Marcu 17, 1923] 
Letters to the Editor. 
[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
_ can he undertake to return, nor to correspond with 
the writers of, rejected manuscripts intended for 
this or any other part of NATURE. No notice is 
taken of anonymous communications. 
Origin of Radioactive Disintegration. 
In a letter to Nature of September 16, 1922 (vol. 
IIo, p. 379) R. N. Pease directs attention to the 
possibility that the radioactivity of the heaviest 
elements may be due to the disturbing effect of the 
electrons in the atom. This view may be traced 
back to the time of the discovery of radioactivity 
ef. J. J. Thomson, Phil. Mag. 7, 265, 1904, and Lord 
elvin, Phil. Mag. 8, 525, 1904). The problem, 
however, has been seriously complicated by the 
circumstance that, on the basis of ordinary mechanics 
and electrodynamics, the outstanding difficulty has 
not so much been to understand that radioactive 
disintegration can occur as to understand the simple 
law of radioactive decay. For the latter question, 
it seems that the development of the quantum 
theory has prepared the way to a deeper insight in 
‘the sense that the same law may be shown to apply 
to transition processes between stationary states of 
quantised systems. 
On the basis of the quantum postulates alone it 
is an open question whether the nuclear instability 
is a strictly spontaneous process solely dependent upon 
the state of the nucleus itself, or whether external 
influences also play an essential part. A tentative 
argument in favour of the latter view is perhaps 
afforded by the fact that the life-periods of the 
elements at the beginning of the disintegration 
series are very large. This fact suggests the idea 
that the nuclei may be intrinsically stable and the 
radioactivity of these elements induced by the 
action of an external field of force, the origin of which 
may be looked for in the surrounding electrons. 
The regular variation in the life-period of successive 
elements in the disintegration series seems to indicate 
that the disintegration, when once initiated, proceeds 
spontaneously until a stable element is reached. 
the other hand, the occurrence of radioactivity 
in the elements of low atomic numbers (rubidium 
and potassium) might be due to an enhanced efficiency 
of the perturbations due to some sort of resonance 
in the interaction between the nuclear and the 
electronic motion. 
The force exerted by the electrons at a point in, 
or close to, the atomic nucleus will increase rapidly 
with increasing atomic number on account of the 
decreasing dimensions of the electronic orbits belong- 
ing to a permanent group. It will, however, in 
addition, depend intimately on the nature of the 
electronic configuration. If this configuration at 
every moment exhibits central symmetry, the forces 
from the electrons will to a large extent neutralise 
each other. The case is essentially different in the 
recent theory of Bohr, according to which the electrons 
belonging to a perpen group and moving in 
eccentric orbits will approach the nucleus in succession. 
The shortest distance from the nucleus will be 
attained by the electrons moving in orbits with 
azimuthal quantum number equal to 1, and will 
then be given by 


d 
d= ant UN*) - ‘ At) 
approximately. Here N is atomic number, d, the 
NO. 2785, VOL. 111] 
NATURE 
357 
radius of the orbit in the normal hydrogen atom, 
2 
and a= = 72x 1o~* is the constant occurring in 
the theory of the fine structure of hydrogen lines. 
For the uranium atom the above formula gives 
d=15x10-" cm. On the other hand, the inferior 
limit for the diameter of the uranium nucleus, 
derived from the energy of the a-particles from 
uranium on assuming this energy to be due to the 
electrostatic repulsion of the nucleus, comes out of 
the same order of magnitude as the above value of 
d. Atthe moment of closest approach these electrons 
will thus exert forces upon the individual particles 
of the nucleus which may be of the same order of 
magnitude as the electrostatic attraction or repulsion 
between the particles themselves. For still larger 
atomic numbers, d will rapidly decrease while the 
nuclear dimensions will be expected to increase. It 
is therefore seen that for some atomic number not 
far ahead of that of uranium the electrons in question 
would have to pass quite close to the nucleus, and 
thus exert large perturbing forces on the nuclear 
particles. For still larger atomic numbers a motion 
for which the nuclear field is treated as due to a point 
charge would become impossible as the electrons 
in question would have to collide with the nucleus. 
On the whole, it does not appear excluded that the 
presence of radioactivity among the heaviest known 
elements as well as the apparent absence of elements 
of higher atomic numbers may be connected with 
some sort of interaction between the nuclear and the 
external electrons. 
The efficiency of this interaction will be expected 
to depend intimately on certain resonance conditions, 
as is the case for ordinary mechanical systems. 
The frequencies of the motion of the nucleus must 
in general be expected to be of an altogether higher 
order of magnitude than the frequencies in the 
motion of the electrons; but there remains the 
possibility that the nucleus as a whole will rotate 
and this rotational frequency may in some cases be 
comparable with some electronic frequency. The 
case when the nucleus rotates with an angular 
momentum equal to h/27 is of special interest, as 
this value appears to be associated with the most 
stable state of quantised systems. The rotational 
frequency w may then be estimated from the ex- 
pression 

ee I 
w= Ma” : : «+ (2) 
where M and a are the nuclear mass and radius of 
gyration about the axis of rotation. Assuming the 
nuclear dimensions to increase from about 8 x to- cm. 
in helium (Rutherford and Chadwick) to about 
6x1o-™ cm. in uranium (cf. above) this frequency is 
found to decrease from about 10” sec.-' in helium to 
about ro sec.-* in uranium, The latter value is 
essentially larger than the value to be expected for 
valency electrons. This is also necessary in order 
to understand the fact that the radioactive properties 
hitherto on record are independent of chemical 
combinations. It will further be found compatible 
with the assumptions regarding the nuclear dimensions 
to assume the frequencies of nuclear rotation in 
potassium and rubidium to be of the same order 
of magnitude as the electronic frequencies of the 
K and the L electrons respectively in these elements. 
The above considerations, however, are to be 
regarded merely as tentative suggestions, and our 
knowledge of nuclear structure is probably far too 
scanty to permit of any definite conclusions concern- 
ing these questions at present. S. RossELAND, 
Copenhagen, Institut for teoretisk Fysik, 
February 12. 
