144 RADIATION BIOLOGY 



of the atom, and with 7 rays and other nuclear forms of radiant energy 

 the atomic nuclei may be the site of interaction, although all the other 

 forms of interaction may also be present. 



BOUGUER-BEER LAW 



There are two generalized laws governing radiant-energy absorption 

 which are mathematical statements as to the probability of capture of a 

 photon by the absorbing molecules or atoms in the path of the beam in 

 relation to the thickness and concentration of the absorbing substance. 

 It was shown by Bouguer (Erode, 1949; Gibson, 1949; Mellon, 1950) 

 (frequently attributed to Lambert) that the rate of decrease of intensity I 

 is proportional to the thickness x and that —dl/I — n' dx, where ix' is a 

 constant that is an intrinsic property of the absorbing molecules and is 

 a function of wave length. Integrating between the limits of incident 

 intensity /o and transmitted intensity / for a finite thickness h gives the 

 exponential expression for Bouguer's law, / = /oe""'', where e is the 

 natural-logarithm base, 2.718. Beer derived a similar relation for the 

 absorption of solutes in relation to concentration. When combined, 

 the two relations yield the Bouguer-Beer law of absorption, 



/ = /oe-Mofc (3_11) 



and 



- In I/h = - In r = fxcb, 

 or 



In h/I = In \/T = iJich, 



where T = transmittance or ratio of transmitted to incident flux, 



c = solute concentration, 



h — internal cell thickness, and 



jLt = absorption coefficient (Erode, 1949). 

 This relation is shown in Fig. 3-4. As m increases, the absorption 

 increases and the transmittance decreases. 



ABSORPTION AND TRANSMISSION 



Since the measurement of absorption involves only the ratios of the 

 incident and transmitted beams, any convenient system of comparison 

 may be used. Consequently the notation / (J in German literature) 

 has been rather generally accepted as the symbol for the relative beam 

 intensities in terms of radiant energy or radiant flux (ibid.). For the 

 other terms and notations there has been much less agreement, but as 

 the result of a study of the respective literatures, Erode (1949) and Gibson 

 (1949) have developed nomenclatures that are consistent and precise. 

 The nomenclature of Gibson will be used here. It is similar to that of 

 Erode but is somewhat more extensive. 



