608 Dr. N. Bohr on the Decrease of 



P = 10W ; corresponding to a velocity o£ 6 . 10 s and a range 

 of about 10~ 4 cm. in hydrogen at ordinary pressure. 



The number of ions produced by the secondary rays cannot 

 be calculated in the same simple way as the number produced 

 by the direct collisions with the a or /3 particles, for in the 

 case of the secondary rays we cannot neglect the effect of 

 the interatomic forces. From the considerations in section 1 

 it is seen that the conditions for the neglect of the inter- 

 atomic forces is that the value of p corresponding to Q = W is 

 very small compared with Y/v. By help of the expression 

 (1) for Q and the expressions for W and v on p. 585, it can 

 be simply shown that this condition is equivalent to the con- 

 dition that the energy -J?nV 2 of the rays is very great 

 compared with W. This condition is fulfilled for a and ft 

 rays in light gases, but is not fulfilled for rays as slow as the 

 seoondary rays. 



Recently J. Franck and G. Hertz * have made some very 

 interesting experiments which throw much light on the 

 question of ionization by slowly moving electrons. Experi- 

 menting with mercury vapour and helium gas, they found 

 that an electron will rebound from the atom without loss of 

 energy if its velocity is less than a certain value. As soon, 

 however, as the velocity is greater than this value the electron 

 will be able to ionize the atom, and it was shown that the 

 probability that ionization will occur at the first impact is 

 considerable. For other gases the results were somewhat 

 different, but in all cases a sharply defined limiting value for 

 the velocity of the ionizing electrons was observed. These 

 experiments indicate that slowly moving electrons are very 

 effective ionizers. We may, therefore, obtain an approximate 

 estimate of the number of ions produced by the secondary 

 rays, if w e simply assume that each of these rays will produce 

 s ions if their energy has a value between sW and (s-fl)W. 

 This would give for the total number of ions formed 



If Q is very great compared with W this gives approximately 

 T 2ire^mnkx 1 , Q A . Q 

 I = m^p— W l0 «W = Awl0§ W-- " (34) 



This formula applies only to substances for which W has 

 the same value for all the electrons in the atom. For other 

 substances we must take into account that an electron ex- 

 pelled may produce ions, not only in collisions with electrons 

 * Verh. d. JDeutsch. Phys. Ges. xvi. p. 457 (1914). 



