290 Mr Campbell , The number of Electrons in an Atom. 
7. Taking the value of the average potential energy of an 
electron as 6'7 x 10/ ~ 11 ergs, we may proceed to calculate the 
number of electrons in the radium atom. The energy liberated 
by one gram of radium throughout all its known radioactive 
changes is T6 x 10° calories = 6‘7 x 10 1B ergs. The atomic weight 
of radium is 225 and the mass of a hydrogen atom IT x 10~ 24 : 
therefore the energy liberated by a single radium atom is 
T7 x 10 _5 ergs. Hence the value of N, the number of electrons in 
the radium atom, is given by 
N x 6-7 x 10“ n - 1-7 x 10- 5 , 
N= 2-5 x 10 5 . 
If the mass of the radium atom is the sum of the masses of the 
contained electrons we must have 
M 
N = 225 x — , where M is mass of hydrogen atom 
= 4-2 x 10 5 . 
The assumptions that we have made lead to nearly the same 
value for N as the older assumption based on the mass of the 
atom. (It is perhaps pertinent to remark that the assumptions 
were made before the calculations and that they were not inten- 
tionally adopted to give the desired result.) 
8. If, in place of the assumption of § 6, we assume that the 
force acting on any one electron is that due to the presence of a 
total charge — Ne on the sphere in which the electron moves 
(where N is the number of electrons in the atom and e the charge 
on each), we shall obtain a minimum estimate of the N. For if 
our supposed constitution of the atom is at all near the truth, it is 
certain that the force acting on each electron and, therefore, its 
total energy, must be less than that given by this distribution. 
It will be found that the total energy (potential and kinetic) of 
the N electrons moving on the circumference of such a sphere of 
Ne' 
radius a is N x . Hence, if we put a = 10 -8 , e = 34 x 10 lft , 
a 
. (3-4 x 10- 10 ) 2 _ _ r 
we have N- tfti. = 1*7 x 10 J ; 
10-8 • 
N= 1200. 
It should be observed that such an atom must lose its whole 
energy in providing the energy liberated in radioactive processes : 
the system resulting from the disintegration would possess no 
internal energy. Whereas, according to the view which was taken 
in § 6, the redistribution of the electrons in stable orbits after the 
