CH. ix.] SIZE OF ELECTRON 99 



In an atom of sodium, which is twenty-three times 

 as heavy, there must be about 15,000 electrons. 



And in an atom of mercury there must be over 

 100,000 electrons, if atomic mass be wholly due to them. 



Consider then an atom of mercury containing 

 100,000 of these bodies packed in a sphere 10" 8 

 centimetre in diameter. One would think at first 

 they must be crowded ; but there is plenty of room. 

 Each electron is only 10~ 13 centimetre across, and 

 there are only about fifty of them in a row along any 

 diameter of the atom, whereas there might be a 

 hundred thousand in the same length ; hence the 

 empty space inside the atom is enormously greater 

 than the filled spaces. At least a thousand times 

 greater in linear dimension, or a thousand million 

 times greater in bulk. 



The whole volume of the atom is 10~ 24 c.c. ; the 

 aggregate volume of all the electrons composing the 

 atom is 10 5 x 10~ 39 = 10~ 84 c.c. ; consequently the space 

 left empty is 10 10 or ten thousand million times the 

 filled space. 



Even inside an atom of mercury, therefore, the 

 amount of crowding is fairly analogous to that of the 

 planets in the solar system. For though the outer 

 planets are spaced further apart than the inner ones, 

 they are also bigger, to practically a compensating 

 extent. 



Now, going back to what is sometimes called 

 Loschmidt's theorem in the kinetic theory of gases, 

 obtained roughly above 



mean free path 

 ^ diameter of particle 



volume of space available to particles 

 ~ combined volume of all their substance 



