80 ELECTROMAGNETIC RADIATIONS AND MATTER 



Quantitative expression of these ideas followed Planck, who, in 1901, pro- 

 posed that the energy, e, contained per photon in incoming electromagnetic 

 radiation is proportional to the frequency, v, of the radiation. Thus 



e = hv 



where h is the proportionality (Planck's) constant, equal to 6.62 x 10" 27 erg 

 sec/photon (1 electron volt, ev, = 1.6 x 10 12 ergs). 



Let w } ,w 2 , and w 3 be the energies of binding of different atomic or molec- 

 ular orbital states of the electron to the nucleus, and accept Bohr's as- 

 sumption. If e = w } , w 2 , or w 3 , absorption of the incoming radiation will 

 easily occur,accompanied by excitation of the electron from its "ground 

 state," or orbital of lowest energy, to an excited state. If e ^ w y , w 2 , or w 3 , 

 then absorption does not readily occur, although in favorable cases w x can be 

 taken from a larger e, the electron excited to state 1, and the radiation pass 

 on with reduced energy (e - w, = hv 2 ) and lower frequency (longer wave- 

 length). This is one aspect of the famous "Compton scattering." 



If f is greater than some critical value, w, the ionization energy, the elec- 

 tron can be ejected completely from the atom or molecule, and may have any 

 kinetic energy up to and including e — w. Since the electron has a mass of 

 9 x 10 _28 g, the kinetic energy (1/2 mv 2 ) is less than, or equal to, e — w. 

 Now a negative particle of velocity v, just like any other member of the elec- 

 tron cloud about a molecule, but moving with high velocity, is a very good 

 ionizer itself. Hence the ionization process continues along a track through 

 the tissue until all the incoming energy, e, has been dissipated either as heat 

 or in producing ions. 



The Laws of Absorption 



In the tables of properties of em radiations, the bases of the techniques for 

 handling them were implied. What happens when absorption takes place 

 was also indicated. We consider now the extent of absorption, and its con- 

 verse, the depth of penetration. 



In brief and in summary, absorption of electromagnetic radiations is 

 governed only by the laws of chance. The chance that a photon will be ab- 

 sorbed depends only upon the number of target electrons and nuclei in its 

 path. From the fact that the higher energy (shorter wave length) radiations 

 penetrate deeper into any given material, it is inferred that they are more 

 difficult to capture — have a "smaller capture cross-sectional area." Con- 

 versely, the denser the target material the greater is the number of potential 

 targets per centimeter of the photon's path, and hence the greater is the ab- 

 sorption per unit length of path. 



These ideas are expressed quantitatively in Lambert's law. The rate of 



