LIGHT ABSORPTION 55 



The general picture, then, is that photons absorbed by electrons are 

 usually re-emitted backward by free electrons, as in metals, and may be 

 re-emitted primarily in the incident direction if the photon energy does 

 not match any of the energy states available to the electrons. 



These possibilities are sufficient to enable us to learn many things 

 through the use of light. The phenomena which we shall discuss include 

 (1) light absorption, (2) birefringence, (3) dichroism, and (4) action 

 spectra. 



1 . Light absorption 



If photons impinge on matter, each atom and molecule near which 

 the photons pass has a probability of absorbing the photon. If we call E 

 the probability per molecule of absorbing a photon of a particular 

 energy, then the total probability of a photon's being absorbed is pro- 

 portional to E and to the number of molecules along the photon path. 

 The number of molecules along the path of a photon is the product of 

 the number per centimeter and the path length in centimeters. Since the 

 number per centimeter is proportional to the concentration of molecules, 

 we can now write the average number of absorptions in a given solution of 

 these molecules as Enx, where n is the concentration in molecules per 

 cubic centimeter and x is the path length in centimeters. 



A more usual form of this expression is obtained by multiplying and 

 dividing by Avogadro's number, N A , the number of molecules per mole: 



This expression, whose magnitude has been changed not at all by our 

 operations, is now the product of the probability of absorption per mole, 

 the molar concentration, and the path length. This is written as E m cx. 

 This expression, as stated above, is the average number of absorptions 

 per photon in the particular experimental situation. We may find the 

 fraction of photons which is not absorbed by using the Poisson formula 

 for the fraction of zero cases where the average, a, is the expression just 

 above : 



p (a) = e~ a = e- EmCX . 



This fraction of photons not absorbed then represents the fraction of 

 light, measured in intensity units, which passes through the solution. 

 We write this as I x /I (the fraction of the incident intensity, I , which 

 gets through a thickness .r) : 



* x _ P —E m cx 

 j e 



Jo 



