XIII. ACTION SPECTRA AND ABSORPTION SPECTRA 423 



monochromatic radiation may be defined as the number of quanta 

 incident in unit time upon unit area of a surface normal to the beam 

 (see also last paragraph of this subsection). If the beam enters a 

 homogeneous absorbing medium, a given fraction of the incident 

 quanta is absorbed in passing through a given thickness of the me- 

 dium, the fraction being determined by the number of absorbing 

 molecules presented by the medium per unit thickness. This means 

 that intensity is always decreased by a given amount in passing 

 through a given thickness. Thus, if dl is an infinitely small unit of 

 thickness, and dl is the change in intensity of a monochromatic beam 

 in passing through this thickness: 



dl/dl = -kl (3) 



where / is the intensity at any point and kissi constant. Integration 

 of equation (3) yields: 



or, in exponential form : 



In (I/h) ^ -kl . (4) 



I = h e-^ (5) 



where /o is the intensity of the incident beam, and I is the intensity 

 after having passed through thickness I. The constant, k, in equa- 

 tions (3-5) is usually called the absorption coefficient. 



Either equation (4) or (5) is an expression of the Bougeur-Lambert 

 absorption law, which is often written with common logarithms and 

 in the reciprocal form 



log ih/I) = k'l (6) 



where k' is a constant, usually called the extinction coefficient. When 

 based on the same unit of path length, /, k' = /c/2.303. The corre- 

 sponding exponential form is sometimes used 



/o// = 10*'' (7) 



The relationship may be found expressed in any of these forms (equa- 

 tions 4-7). 



Since the fraction of the quanta absorbed is directly proportional 

 to the number of absorbing molecules, we may also write : 



log (/o//) = tCl (8) 



