a. Particles with Light Atoms. 



50; 



Thi< formula becomes infinite in the neighbourhood of 

 <£ = 14° 29'. In fact, there will be a considerable increase in 

 the number of scintillations near this angle, since a large 

 change in p makes little difference in the deflexion. A 

 finite formula can be obtained by expressing the whole 

 number deflected through angles greater than any given 

 angle, ^sear the limiting angle the field of the microscope, 

 however small, will cease to be uniform. 



To the above number v must be added the effects of the 

 recoiling H particles. Their number is 



sm 6 ad 



QNtco 



e 2 W 

 ^25see 3 0. 



V 4 M s 



The whole number of scintillations observed is thus 



QNfo 



1 e 2 E 2 ( 

 V 4 M 2 1 



cosec 3 <j) 



2cosec 2 <£ — 17 

 \/(cosec 2 — 16) 



+ 25 sec 



°°<k} 



They are of three types, slow a particles, fast a. particles,, 

 and II particles. Since w=V§cOs#, the last are very much 

 faster than either of the first. 



4. It is of great interest to see how these H particles may 

 be expected to behave. In passing through matter they will 

 be retarded like a particles, and we may calculate their 

 range. To do this we take Bohr's formula * 



V 3 M 



d\ r _ ^M^ 



m 



Here N is the number of atoms per c.c, e ni refer to an 

 electron, k is a numerical constant, and n s the natural fre- 

 quency of any of the electrons in the atom. For a H particle 

 E is to be halved and M quartered. The result thus does not 

 affect the factor outside the sum, while inside we have to 

 add a term r log 2, where r is the number of electrons in the 

 atom. Thus the range of a H particle will be slightly less 

 than that of an a particle of the same initial velocity. The 

 most important case is where the H particles are travelling 

 through hydrogen. For this Bohr takes r = l and so we have 



m 



stead of 



dx 



dY 

 dx 



=*-^ 8 -(logBV»+log2) 



^logBV* 



* Bohr, Phil. Mag', vol. xxv. p. 10 (1013). 



