EXCITATION OF POLYENES AND PORPHYRINS 



83 



typical polyene is shown at the left side of Fig. 2-7. Between any two 

 states the intensity of emission is proportional to the intensity of absorp- 

 tion. By quantum-mechanical laws the time required to emit a photon 

 is inversely proportional to the intensity of emission and therefore to the 

 intensity of absorption. 



TRIPLETS SINGLETS 



de'f'g 



d'ef'g 



'Z>° 



'd° 



TRIPLETS 



SINGLETS 



10" 



7 ,^^^7- 



^ / 



/ 

 / 



\o 



\c -^ 



/ 



/ / 



/ 

 I 



' 10-9 



10' 



'5° 



d^e'fO< 



1 T^ 



/ /lo-' 



/ <^rio-'oT 



^^^ 10-8 



d^e^f 'A 



107 

 (10-5 ) 



[10-^] 



I 



I '0 



I 



t 



de'f'n'g 



-13 



j2 ^2 2 



a ej n g< 



10" 





I ,0-13 



10' 



-13 



WW ,( 



F 



10-9 



,2 2 „ 2 J 



a e J n g < 



J 2 2 ,,2 

 d e J ng 





no- 



1-13 



'u 



/ 

 / 



— / 



/io-^ 

 ^[10-10] 



,2 2.2 2 



d e J n 



k 



10" 



(10-5 ) 

 [10-3] 



F 



10"' 



GROUND 



Fig. 2-7. Emission of light by excited organic molecules. Left-hand side, lowest 

 excited states, B type; right-hand side, U type. Solid lines, radiation; dashed lines, 

 radiationless; heaviest lines, most probable route. Typical time constants for each 

 type of energy jump are given as to order of magnitude, in seconds, for solution in 

 viscous light-atom solvents or glasses at low temperature. Figures in parentheses are 

 possible values under thermal quenching at room temperature. Figures in brackets 

 are possible values in the presence of heavy atoms, as in iodoform solution. 



Time Constants.^ Empirically, for hydrocarbons, the time constant r 

 in seconds is given approximately by 10~V«max- Thus, allowed singlet- 

 singlets, with e,nax of the order of 100.000, have a r of about 10"^ sec. 

 Forbidden singlet-singlets, with €,„ax about 10,000 (in polyenes), have a 

 T of about 10~* sec. For a strong singlet-triplet, with e„,,x about 1, r will 

 be about lO""* sec. These emissions are indicated by the solid vertical 

 lines in Fig. 2-7. 



1 The author is indebted to Dr. M. Kasha for several informal discussions develop- 

 ing the general picture of emission processes given here. 



