Vol. 8, 1922 
PHYSICS: B. DAVIS 
61 
IONIZATION AND RADIATION POTENTIALS AND THE SIZE 
OF THE ATOM 
By Bkrgkn Davis 
Phoenix Physicai, Laboratory, CoIvUmbia University 
Communicated by W. Duane, February 28, 1922 
Professor A. S. Eve has recently published an interesting note on a 
relation between the ionization potential and the size of the atom. (Na- 
ture, June 30, 1921). 
For some time I had been accumulating data for a similar comparison, 
but from a somewhat different point of view. Eve considers that the size 
of the atom is determined by the radius of the outer ring. The work 
(ionization potential) required to lift an electron from this ring by the 
Bohr model is proportional to 1/a. The product Ixa should be a constant. 
Trials of this relation are made for a number of elements using both the 
cube-roots of the atomic volumes and estimates of the diameters of atoms 
made by W. L- Bragg from crystal structure and measurements. (Phil. 
Mag., Aug., 1920). The results obtained by Eve showing the degree 
of constancy (and departures from constancy) are repeated here in columns 
6 and 7 of the table. 
The boundary of the atoms, however, should not correspond exactly 
with the outer ring, but should extend beyond it. If the electron ring 
were the limit in the solid state, it would require no work to remove an 
electron ftom an atom in this state. The photo-electric effect shows that 
work is required, that it is less than the ionizing potential, but is approx- 
imately the same as the radiation potential. I here consider that the limit 
of the atom is the ring or distance from the center that an electron needs 
to be lifted to produce the radiation potential. That is, an atom in the 
solid state of matter is ionized at a potential about equal to the radiation 
potentials in the gaseous state. The ionizing potential is given by 
/ = A/a, 
where ^4 is a constant and a is the radius of the electron ring or orbit. 
If b is the distance from the atomic center then an electron must be lifted 
to produce radiation, then the radiation potential is given by 
R = A/a- A/b, 
where A/b is the work required to remove an electron from position b 
entirely from the atom in the gaseous state. 
I-R = A/b, 
Th product (I — R)b or, for comparison with atomic volumes, (/ — 
R)^yA.V. should be a constant. The last two columns of the table show 
