1288 THE PIGMENT FACTOR CHAP. 32 



These estimates seemed to fulfill the requirements of the theory of the 

 photosynthetic unit (300-2400 transfers during the excitation period) and 

 to be at least not inconsistent with the spectroscopic facts (the red band 

 shift in vivo is »0.4 m/x, but it could be attributed largely to complexing 

 with proteins; the shape of the red absorption band is approximately the 

 same in vivo as in vitro). 



However, the numerical values used in Forster's calculations require 

 correction. He used ^ = 3 X 10"^ sec. as the average hfe-time of the 

 excited state. A larger value, 8 X 10~^ sec, was derived on page 633 from 

 the integral of the absorption curve, but much more recent calculations 

 (cf. chapter 37C, section 1) gave only 1.3 X 10"^ sec. A much more radical 

 correction is required by the fact— neglected by Forster — that the yield of 

 fluorescence of chlorophyll in the living cell is low, perhaps only 0.1% (as 

 against 10% in organic solvents). This indicates that the "natural" life- 

 time of excitation (as derived from band intensity) is shortened — -perhaps 

 by a factor of 10^ — ^by energy dissipation. The effective t thus may be of 

 the order of 10"", rather than 10-^ sec. Even a few hundred excitation 

 jumps during this period will reduce the "visiting time" below 1 X lO^'^ 

 sec, and thus destroy the coupling with molecular vibrations. (Inciden- 

 tally, a "visiting time" of such brevity should also affect unfavorably the 

 probability that excitation Avill actually cause the photochemical change 

 while "visiting" the chlorophyll molecule associated ^^•ith the reaction 

 center, since this energy transfer, too, depends on the conversion of elec- 

 tronic energy into the kinetic energy of atomic nuclei.) 



From considerations of this type, Franck and Teller (1938) concluded 

 that, in the hving cell, energy propagation by the "slow" transfer mech- 

 anism cannot extend over the number of molecules required by the theory 

 of the photosynthetic unit. 



The concept was nevertheless revived by Duysens (1952). He derived 

 from Forster's equations the conclusion that at a concentration [k]o = 

 1000/NAdl(m./l.), where do is the "critical distance" given in equation 

 (32.6), and TVa, Avogadro's number (6 X 10'^), an average of about 15 

 energy transfers will occur during the lifetime of the excited molecule — 

 assuming an at random distribution of the acceptor. With increasing con- 

 centration, [k] > [k]o, the average number of transfers will increase propor- 

 tionally. It was estimated above that with t = 3 X 10~^ sec, [k]o for 

 chloroph3dl a is 7.7 X lO^"* mole/1.; the pigment concentration in the 

 grana is much higher, ^0. 1 mole/1. True, the lower actual yield of fluores- 

 cence in vivo does not permit an estimation of the average extent of energy 

 migration simply from this ratio of concentrations; nevertheless (using a 

 natural life-time of 4 X 10~^ sec.) Duysens arrived at a relatively optimistic 



