40 BIOLOGICAL EFFECTS OF RADIATION 



impact); u stands for the speed of an electron after impact; 4> and 6 for 

 the angles made with the direction of the incident photon by those of the 

 recoihng electron and the scattered photon, respectively. 



Conservation of energy requires that the energy of the incident photon, 

 hv, be equal to the simi of the energy of the scattered photon, hv' , and that 

 of the recoihng electron, which latter in relativistic mechanics is given 

 by the expression 



where mo stands for the rest mass of the electron and ^ for u/c. Thus, 



Conservation of momentum requires the following two equations, 

 referring respectively to the momentum components parallel and per- 

 pendicular to the direction of the incident photon, in the plane common 

 to the three directions of incident photon, scattered photon, recoihng 

 electron: 



hv hv' vioU .„,s 



— = cos 6 -\- -j -^ry, COS (/) {_21) 



c c (1 — P')" 



= — sm d + ^^ _ ^,y^ sm <t> {22) 



Ehminating 4> and u between these three equations, we arrive at a 

 relation between v' , v, and d, which may immediately be translated into 

 the following relation of simpler aspect: 



V - X = A(i _ cos e) - {23) 



mc 



This is a prediction of the wave-length which should belong to the X-rays 

 scattered at angle 6; that is to say, an observer placing his detecting 

 apparatus somewhere along the line leading outward from the scattering 

 substance at an angle 6 to the incident beam should detect X-rays of the 

 wave-length given by formula {23). This prediction is verified by experi- 

 ment. Eliminating 6 and v' between equations {20), {21), and {22), 

 one gets a relation between u, v, and <^. This may be translated into a 

 prediction of the energy which should belong to electrons recoihng in 

 the direction </>; that is to say, an observer placing a device for detecting 

 electrons, somewhere along the line leading outward from the scattering 

 substance at an angle 4> to the incident beam, should observe electrons 



