Ehrenhaft’s Sub-Electrons.

(Bär. Annalen d. Phys. B. 67, 1922, No. 3, p. 157).

If usually for the elementary quantity of electricity (the charge of one electron) \(E\) one obtains the value \(2\)—\(6.5 \cdot 10^{-10}\) electrostatic units, then Ehrenhaft, on platinum particles, obtained \(E = 5.4 \cdot 10^{-12}\), and Przankevich even \(2 \cdot 10^{-13}\).

The determination of the relative magnitude of the electric charge on submicroscopic particles makes it possible, to a certain degree, to judge the quantization of the elementary charge of electricity.

Indeed, if particles with charges No. 3 are suspended, then

\[ nE = mg \]

and if \(E\) is the elementary charge of electricity, then \(n\) must be small whole numbers. This result is also given by the investigations of Ioffe, Meyer, and Gerlach.

Ehrenhaft and his school obtain considerable deviations. Why? First, with small particles Brownian motion can introduce an error. Therefore, for small particles one must use low magnification. Further errors are introduced by the use of the Stokes–Cunningham formula on the relation between the velocity of fall of a particle and the force:

\[ F = \frac{6\pi Ha v}{1 + A\frac{l}{a}}, \tag{1} \]

where \(a\) is the radius of the particle, \(H\) the coefficient of internal friction, \(v\) the velocity, \(l\) the mean free path of a gas molecule, \(A\) a coefficient depending on the kind of collisions of gas molecules with the particle. On the one hand, the particles may be non-spherical (as is required by the formula); on the other hand, the density of the particles may be unequal to the density of the original material.

From the fall in an electric field and without a field one can find the density \(\varepsilon\), if formula (1) is accepted. Observations show, however, that when the gas pressure is changed, \(A\) is not constant. Bär, taking these circumstances into account, makes measurements of \(E\), observing in a Millikan condenser and at low magnification particles of paraffin, selenium, and platinum.

The experimental material obtained leads him to the conclusion that there is no need to abandon the constancy of the elementary electric charge and Millikan’s number \(4.8 \cdot 10^{-10}\), and that the observed deviations, which were obtained by him as well, are explained by the above-mentioned causes.

In particular, with respect to the charges on \(Pt\)-particles, it should be acknowledged either that \(A\) is very small (down to 0.077), whereas from experimental determinations the coefficient \(A\) is of order 1, or that the density \(\varepsilon\) is small (down to 0.2, whereas the density of platinum is 21.4). Bär considers the second supposition more probable, which is due to the spongy structure of the particle (such sponginess is obtained in electrical sputtering).

When particles are formed by evaporation or mechanically, one should expect changes in the density of the particles due to adsorption (which must be especially pronounced for small particle sizes). In some cases an Olschicht (Silvey) or Oxydfilm (Derieux) is also possible.

And these experiments show, as was pointed out earlier as well, that the question requires still further investigations.

B. V. Ilyin.