The Size of Electron

In the same year when Einstein published his general relativity, Compton published his paper on the size of electron in Physics Review. It was speculated that the size of electron is close to the size of atoms, which were still called "elements. " Althouth it has become evident that the bounded electrons in atoms should be decribed by wave function rather than classical particles, Compton's estimate of the size of electron did provide some new insight into the atoms whose internal structures were still unknown. This is equivalent to say the size of the earth is close to the size of the solar system! It could be argued that Compton's estimate challenged the original solar-system model for atoms proposed by Rutherford.

Arthur H. Compton

Phys. Rev. 14, 20 – Published 1 July 1919

Synopsis.—Attention is called to two outstanding differences between experiment and the theory of scattering of high frequency radiation based upon the hypothesis of a sensibly point charge electron. In the first place, according to this theory the mass scattering coefficient should never fall below about.2, whereas the observed scattering coefficient for very hard X-rays and γ-rays falls as low as one fourth of this value. In the second place, if the electron is small compared with the wave-length of the incident rays, when a beam of γ-rays is passed through a thin plate of matter the intensity of the scattered rays on the two sides of the plate should be the same, whereas it is well known that the scattered radiation on the emergent side of the plate is more intense than that on the incident side.

It is pointed out that the hypothesis that the electron has a diameter comparable with the wave-length of the hard γ-rays will account qualitatively for these differences, in virtue of the phase difference between rays scattered by different parts of the electron. The scattering coefficient for different wave-lengths is calculated on the basis of three types of electron: (1) A rigid spherical shell of electricity, incapable of rotation; (2) a flexible spherical shell of electricity; (3) a thin flexible ring of electricity. All three types are found to account satisfactorily for the meager available data on the magnitude of the scattering coefficient for various wave-lengths. The rigid spherical electron is incapable of accounting for the difference between the emergent and the incident scattered radiation, while the flexible ring electron accounts more accurately for this difference than does the flexible spherical shell electron.

It is concluded that the diameter of the electron is comparable in magnitude with the wave-length of the shortest γ-rays. Using the best available values for the wave-length and the scattering by matter of hard X-rays and γ-rays, the radius of the electron is estimated as about 2 × 10−10 cm. Evidence is also found that the radius of the electron is the same in the different elements. In order to explain the fact that the incident scattered radiation is less intense than the emergent radiation, the electron must be subject to rotations as well as translations.

• Received 17 March 1919

DOI:https://doi.org/10.1103/PhysRev.14.20