THE HOMOGENEITY OF VISUAL PIGMENT SOLUTIONS 



obtained and it is necessary to analyse the results. The factors 

 involved in such an analysis may be best considered with reference to 

 simple theory. 



THEORY OF THE BLEACHING OF A BINARY MIXTURE 



Provided the optical density is small, the complex equation 

 describing the bleaching kinetics of visual purple (Chap. 3, equation 

 16) may be replaced by, 



log,cJct = ciyIt (1) 



or, in the alternative exponential form 



c, = Co . e-^y'' (2) 



In these equations, Cq is the initial concentration of visual purple and 

 Cf, that after t sec exposure to the bleaching light. The symbols a, 

 y and / were defined in Chap. 3, p. 68. 



The errors involved in the use of equations (1) or (2) instead of the 

 more exact one, are less than 5 per cent provided the optical density 

 (logio//A) of the solution does not exceed 0-12 at the bleaching 

 wavelength. 



Equation (2) shows that the proportion of visual purple remaining 

 (cJcq) at any time during the course of the bleaching is exponentially 

 related to the time of exposure. The kinetics of bleaching thus follow 

 the law of organic growth (or decay) and hence resemble those of 

 unimolecular reactions or of the decay of radioactive substances. 

 The reason for this Hes in the fact that the amount of light absorbed 

 by a solution is proportional to its density — when this is small 

 (Chap. 1, p. 19). Since the rate of bleaching is proportional to the 

 Hght absorbed, and since the optical density is proportional to the 

 concentration, we have the rate determined by the concentration — a 

 necessary condition for the law of organic growth to apply. 



In Fig. 6.4, cJcq, expressed as a percentage, is plotted against a 

 time scale for a number of values (100, 50, 25, 10 and 1) of the 

 parameter ay/. The family of curves shown can be interpreted as 

 follows. 



In the first instance we may regard ay as invariable, in which case 

 the family represents the time courses of bleachings in various 

 intensities of light of a constant wavelength. Inspection of the curves 

 in Fig. 6.4 then shows that doubhng the intensity (for example) halves 

 the time required to reach a given degree of bleaching. The amount 



165 



