THE ENERGY RELATIONS IN PHOTOSYNTHESIS 331 



The efficiency was determined in a manner quite similar to the method 

 used in the experiments just described ; E designates the absorbed radiant 

 energy and W the energy transformed in photosynthesis. The latter was 

 determined in the same manner, with the assumption that the following 

 equation represents the reactions: 6 (CO2) -\- 6 (H2O) = (CeHiaOe) + 

 6 (O2) — 674,000 calories. 



The ratio W/E, or the quantity of chemical work done by one calorie 

 of absorbed radiant energy is designated by •1' and is dependent upon the 

 intensity of incident radiation. With increasing intensity <& becomes 

 smaller, and with decreasing intensity approaches a limiting value of <&o- 

 In the previous detenninations as already noted, <I>o was calculated by 

 extrapolation from two values of 4> measured at two different intensities. 

 As the course of curve of f^ with different intensities of light is not 

 definitely known, ^ was determined at very low light intensities. <^o was 

 taken as the value obtained with the lowest light intensity. It has already 

 been mentioned that the rate of photosynthesis varies greatly with differ- 

 ences of cultural conditions of the alga, and in these experiments cultures 

 which showed a high photosynthetic efficiency were used. Warburg and 

 Negelein conclude that the efficiency decreases with decreasing wave length. 

 This is shown in Table 39. The value in the green light is somewhat ques- 

 tionable on account of the uncertainty of complete absorption. It was 

 also found that there is apparently no relation between ^q and the co- 

 efficient of absorption of the different wave lengths by the methyl alcoholic 

 solution of the pigments of the alga. 



TABLE 39 



Photosynthetic Efficiency of Chorella with Light of Different Wa.'.-e 

 Lengths. (From Warburg and Negelein.) 



Red 



"k = 660 \i\i Yellow Green Blue 



610-690^1 ?. = 578mi >. = 546 ^fA ?. == 436 ^n 



*o per cent 59 53.5 44.4 33.8 



Warburg and Negelein endeavored to apply Einstein's law of photo- 

 chemical equivalence to these results. This law is based upon the quantum 

 theory of Plank, according to which energy is absorbed or radiated only 

 in integral units equal to Jiv in which h is the Plank constant (6.547 X 10"-'' 

 ergs per sec.) and v is the frequency. Einstein formulated his theory of 

 photochemical action on the assumption that the occurrence of a photo- 

 chemical reaction is due to the absorption of quanta of radiation, each 

 molecule requiring one quantum, hv, of a frequency v, characteristic of 

 the absorbing molecule. Thus Einstein proposed the following formula: 



Q 



n = — — 



hv 

 in which O is the absorbed heat required to produce the chemical reaction, 

 n is the number of molecules dissociated by light of the frequency v. Each 



