The absorption continues to increase with frequency and finally tends to 

 a constant asymptotic value. The maximum mean free path for the radiation 

 (the path length needed to decrease the intensity to l/e of its initial 



value) occurs at — p-= 100 and equals l/a = 67 cm. Thus, it can be seen 



mc 

 that there is no hope of finding a window at any frequency interval above 



1 o 



10 cpSo Furthermore, it will be shown in the next subsection on the 

 photoelectric effect that this lower limit can be extended to about 10 cps. 



B„ 



1 5 

 The Photoelectric Effect (> 3 x 10 cps ) 



The photoelectric effect arises when an electron in an atom or 

 molecule absorbs a photon from incident radiation and makes a transition 

 to the continuum, becoming a free particle. This effect, then, is effective 

 at photon energies greater than the ionization energy of the atom or molecule, 

 and the absorption spectrum is continuous. 



For the calculation, the absorption due to water will be approxi- 

 mated by that of hydrogen. The ionization energy of water is 12.56 volts 

 and that of hydrogen 13.6 volts, so that the absorption per molecule or atom 

 is nearly the same. For frequencies much larger than the ionization frequen- 

 cy of the atom, the absorption coefficient is 



a = N $, 



^ (137)^ 



41(2 



where N is the number of atoms per cm , Z the nuclear charge, (|)„ the Thomson 



scattering cross-section. For hydrogen in water, Table II gives values 

 of a as a function of frequency. 



TABLE II. ABSORPTION OF GAMMA RAYS BY HYDROGEN 

 (photoelectric effect) 



X A 1 



hv 



mc 



a 



1 

 .24 



5 X 

 10-8 



1 

 .024 



10 



20 



40 



80 



,0024 





.00016 



,5 



,0012 



5.5 



.0006 



,0003 



800 



,00003 



180000 



It is seen that the absorption falls off sharply with increasing 

 frequency (v ' from the formula), until it reaches the very small value of 

 5xl0~ per cm at — ^ = .1. However, Table I shows that in this frequency 



mc 



range the Compton effect is very appreciable and rising with decreasing 

 frequency so that there is little penetration by the radiation. 



