Absorption Cross Section of Molecules with Respect to Slow Electrons
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Absorption Cross Section of Molecules with Respect to Slow Electrons.
1) H. F. Mayer. Über das Verhalten von Molekülen gegenüber freien langsamen Elektronen. Ann. d. Phys. 64, p. 45, 1921.
2) C. Ramsauer. Über den Wirkungsquerschnitt der Gasmoleküle gegenüber langsamen Elektronen. Ann. d. Phys. 64, p. 513, 1921.
P. Lenard showed in 1903 that the absorption of free electrons in matter proceeds according to the ordinary absorption, exponential law:
\[ J=J_{0}e^{-apx}\ . . . . . . . . . . . . . . . . . (1) \]
where \(J_{0}\) is the initial intensity of the electron beam, \(J\) is the intensity of the beam after passing through a layer of gas of thickness \(x\) and at pressure \(p\), and \(a\) is the specific absorptive capacity, evidently proportional to the cross section of the electron beam absorbed by one molecule.
Lenard found that the quantity \(a\) increases as the velocity of the electrons decreases, asymptotically approaching a constant value beginning with velocities corresponding approximately to 10 volts. The phenomenon of the absorption of electrons in gases was for many years studied in detail by Lenard’s pupils in all directions.
Both papers reviewed here, which came from Lenard’s laboratory, are devoted to the question of the dependence of the quantity \(a\) on the gas pressure and on the velocity of the electrons for various substances. The methods of the two authors are entirely different. Mayer, in order to obtain slow electrons, uses a cathode with a heated tungsten filament and, by applying additional opposing electric fields, selects cathode rays sufficiently homogeneous with respect to velocity. Ramsauer uses photoelectrons, obtaining greater homogeneity of the electrons, but losing in the possibility of a broad variation of velocities.
When a parallel beam of electrons passes through a thickness of gases, the following cases are possible:
1) The electron undergoes no change whatever with respect to the direction and velocity of its motion.
2) The direction and velocity of motion of the electrons are changed somewhat, the velocity remaining of the order of the electronic one, changing relative to the mean within very narrow limits (diffusion).
3) The velocities and directions of the electrons after passing through the substance are distributed according to the ordinary Maxwell law; the absolute values of the velocities become of the order of molecular ones (absorption).
4) The velocities and directions are distributed according to the same Maxwell law; however, the maximum velocity remains of the order of the electronic one (reflection).
Ramsauer’s method was developed for the purpose of studying the total perturbation in the motion of electrons, consisting of diffusion, absorption, and reflection; in Mayer’s work it was possible to determine only the number of absorbed electrons. However, in the range of velocities in which both authors worked (1–10 volts), the number of absorbed electrons is so large in comparison with the number scattered or reflected that the quantities determined by both authors for the same substances practically coincide. In the table we give the results of Ramsauer’s measurements.
Table 1.
| Substance | \(v\) | \(q\) | \(r\) |
|---|---|---|---|
| Air | 0.80 | \(8.9 \cdot 10^{-16}\) | 1.4 |
| Hydrogen | 0.85 | \(12.6 \cdot 10^{-16}\) | 3.4 |
| Nitrogen | 0.75 | \(9.2 \cdot 10^{-16}\) | 1.4 |
| Helium | 0.75 | \(5.5 \cdot 10^{-16}\) | 2.3 |
| Argon | 0.75 | \(0.75 \cdot 10^{-16}\) | 0.14 |
| Argon | 1.10 | \(1.00 \cdot 10^{-16}\) | 0.30 |
In the table \(v\) is the velocity of the electrons in volts, \(q\) is the cross-section of the flux of electrons absorbed by one molecule, where \(q\) is calculated on the basis of \(a\) (formula (1)), determined experimentally; \(r\) is the ratio of \(q\) to the cross-section of the molecule, calculated from the data of the kinetic theory of gases. The quantity \(q\) is entirely independent of the gas pressure and practically does not depend on the velocity of the electrons for small velocities. The only exception is argon, for which \(q\) increases strongly with even a small change in velocity. Exactly the same, but more complete, results were obtained by Mayer; they are shown in the drawing. Along the abscissa axis are plotted quantities proportional to the velocities in \(\sqrt{\mathrm{volt}}\), and along the ordinate axis the values of \(a\); the curves have been drawn exactly through the numerous points determined experimentally. We see that for all gases, with the exception of argon, the curves asymptotically
approach parallelism with the axis of abscissae, i.e., independence from velocity. For argon there exists, as is seen from the drawing, a sharp “selective” absorption with a maximum near 12 volts. It should be noted that the electron beam in Mayer’s experiments was not sufficiently homogeneous; the author estimates its effective “width” at 0.5 V. It must be thought that with electrons of a more homogeneous curve for argon would have turned out even sharper. The authors do not draw final theoretical conclusions from the results they have found, proposing further elaboration of the phenomenon, called by them “selective absorption” of electrons. Let us note the extremely small value of \(q\) for argon at the base of the absorption band. The argon molecule is, as it were, “transparent” to electrons, in contrast to the molecules of the other gases studied, for which the “absorbing cross section” is in all cases larger than the “kinetic cross section.” The study of \(q\) for various substances represents an extremely promising method for determining the spatial configuration of molecular electro-magnetic fields.
S. Vavilov.