ELECTROMAGNETIC RADIATION; NATURE AND SPECTRUM 81 



absorption is directly proportional to the amount to be absorbed; or 



-dl/dx = k'l 



where x is thickness and / is intensity, or number of photons passing 1 cm 2 

 per sec. This is one of the natural functions (Chapter 1) for which / is ex- 

 pressed explicitly as 



/ = /, 



-k'x 



where I is the intensity when x = 0, just as the radiation enters the ab- 

 sorbent; k' is a constant, characteristic of the absorbent (larger, the better 

 the absorption capacity of the medium), called the absorption coefficient. The 

 plot of / vs x is shown in Figure 1-2 (c). 



Since In I /I = k'x, conversion to common logarithms by dividing by 

 2.303 gives log I /I = kx, where k' = 2.303 k, and k is called the "extinction 

 coefficient." 



Lambert's law is applicable over the whole electromagnetic spectrum, 

 and, you will remember from Chapter 3, is useful also to describe the ab- 

 sorption of matter waves. It is an obvious but very important point that the 

 extinction coefficient of a substance will be different at different wave- 

 lengths. From the far infrared, through to the near ultraviolet, the extinc- 

 tion coefficient is large only for particular wavelengths. Such specificity is a 

 property of molecular absorption. If these molecules are suspended or dis- 

 solved in a medium, k will be directly proportional to the concentration, c 

 (Beer's law). Thus k can now be factored into ac, where a is called the molec- 

 ular extinction coefficient. Formally then: 



log I /I = acx (Beer-Lambert law) 



The specificity for absorption of selected wavelengths disappears from the 

 far ultraviolet through to gamma radiation — continuous absorption occurs 

 accompanied by ionization — and the extinction coefficient decreases more 

 or less linearly with decreasing wavelength (i.e., with increasing energy 

 /photon). Thus ultraviolet light penetrates only a small fraction of an inch 

 of tissue; and the k for tissue for near ultraviolet is very large. By contrast, 

 soft X rays penetrate tissue with only a small amount of absorption per cm; 

 and k is smaller. However, each photon of X rays absorbed carries roughly 

 1000 times more energy than each photon of near ultraviolet, and therefore 

 only 1/1000 as much absorption is required to do the same damage. It is 

 seen then that the important quantity is the energy absorbed per unit volume, 

 because this determines the subsequent effect: warming of tissue, triggering 

 of the optic nerve fiber, providing the energy for photochemical synthetic 

 processes, or ionization and rupture of molecular bonds. 



