90 PROBLEMS IN PHOTOSYNTHESIS 



For vessel 2 



xo, = 8 X 3.51 = 28.1 m1 



As illumination occurs only for 1 5 min, during the five cycles of 6 min we 

 have 



if = xojit = 28.1/7.36 X 15 = 0.254 



This quantum yield corresponds to that calculated under a. 



c. The same arrangement as under b. Only the average values of the pres- 

 sure changes during illumination are noted. From the values observed, 

 part li of the curve in Figure 36 is obtained 



after 1 min 1.9 mm 

 after 2 min 3.0 mm 

 after 3 niin 3.7 mm 



The tangent for / = on addition of the measured light indicates the 

 pressure change per minute. In Figure 36 tan a = 2.35. To determine 

 the quantum yield in the light reaction alone we have 



xo, = 2.35 X 3.51 = 8.24 ^1 



and 



^ = 8.24/7.36 = 1.1 



d. If there were no back reaction, the gain in pressure in the first three min- 

 utes of the cycle could be expressed as a straight Jine. After removal 

 of the measured light, no pressure change would occur as respiration would 

 be compensated. This behavior is illustrated by the dotted line in Figure 

 36. As the average value of the pressure after the third minute without 

 measured light is 1 .6 mm, the pressure difference between the two lines 

 for one cycle is 2.1 mm. Warburg calls this value the splitting effect. 

 For the dotted line (tan 0) we find the quantum yield 



^ = xoJit = 1.6 X 3.51/7.36 X 3 = 0.26 



§ 38 Some Mathematical Considerations 



The mathematical treatment of the splitting of the photosynthetic process 

 worked out by Warburg (49) and Burk (10) is of particular interest. 



Let the measured light provoke in the time / the production of x jA Oo per 

 unit of volume, the fraction used for the back reaction be/, and the concentra- 

 tion of the substance responsible for this back reaction be c (expressed in yul 

 O2 per unit of volume) . When / is the absorbed light intensity in ^tl quanta/ 

 min per unit of volume, the quantum yield is 



lA 02/min 

 ni quanta/min 



As the quantum yield in the light reaction is 1 , 



fil 02/n^in = /xl quantaniin 



