The Structure of Radioactive Atoms and the Origin of α-Rays1 (E. Rutherford. Phil. Mag., 7, 4, 580). Comparing the results of experiments on the scattering of α-particles when heavy and light atoms are bombarded by them and

the results of research on the velocity of emission of α-particles in radioactive decay, Rutherford arrives at the following conception of the structure of the nucleus of heavy elements. The center of the nucleus is occupied by an extremely compact, positively charged mass. The radius of the center is not more than \(1\cdot 10^{-12}\) cm. Around the center, in the region up to \(r=1.5\cdot 10^{-12}\) cm, there revolve electrons and charged satellites of small mass. Further, up to \(r=6\cdot 10^{-12}\) cm, there extends a comparatively large region occupied by neutral satellites of the central nucleus. The enormous electric fields of the latter cause a strong polarization of the neutral satellites; as a result, an attraction arises between the central nucleus and a satellite, holding the satellite near the nucleus. In radioactive decay α-particles with atomic weight 4 are emitted. The possibility is not excluded, however, of the existence of satellites with atomic weights 3, 2, and 1. The electrons neutralizing the charge of the satellite nucleus revolve in orbits very close to the nucleus, which become possible only thanks to the presence of the exceptionally strong field of the central nucleus. They are entirely different from the ordinary orbits of electrons in the neutral helium atom. The orbits of the satellites of the central nucleus are quantized. Large velocities of the satellites and higher quantum numbers belong to orbits lying closer to the central nucleus. Radioactive decay proceeds according to the following scheme. One of the neutral satellites, for an unknown reason, loses its equilibrium and flies off its orbit. It begins to move away from the nucleus, overcoming the force of attraction, which depends on the polarization of the satellite; this work is performed at the expense of the kinetic energy possessed by the satellite as it revolved in its orbit. When the neutral satellite reaches the region where the field strength of the central nucleus falls below a certain limiting value, the electronic orbits of the satellite become impossible, and the satellite disintegrates. The energy necessary for removing the electrons from the satellite nucleus is, at least in part, also taken from the kinetic energy of the satellite. From the moment of disintegration, instead of a neutral satellite there appears a positively charged α-particle, upon which the repulsive force of the nucleus begins to act; the velocity of the α-particle increases. Thus, denoting the kinetic energy of the emitted particle by the letter \(E\), we shall have:

\[ E=E_1-E_2-E_3+E_4, \tag{1} \]

where \(E_1\) is the kinetic energy of the satellite in its orbit; \(E_2\) is the energy which the satellite expends in passing from the orbit to the distance at which its disintegration occurs; \(E_3\) is the energy lost by the satellite in disintegration; \(E_4\) is the energy acquired by the α-particle under the action of the repulsive forces of the central nucleus. The magnitude \(E\) can be calculated from observations of the range of α-particles, and therefore expression (1) may serve to test the theory and to determine the values of the quantities entering into \(E_1\), \(E_2\), \(E_3\), and \(E_4\). The force, due to polarization, which holds the neutral satellite near the nucleus is given by the equation:

\[ F=\frac{Z^2 e^2}{r^3}\cdot\frac{(2r^2-a^2)}{(r^2-a^2)}, \]

where \(r\) is the radius of the circular orbit of the satellite, \(a\) is the radius of the satellite, \(Ze\) is the charge of the central nucleus. At equilibrium this force must be equal to the centripetal force \(\frac{mv^{2}}{r}\), where \(m\) is the mass of the satellite, \(v\) its velocity. The transition to quanta is effected by introducing the quantum relation for possible orbits: \(mvr = nh\) (\(h\) is Planck’s constant divided by \(2\pi\)). In this way the quantities \(E_1, E_2\) can be expressed in terms of \(r\) and \(a\); \(E_1, E_3\) are combined; their difference, a certain quantity \(A\), is constant for the given atomic number. Finally the energy \(E\) can be represented in the form of the relation:

\[ E = A + Bn^{4}(1 - bn^{2}), \tag{2} \]

where

\[ B = \frac{m^{4}h^{4}}{8a^{3}m^{2}Z^{2}e^{2}}; \tag{3} \]

\[ b = \frac{h^{2}}{maZ^{2}e^{2}}. \tag{4} \]

