590 Dr. N. Bohr on the Decrease oj 



We see that X is equal to the average number of electrons 

 inside a cylinder o£ radius \/p' 2 + d 2 . Since X decreases for 

 decreasing p, we shall only have to consider its value for 

 p=0. Substituting for a we get 



M 2 m 2 V 4 



If we consider a gas at ordinary temperature and pressure 

 and introduce the numerical values for e, m } E, M, and N, 

 we obtain both for a and ft rays approximately 



■v _ o.a 1037 n & x 



This expression varies very rapidly with V, and gives quite 

 different results for a and for ft particles. 



For a rays from radium C we have V=1'9 . 10 9 , this gives 

 X =1'7 . n&x. Now the range of a rays from radium C in 

 hydrogen and helium is about 30 cm., and according to 

 Rutherford's theory, the number n of electrons in a molecule 

 of these gases is equal to 2. We therefore see that X will 

 be large compared with unity, provided the sheet of matter 

 be not exceedingly thin compared with the range. For 

 other gases X will be even greater, since the product of the 

 number of electrons in the molecule and the range of rays is 

 greater than for hydrogen and helium. In case of a rays we 

 may therefore expect that the formulae- deduced above should 

 give a close approximation. In order to get an idea of the 

 order of magnitude of the variation to be expected in the loss 

 of energy suffered by an a. particle, consider for instance a 

 beam of a rays penetrating a sheet of hydrogen gas 5 cm. 

 thick. Using the experimental values for the constants, we 

 get from (11) w = 3.10 3 approximately. Introducing this in 

 (10) we see that the probability variation is very small. 

 Thus about half the particles will suffer a loss of energy 

 which differs less than 1 per cent, from the mean value, and 

 less than 1 per cent, of the particles will suffer a loss which 

 differs more than 5 per cent. In section 4 we shall return 

 to this question and compare the formula (12) with the 

 measurements. 



For ft rays of velocity about 2 . 10 10 , we get for a sheet of 

 aluminium 0*01 gr. per cm. 2 — a thickness corresponding to 

 that used in the experiments discussed in section 5 — 

 \o=l'6.10~ 2 . Since this is very small compared with 

 unity, it is clear that the assumptions used in deducing the 

 formulae (8) and (12) are in no way satisfied. Still, it 



