the molecule will lose all or part of its energy of excitation by emitting a 

 photon. Since the restrictions which limit the probability of a transition 

 apply equally to absorption and emission, a high absorption coefficient 

 corresponds to a short half life of the excited state. For example, the 

 direct optical excitation of a normal molecule from its ground singlet state 

 to an excited triplet state (with a half life of lO"'' sec) would be so improb- 

 able that it would not be observed in the absorption spectrum under ordi- 

 nary conditions. These conditions were put in quantitative form by Ein- 

 stein in 1917 (Herzberg, 1950, pp. 20, 381). If the effect of possible 

 degeneracy of the levels is neglected, the Einstein relation can be put in 

 the following form: 



NaC In 2 _ 1 



aT\., — 



Stt X 10» v^ 



X 4 (1-1) 



where Na is Avogadro's number, c is the velocity of light, and v is the 

 freciuency of the radiation absorbed or emitted. The Beer's law extinc- 

 tion coefficient, off is defined by the following equation, in which in is the 

 concentration of the absorbent in moles per liter, / is the length of the 

 light path in centimeters and /n and Iir are the intensities, respectively, of 

 the incident and transmitted light: 



tr — InC 



It should be noted that the product ary, is inversely proportional to the 

 square of the fre(}uency. While Eq. (1-1) applies only to monochromatic 

 light (and therefore approximately to atomic spectra), it can be modified 

 to apply to the broad-band absorption and emission of a molecule. For 

 the latter application, a must be known as an empirical function of u, and 



