170 RADIATION HIOLOGY 



electronic conligurutioii, are thus concealed, reducing the amount of infor- 

 mation available in the spectrum. The possible vibrational transitions 

 are limited by the Franck-Condon principle (Rice and Teller, 1949), 

 which simply recognizes that the duration of the electronic transition is 

 brief compared to the duration of a molecular vibration, so that the posi- 

 tion of the atoms camiot change appreciably during the act of absorption. 

 Hence only transitions to excited-state vibrational levels, involving 

 atomic configurations similar to those in the vibrational levels associated 

 with the ground state, are probable (Fig. 5-3). 



Broadening of this type may also be reduced by a reduction of the 

 temperature of the absorbing substance; the reduction in thermal molecu- 

 lar energy decreases the molecular population in the higher vibra- 

 tional energy levels and thus reduces the number of possible transitions. 

 Indeed, at li(iuid-air temperature or below, all molecules must commence 

 a transition from the lowest vibrational energy level. 



INTENSITY 



The total intensity of an absorption band, i.e., the integrated absorp- 

 tion over the band, is dependent on the difference in scale and symmetry 

 of the electronic configurations for the initial and the excited states 

 (Heitler, 1944). A net time-average displacement of charge along some 

 molecular axis must accompany the absorption of radiation. If the elec- 

 tronic configurations of the two energy levels are of such a symmetry 

 that a transition from one to the other does not provide such a time- 

 average displacement, then a transition between these levels cannot be 

 induced by radiation, i.e., absorption cannot occur. Such a transition is 

 said to be "forbidden." 



In benzene, the electronic configurations of the ground and the first 

 excited singlet energy levels are of such a symmetry that a transition 

 between them is forbidden (Sklar, 1942). This transition, which is 

 associated with the benzene absorption maximum at 2550 A, can occur 

 only if accompanied by a particular molecular vibration which so dis- 

 torts the molecule as to alter the symmetry of either the ground or the 

 first excited energy levels and thus gives rise to a small time-average dis- 

 placement of charge. The intensity of such forbidden absorption bands, 

 which re(iuire the participation of a molecular vibration, is generally low. 

 Thus for the benzene absorption maximum at 2550 A, € = 120; this may 

 be contrasted with the intensity of the "allowed" benzene absorption 

 band at 1835 A which is about 380 times as great (c = 4G,000) (Piatt and 

 Klevens, 1947). In general, the greater the time-average displacement 

 of charge, the greater the integrated absorption. 



For a given integrated absorption, the intensity of the al)sorption maxi- 

 mum will ob\iously depend in\ersely on the width of the l)and and thus 

 directlv on the duration of the excited state. 



