6 BIOPHYSICALLY ACTIVE X-RAYS 



circumstances the kinetic energy of the electron is converted into a 

 single quantum of radiant energy of short wavelength. Some of the 

 high-speed electrons do not have such favorable encounters. They 

 may pass close to the nuclei of the atoms of the target and may be de- 

 flected. At each such deceleration some kinetic energy is converted 

 into radiant energy, but of longer wavelength. The closer the electron 

 approaches the nucleus, the greater is its loss in velocity and energy 

 and the greater are the energy and frequency of the radiant energy or 

 released photon. 



The great majority of the electrons undergo no such collisions but 

 dissipate their energy in penetrating the target. This energy manifests 

 itself as thermal motions of the atoms. Thus much of the kinetic 

 energy of the electron stream appears as heat. 



The shortest wavelength of the radiant energy emitted by the target 

 is quantitatively obtainable from the relation proposed by Einstein in 

 1905 on theoretical grounds and verified experimentally by Duane and 

 Hunt [1915], namely, that the kinetic energy 



„ eV he 



E = = hv = — 



300 X 



where E is the kinetic energy of the colliding electron of electrostatic 

 charge e (4.8025 X 10 -10 esu), V the difference in potential between 

 filament and target in volts, 300 the conversion factor which makes 

 possible the use of volts for V instead of absolute units, h is Planck's 

 radiation constant (6.624 X 10 -27 erg second), v the frequency of the 

 emitted photon or x-radiation of wavelength X. The velocity of light c 

 enters the relation because c = v\. 



Upon substituting these values in the above equation, it is found that 



XV = 12,395 



where X is expressed in angstrom units (1 A = 10 8 cm) and V in volts. 

 For instance, it may be desirable to know the shortest x-ray wave- 

 length emitted by the target when an electron, arriving under a difference 

 of potential of 100 kv, between filament and target, is decelerated so 

 that all its energy is converted into one quantum of x-radiation. Under 

 these circumstances 



XV = X X 100,000 = 12,395 



X = 0.12 A = 0.12 X 10 _8 cm 



o 



When compared with the wavelength of visible light (5500 A), the 

 x-radiation has a wavelength about 50,000 times smaller. 



