R. S. BECKER AND M. KASHA 29 



state. In lieu of direct measurement of decay time constant ( which in 

 the absence of any form of quenching would of course be the intrinsic 

 lifetime), we may make recourse to the classical relation (for discus- 

 sion, see Lewis and Kasha, 1945; Kasha, 1950 ) : 



'°={sdi^)^0''<"^'^^'r'* 







This expression allows the intrinsic lifetime t° of a luminescence to 

 be calculated from the absorption band integral, J'edf, evaluated 

 graphically. The average frequency (cm~^) of the transition va, the re- 

 fractive index of the medium n at the same frequency, and the multi- 

 plicity ratio gu/gi for the upper and lower states are the other variables. 

 The constants are ir, and c, the velocity of light. 



(2) Summation of Intrinsic Quantum Yields for a Molecule 

 We define quantum yield or quantum efficiency of a luminescence by 



Number of quanta emitted 

 $ = —^ , 



Number of quanta absorbed 



The total intrinsic quantum yield for a molecule (in the absence of 

 external quenching ) may then be described by 



J] $, = 4>f° + V + <|.i„t = 1 



where ^f° is the intrinsic quantum yield of fluorescence, ^p° is the in- 

 trinsic quantum yield of phosphorescence, and *int is the intrinsic quan- 

 tum yield for internal degradation by thermal steps. In the older 

 literature the incorrect expression ^f° + *int = 1 is assumed, leading to 

 the conclusion that if no fluorescence is observed, internal degradation 

 must predominate. Actually, in general the sum of ^f° + *p° may ap- 

 proach unity (Kasha, 1950), so that $int may be negligible in many 

 molecules, at least in rigid solvents. 



It is of the utmost importance to understand that ^f° and ^p° are 

 complementary in magnitude. Thus, if $int = 0, as seems to be the case 

 in general for rigid molecules, then if (^f° = 0.2, $p° must equal 0.8. In 

 other words, in a fluid solution, even if phosphorescence is not ob- 

 served, due to collisional deactivation, the corresponding triplet state 

 is excited with a probability of 0.8 for each absorbed quantum (and this 

 is followed by deactivation, if fluid). Then, if this triplet state is in- 



