192 Mr. G. A. Schott on the Electron 



§ 4. We shall first show that straj r electrons cannot exist 

 in a permanent atom ; all electrons must be arranged in 

 groups or rings. 



An electron loses energy by radiation whenever it has 

 acceleration ; in fact 



2Ce 2 fff ft \ 



Xl ~ 3(l-/3 2 ) 2 I p 2 + C 2 (l-/3 2 ) J ' 



This expression was first given by Lienard ; it has been 

 confirmed by different methods by Abraham and by myself. 

 Both terms in R are positive ; its least value is therefore 

 given by /3 = or j3= constant. We find in this case, with 

 the numerical values of § 3, 



K = 2-4xl0 7 (1 _^ g erg/sec, 



for an orbit of atomic size, and greater in proportion for a 

 smaller orbit. Comparing this with the value of the kinetic 

 energy of an a or particle, we see that /3 is necessarily 

 extremely small. Hence we may calculate its energy and 

 the radius of the orbit as if it obeyed the ordinary laws of 

 mechanics. 



Its kinetic energy is E = J C 2 ra/3 2 . 



Let it move in a circle of radius p under the action of an 

 opposite charge ve. If the charge be central we have 



C 2 m/3 2 ve* 

 P ~P*' 

 If it be a sphere of uniform electrification of radius b, 



C 2 m/3 2 _ ve*p 

 p ~ V ' 



In any case, G* m /3*> V *P\ 



2CV/3 4 

 'dp 

 R 4e 2 j3 2 Ave* 



To the present approximation R = — Q ' g ; hence 



E ~ ZCmp 2 - 3C*m'b l 



v.2.10 9 . 





In other words, a single electron cannot move in a circle 

 of atomic radius for any appreciable time. It will either 

 pass out of the atom, fall into one of the groups of electrons 

 already existing in the atom, or ; as its velocity diminishes 



