26 : 2/ Absorption Spectrophotometry 



487 



If scattering occurs as well as true absorption, one may rewrite the 

 preceding by setting 



M 



Ma + Ms 



(4) 

 If /x s is too 



where the subscript a means absorption and s scattering 



large relative to fx a , some energy will be scattered more than once, 



re-entering the original beam. Then Lambert's 



law will no longer be valid. However, in 



many cases this rescattering is not important 



and Lambert's law is useful. If the scattering 



is too great, it is possible sometimes to use 



not the light transmitted in the original 



direction as shown in Figure 5, but instead, 



all the transmitted light. 



Equation 3 is a correct form of Lambert's 

 law only if \x is constant over the wavelength 

 band present. The value of \x will in general 

 vary with the wavelength. In this case, one 

 may represent the initial intensity I as an 

 integral over the range of wavelengths present. 

 This is expressed by 



4 = / Ioa d\ (5) 



where I 0A dX is the incident intensity between 

 A + dX. For each I QK dX, jx will be constant, 

 so that a more general form of Lambert's 

 law is 



Ax 



Figure 5. Attenuation of 

 light on passing through a 

 sheet the thickness of which 

 is Ax. The incident inten- 

 sity is I Xi and the attenuated 

 intensity leaving the sheet 

 is I 2 . 



I-jhx 



■UX 



dX 



(6) 



Because fx depends in a complex fashion on A, there is no way of simplify- 

 ing the preceding integral. Equations 5 and 6 are very complicated to 

 use. For precise work, narrow bands of wavelengths are used. 



Since absorption is a probability phenomenon, one expects that the 

 more absorbers there are in the light beam the greater will be the 

 absorption. For solutions with low concentrations, when Lambert's 

 law is valid 



fx = pc (7) 



where c is the concentration of the absorbing molecule and /?, the 

 extinction coefficient, is a constant. This is called Beers law. At high 

 concentrations, Beer's law and Lambert's law fail. In any experiment, 

 one must be sure that the concentration range is such that these laws 

 are valid at the wavelengths used. 



