262 RADIATION BIOLOGY 



is given by the relation E = hv, where E is the energy in 1 photon, called 

 a quantum; h is Planck's constant, 6.56 X 10~-' erg-sec; and p is the fre- 

 quency of light per second. In the case of red light having a wave length 

 of 7000 A, or 7 X lO"'^ cm, the frequency is obtained by dividing the 

 velocity of light, 3 X 10^° cm/sec, by the wave length, 7 X 10~^ cm, to 

 give a frequency of 4.3 X 10'^ per second. The physical chemist carries 

 out his calculations in terms of moles of 6.02 X 10'^ molecules rather 

 than single molecules, and the energy of the light for a mole is obtained 

 by multiplying the energy of 1 photon by 6.02 X 10'-^ and convert- 

 ing this to calories by means of the relations 10^ ergs = 1 joule and 

 4.18 joules = 1 cal. The energy of red light is thus 



6.02 X 10-^ X (>.56 X 10--^ X 4.3 X W ,^ _^^ , , , 

 ^ ^g ^Q^ = 40,500 cal/mole. 



By similar calculations, blue light of 4000 A furnishes 71,500 cal/mole. 



It is clear that photosynthesis calls for energy of high intensity, at least 

 as high as 112,000 cal/mole, whereas red light of wave length 7000 A 

 furnishes only 40,500 cal/mole. This is only about one-third enough. 

 Photosynthesis, however, certainly takes place very effectively in red 

 light, and a mechanism must be found by which the energy of at least 

 3 photons can be utilized for each molecule of carbon dioxide consumed 

 and oxygen evolved. If any steps are less than 100 per cent efficient 

 energy-wise, if activation energies are required, or if exothermic reactions 

 are involved, the photosynthesis with red light will require more than 

 3 photons per molecule. 



Although 3 photons together theoretically contain enough energy to 

 effect photosynthesis, it is highly improbable that 3 or more photons can 

 collide simultaneously with a molecule of carbon dioxide and a molecule 

 of water. Thermodynamically 3 or more are required, but the mecha- 

 nism of the utilization of the energy is uncertain. Successive reduction 

 by hydrogen released from water is now considered to be a likely mecha- 

 nism. This is discussed fully in other chapters of this volume. 



In actual photosynthesis it is to be expected that more than the mini- 

 mum of 112,000 cal will be required. The relation between energy 

 absorbed and plant product is calculated and reported in two different 

 ways: the quantum yield and the energy efficiency. 



The quantum yield $ is defined in photochemistry as the number 

 of molecules undergoing chemical change per photon or per quantum 

 absorbed: 



No. of molecules undergoing chemical change 



(J) = 



No. of photons absorbed 



If the primary activation of one molecule by a photon is followed by a 

 chemical reaction that involves two molecules, the quantum yield is 2. 



