LIGHT ABSORPTION BY PIGMENTS in VIVO 1865 



molecular dispersion. The optical density is thus reduced, in consequence 

 of particle formation, in the ratio: 



(^^^■'^'^^ Ds " In il/Tfp 



which is dependent only on Tp, the transmission of a single particle, and 

 not dependent on the concentration of particles. According to this reason- 

 ing, the "flattening" effect of particle formation on the absorption band 

 should be independent of concentration. In other words, the "sieve 

 effect" persists as "bunching effect" even when the concentration of parti- 

 cles is so high that no beam can traverse the cell without passing through 

 several particles (c/. below) . 



Relationship (37C.17) can be derived even more simply by applying 

 Beer's law first to the pigment "solution" in the particle, and then to the 

 "solution" of particles (considered as giant molecules). If the absorption 

 coefficient of a single molecule (its "cross section for photon capture," 

 to use the language of corpuscular physics) is a, and the number of mole- 

 cules per unit area of the particle is n, we have, for the transmission of a 

 single particle : 

 (37C.18) Tp = (I/h)p = e-n-y 



and for the absorption : 



(37C.19) ^p = 1 - Tp = 1 - e-n^ = 2 



where 2 can be considered as the photon capture cross section of the particle 

 as a whole. Applying Beer's law a second time, to a suspension contain- 

 ing A^ particles per unit area, we obtain : 



(37C.20) {I/h)p = e-N^ = e-m-e-'n = e-^d-^p) 



(37C.21) Dp = In (//7o)p = A^(1 - Tp) 



If the same total number of molecules, nN, is distributed at random over 

 the same area. Beer's law gives : 



(37C.22) Ds = In (h/Ds = nN<r = N In (l/T)p 



Thus, we again obtain relation (37C.17) between Dp and Dg. 



The validity of these derivations is limited to a range of particle con- 

 centrations in which the total volume occupied by the particles is small 

 compared to the volume of the suspension. (In the limit when particles 

 are densely packed, the difference between the suspension and a solution 

 containing the same total number of molecules obviously must disappear.) 



Practically, suspensions used for absorption measurements fulfill this 

 condition. Therefore our statements (Part 1, Vol. II, pp. 714, 716) 

 that the effect of "bunching" must disappear when each beam traversing 



