24 



BIOPHY SIC ALLY ACTIVE X-RAYS 



where ra is the mass of an electron initiating the scattering supposed 

 to be at rest inside the carbon block, c is the velocity of light, and h is 

 the Planck constant. This relation indicates that AX is larger for a 

 greater angle <£ at which the scattered radiation is measured, being zero 

 in the direction of the incident beam where <£ is zero. 



\2/-axis 



E=hv 



XAy\A-> 



Incident photon 



r 



Original position of electron 

 at rest 



Modified x-radiation 

 increased 

 in wavelength 



> a;=axis 



Recoiling electron 



Fig. 1-10. A diagrammatic representation of the Compton effect. Note the 

 increase in wavelength (X + AX) of the x-ray photon scattered by the stationary 

 free electron e, and the resulting direction and velocity of the electron after the en- 

 counter. 



Through the explanation of this extraordinary change in wavelength 

 A. H. Compton proved the existence of a collision phenomenon in which 

 an incident quantum of x-radiation or photon of energy content hv 

 collides with a free electron in the absorbing material. The photon 

 acts as if it were a perfectly elastic entity colliding with a perfectly 

 elastic electron. The incident photon may be pictured as colliding 

 elastically with a stationary electron, and giving it a glancing blow. 

 In this process it communicates energy and momentum to the deflected 

 electron and in turn loses an amount equal to that passed on to the 

 electron, but in such a way as not to violate the laws of conservation 

 of energy and momentum. This collision is represented pictorially 

 in Fig. 1-10. Here the incident x-ray photon, of energy content E = hv, 

 is shown colliding with an electron at rest of mass m . The incident 

 energy E is divided between the modified photon bouncing off at angle <j> 

 with energy E^ and the electron recoiling at angle d with energy E g . 

 The law of conservation of energy demands that 



E =E <b +E ( 



<t> ~ u e 



or that 



hv = hvi + m c' 



W 1 - 8 2 J 



