ABSORPTION 15 



cent of an incident 100 units of energy, 80 units would pass through this 

 first centimeter. These 80 units would then be incident on the second 

 centimeter of the absorbing medium, and this second centimeter would 

 absorb 20 per cent of the 80 units incident on it and transmit 64 units; 

 the next centimeter would absorb 20 per cent of the 64 units and trans- 

 mit 51.2 units of energy; and successive centimeter layers would trans- 

 mit 41, 32.8, 27.2 units, etc. 



The energy loss of an x-ray beam passing through matter is, however, 

 also dependent on the wavelength. Long wavelengths (soft x-rays) 

 are absorbed much more readily than short waves (hard x-rays). It 

 has been found experimentally that for restricted wavelength regions 

 the absorption varies as the cube of the wavelength. 



Therefore, if the wavelength of the incident radiation on tissue is 

 composed of a beam of soft x-rays, it is found that the first centimeter 

 of tissue absorbs 63 per cent of the incident energy, while successive 

 layers would transmit 37, 13.7, 5.1, 1.9, and 0.7 per cent. To appreciate 

 the difference in opacity in changing from hard to soft x-rays, compare 

 this last value with the effect of the shorter wavelengths where the fifth 

 layer transmitted 32.8 per cent. 



The energy loss is also dependent on the kind of material used as an 

 absorber. The loss is proportionally larger for a greater density of the 

 absorbing substance. This implies that absorption is an additive atomic 

 property and depends only upon the number and kind of atoms compos- 

 ing a molecule. The absorption varies as the fourth power of the atomic 

 number, for a given wavelength. 



It has been found empirically that the absorption may be represented 

 approximately, over restricted regions of wavelengths, by what is gen- 

 erally known as Owen's law, namely, that the absorption coefficient per 

 atom (fx a ) in the path of the x-ray beam is given by 



Ha = CX 3 z 4 



in which C is an experimental constant and z the atomic number. When 

 X is limited to the restricted radiation of wavelengths less than the K 

 characteristic wavelengths of the absorbing atom, as for instance in the 



o 



use of filters of Al and Cu for X between 0.50 and 0.71 A, then the experi- 

 mental constants C A i and C Cu are 0.0217 and 0.0221, respectively. 



Using Owen's absorption law, let us compare the relative opacity of 

 bone and fleshy tissues exposed to the same beam of monochromatic 

 x-rays. Fleshy tissues are composed chiefly of H and O. Their absorp- 

 tion is comparable to water. The molecular absorption of H 2 is 

 proportional to 



2 X l 4 + 8 4 = 4098 



