Mr Campbell, The number of Electrons in an Atom. 289 
5. The greatest kinetic energy, which can be possessed by an 
electron moving within an atom, may be identified with some 
show of reason with the least kinetic energy which an electron 
moving outside an atom is found to possess. The slowest electrons 
which have been observed experimentally in a gas outside a radio- 
active substance are the 8 rays discovered by Prof. Thomson : the 
speed of these rays has been measured by Ewers as 
325 x 10 8 cm./sec. 
These electrons have doubtless lost some part of their energy in 
breaking away from the atom, but the energy spent in this 
process is known : it is the energy required to ionise a molecule. 
This energy is that acquired by an ion in falling through a 
potential difference of 20 volts, i.e. that possessed by an electron 
moving with the speed of 8 x 10 8 cm./sec.: it is of the same order 
as that possessed by the particles in the 8 rays. Accordingly we 
shall take the value of the greatest kinetic energy which an 
electron can possess without breaking free from its orbit as twice 
that of a particle in the 8 rays, i.e. 
2x|/ix (3-25 x 10 8 ) 2 = 6-7 x lO" 11 ergs, 
where /jl is the mass of an electron*. According to our assump- 
tion this quantity is also the potential energy of the electron 
in its orbit, which is liberated when the orbit becomes unstable. 
0. This estimate of the average potential energy of an 
electron derives some support from theoretical considerations. If 
Ave suppose that the forces restraining the electron in its orbit 
are similar to those which would act on a small particle carrying 
the same charge as the electron and moving at the surface of a 
uniform sphere of electricity of radius a, the total charge in 
Avhich is equal and opposite to that on the particle, the potential 
energy of the electron is 
v- or kx(Hx 10 8 ) 2 , 
2a 
if the radius of the sphere is identified Avith the conventional 
value for the radius of the atom, 10~ 8 cm. It may be objected 
that if there are N electrons in the atom the charge on the sphere 
will be — Ne and not — e: but it must be remembered that the 
other electrons exert forces Avhich tend to counterbalance that 
due to the charge on the sphere : it is probable that the resultant 
force is more nearly equal to that due to a total charge — e than 
that due to a total charge — Ne. 