If \(A\), \(B\), and \(b\) are determined by fitting for the element of the given atomic number \(Z_0\), then for another atomic number \(Z\) the energy \(E\) will be:

\[ E = A\sqrt{\frac{Z}{Z_0}} + \frac{BZ_0^{2}}{Z^{2}}\, n^{4}\left(1 - \frac{Z_0^{2}}{Z^{2}}\, b_0 n^{2}\right) \tag{5} \]

\(E\) is also known from experiment for the element \(Z\), while in the right-hand side of equation (5) we can vary only \(n\). If \(n\) varied continuously, it would always be possible to find such a value of it as would satisfy equation (5) exactly. In fact, \(n\) can be assigned only integer and half-integer values, and therefore relation (5) can serve to verify the theory. How well the theoretical and experimental values of \(E\) agree may be seen from the following table:

TABLE 1.

Equally good agreement is also obtained for other elements. The mean difference between the observed and calculated values of \(E\) is \(0.4\%\), whereas a change of \(n\) by \(1/2\) causes a change of \(E\) by \(3\%\). Thus the values of \(n\) satisfying relation (5) are established quite definitely, and the agreement of the theory with experiment should be regarded as satisfactory.

From the values of the constants \(A\), \(B\), and \(b\) one can determine the dimensions of the satellites and their orbits. For \(Z = 84\) and \(n = 28\), the radius of the satellite orbit is \(r = 2.24 \cdot 10^{-12}\ \mathrm{cm}\). The distance from the center at which the satellite decays, for \(Z = 92\), proves to be \(6.8 \cdot 10^{-12}\ \mathrm{cm}\). The radius of the satellites \(a\) is equal to \(6 \cdot 10^{-13}\ \mathrm{cm}\). The size obtained for the satellite is in agreement with the data of Chadwick and Bieler concerning the distance from the center of the \(\alpha\)-particle at which the nuclear field becomes anomalous. The electronic orbits of the satellite thus prove to be extremely small, close to the nucleus.

Besides particles of short range, radioactive elements emit a small number of particles of long range, whose origin has not yet been elucidated. From the standpoint of the theory set forth, the particles of long range must be satellites that have flown off from deeper orbits. The corresponding values of \(n\) will be, for particles with a range of \(11.3\ \mathrm{cm}\), \(32.5\); for particles with a range of \(9.3\ \mathrm{cm}\), \(31\). It should be noted, however, that the calculated and observed values of \(E\) agree far from exactly. This discrepancy may in part be attributed to the inaccuracy of the experimental data, due to the small number of long-range particles and to the difficulty of experiments with them.

According to Rutherford, \(\beta\)-decay and the origin of \(\gamma\)-rays take place as follows. The electrons that separate off in the decay of the satellite fly toward the nucleus and begin to revolve around it in small orbits with extremely high velocities, approaching the velocity of light. If one of them loses stability, an electron is ejected—\(\beta\)-decay. The ejection of both \(\alpha\)- and \(\beta\)-particles can cause a rearrangement of neutral satellites, passing from one of the possible quantum orbits to another. The difference in energy between the one orbit and the other is emitted in the form of \(\gamma\)-rays. The number of occupied orbits is not large, while the number of possible transitions is very considerable. One has to select the possible transitions by using optical analogies. The correspondence between the calculated transition energy and the frequency of the observed \(\gamma\)-rays is obtained quite satisfactorily.

V. Levshin.

1. The present abstract chiefly gives an account of the verification of Rutherford’s theory. For a more detailed exposition of the foundations of the theory, see Rutherford’s article published in UFN, 8, 35, 1928. ↩