584 Dr. N. Bohr on the Decrease oj 



the atom, and the energy transferred to the electron will 

 therefore be very nearly the same as if the electron were 

 free. If, on the other hand, the time of collision is long 

 compared with the time of vibration, the electron will behave 

 almost as if it were rigidly bound, and the energy transferred 

 will be exceedingly small. The effect of the interatomic 

 forces is therefore equivalent to the introduction of an upper 

 limit for p in the integral (4), of the same order of magnitude 

 as Yjv. The rigorous consideration of the general case would 

 involve complicated mathematical calculations, and would 

 hardly be adequate in view of our very scanty knowledge as 

 to the mechanism of the forces which keep the electrons in 

 their positions in the atom. However, it is possible over a 

 considerable range of experimental application to introduce 

 great simplifications and to obtain results which to a high 

 degree of approximation are independent of special assump- 

 tions as to the action of the interatomic forces. 



The calculation of the total loss of energy suffered by the 

 a or /3 particle is very much simplified if we assume that, for 

 all collisions in which the interatomic forces have an appre- 

 ciable influence on the transfer of energy, the displacement 

 of the electron during the collision is small compared with p 

 as well as with the maximum displacement from which it will 

 return to its original position. It can be simply shown that 

 the displacement of the electron during the collision if it 

 were free would be of the same order of magnitude as the 

 above quantity a. The first assumption is therefore equi- 

 valent to the condition that Y/v is great compared with a. 

 The second assumption is equivalent to the condition that 

 the value for Q which we obtain by putting p = Y/v in (1) 

 is small compared with the energy W necessary to remove the 

 electron from the atom. Under these conditions we get by 

 a simple calculation, the detail of which was given in the 

 former paper, that the effective upper limit p v for p in the 

 integral (4) is equal to 



Pv ~2ir v' 



where & = 1*123. Introducing this, we get for the integral 

 in (4), performing the integration from p = to p=p y and 

 neglecting a 2 in comparison with p v 2 , 



kY*m 



loo- 



(?)-M: 



2irvEe(M. + m] 



