504 Mr. C. G. Darwin on Collision of 



Bohr's theory does not supply a definite value for the 

 range, as his approximation ceases to hold for low velocities. 

 We can get an estimate by adopting Geigers empirical 

 formula 



V3 = V.(l-|) 



clV 

 and making *— have the proper initial value. Since 



Am = _ i Vp 



\dxh 3 R 



we have 



^=^logBV.», and |g = ^(logBV„ 3 + log2), 



where the accent refers to the H particle. 



Taking V = 2xl0 9 cm. per sec, A = 2-4xl0 3i and 

 R=ol cm. we deduce R/ = 2S cm. For heavier substances 

 higher multiples of log 2 will occur and the range will 

 be relatively less. Now consider a collision of the most 

 favourable type possible, when an a particle at its highest 

 velocity strikes a nucleus straight on. If the a particle 

 is from RaC the initial velocity of the H particle is 



Q 



x X 2 x 10 9 cm. per sec, and its range is therefore 

 28x(^J cm. or 117 cm. It should probably be more than 



this, as for these high speeds the range should be more 



nearly proportional to the fourth than to the third power of 



the velocity. Thus the H particles ought to be easily 



observable provided they can be made to occur in sufficient 



numbers. 



The H particles should be more scattered than a particles 



by their atomic encounters, for the angle of most probable 



E * 

 scattering depends on r— , and so is twice as great for H as 



for « particles. 



5. The experiments of Geiger and Marsden confirmed very 



completely the nuclear hypothesis, but it might be argued 



that some other law of force might give the same result. It 



might be difficult to give a general proof that this is not so, 



but we can show that no force proportional to some power 



of the distance other than the inverse square can give the 



observed dependence of v on V. If the force is as the inverse 



* Darwin, Phil. Mag. vol. xxiii. p. 907 (1912). 



