98 ELECTRONS AND IONS [CH. ix. 



travelling unit distance. But in saying this we are 

 ignoring the forces between the particles, as well as 

 their motion, and are not considering a swing round 

 as a collision. 



Nevertheless, as regards order of magnitude 



Ax 1 d* 



/yi . _ 



mra? n^a" tra 2 ' 



where d? is the cubic space allotted to each particle, 

 while ira z is the actual bulk of each. 

 Therefore approximately 



a; total space occupied 



a ~~ a few times the aggregate volume of the particles* 



a statement roughly analogous to Clausius' or 

 Loschmidt's theorem in the kinetic theory of gases. 



Hence the mean free path can be estimated by 

 considering how much space the substance of all the 

 electrons in an atom occupies, as compared with all 

 the space which the atom occupies itself. In other 

 words, we have to consider what the size 10~ 13 for an 

 electron's diameter means, as compared with the size 

 10" 8 for an atom's diameter. In the solar system the 

 diameter of the earth is 24 ^ 00 th part of the diameter 

 of its orbit round the sun. Consequently if the earth 

 represented an electron, an atom would occupy a 

 sphere with the sun as centre and four times the 

 distance of the earth as radius. 



In other words, if an average atom is composed of 

 electrons, they are about as far apart in that atom in 

 proportion to their size as the planets in the solar 

 system are in proportion to their size. 



In an atom of hydrogen there would have to be 

 roughly 1,000, or say more exactly 700, electrons in 

 order to make up the proper mass. 



