SCATTERED X-RADIATION 25 



Here m = ?n /(l — B 2 ) 112 is the relativistic mass of the electron of 

 energy content mc 2 , and mq is identified as its rest mass. 3 = v/c, 

 where v is the recoil velocity of the electron and c the velocity of light. 

 These equations involve relativity calculations because of the high 

 velocity of recoil of the electron, necessitating the use of an effective 

 mass (m) which is greater than the rest mass (m ). 



The next step is to consider the application of the law of conservation 

 of momentum as applied to the collision. This law leads to two equa- 

 tions, one for the momentum along the x axis, or the x component, here 

 chosen in the direction of the incident x-ray photon, and one at right 

 angles to it, the y component. 



hv hvi . J . 



— = — cos -\- mv cos d (x component) 

 c c 



= — sin — mv sin 6 (y component) 

 c 



The x-ray photon E of energy content hv, considered as a colliding entity, 

 is moving with the velocity of light c. It has a relativistic mass of 

 hv/c 2 . Its linear momentum is hv/c. From these relations the increase 

 in wavelength (AX) can be computed, recalling that c = v\, and is found 

 to be 



ft , 

 AX = (1 — cos 0) 



m Q c 



Evaluating h, rriQ, and c, we find that 



AX = 0.0242 (1 - cos 0) 



where X is expressed in 10 -8 cm, i.e., angstrom units (A). 

 For values of 4> equal to 90° 



AX = 0.0242 A 



For values of equal to 0° 



AX = 



This result shows that the increase in wavelength is independent of the 

 original or incident wavelength and that the modified scattered radia- 

 tion depends for its increase in wavelength upon the direction in which 

 it is scattered. For back scattering, where = 180°, the increase in 



o 



wavelength AX amounts to 0.04848 A. 



The conclusion is that the softest scattered radiation appears in the 

 direction = 180°, and that this modified scattered radiation hardens 

 as approaches zero, at which point its wavelength increase is zero. 



