THE PHYSICAL CHEMISTRY OF VISUAL PURPLE 



First case — non-absorbing impurities and photoproducts. In the 

 first instance suppose that the visual purple solution is free from all 

 light-absorbing impurities and that the bleaching is carried out by 

 light which the photoproduct does not appreciably absorb. 



Consider a parallel beam of the monochromatic Hght to fall on a 

 solution contained in a cylindrical optical cell arranged coaxially 

 with the direction of the Hght beam. It is assumed that Beer's and 

 Lambert's laws of hght absorption hold. These state that 



/, = /(/ - e-^\ (1) 



Those layers of the visual purple solution which first receive the hght 

 beam weaken it for those at the rear. Consequently the front layers 

 bleach before the rear ones. Nevertheless, equation (1) and the 

 following argument hold when there is a concentration gradient 

 along the optical axis, if it is understood that by c is meant the 

 effective concentration at any time if the solution were mixed. 



From the above definition of quantum efficiency, the rate of 

 decrease in the number of chromophores is equal to the product of 

 the quantum efficiency and the absorbed hght intensity. That is 



-^==^'. (2) 



dt V ^ ^ 



By ehminating /^ between (1) and (2), 

 dt v^ 



-acVX 



which, on rearranging, becomes 



^^ =^rL,dt. (3) 



(1 - e-^^O V 



By making the assumption that y, the quantum efficiency, is indepen- 

 dent of concentration, (3) may be integrated to give 



1 ay// 



^°S« -^^^rZTi = IT • ^ + constant, 



and, since e""^ = ///^ this becomes 



log, — ^ = ?^ . r + constant. (4) 



I — It A 



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