GUEST AUTHOR J. Arthur Campbell Harvey Mudd College
Clarernont, California
Textbook Errors, 33
The Paddle-Wheel Crookes Tube
M a n y chemistry teachers commonly introduce the subject of atomic structure through a study of Crookes tubes.' One ofthese tubes has a small paddle-wheel which can be placed in the radiation, and the radiation then deflected one way or the other with an external magnet. The paddle-wheel rotates and its direction of rotation can be changed by deflecting the beam. Professor Thomas Brown of the Department of Physics of Harvey Mudd College pointed out to the CHEM Study Writers Group in the summer of 1960 that this paddle-wheel experiment is not evidence for the mass of the electron, and that momentum transfer has little to do with the motion of the paddle-wheel. The effect is actually the same as that in a radiometer rotated by light. He referred us to the following quotation from "Conduction of Electricity Through Gases" (J. J. Thomson, Cambridge University Press, 1903): Mechanical effects pmdueed by the rays. A secondary result of the thermal effects produced by the rays are the very interesting mechanical effects which have been especially studied by Crookes and Puluz. A typical example of these is afforded by the wellknown experiment due to Crookes represented in Figure 163 (Crookes tuhe), where the axle of a very light mill with a series of vanes is mounted on glass rails, in a vacuum tube; when the discharge passes through the tuhe the cathode rays strike against the upper vanes and the wheel rotates and travels from the negative to the positive end of the tube. A simple calculation will show that we cannot ascribe the rotation to the momentum communicated to the vanes by the impact of the corpuscles against them; for, take the case when the rays are m powerful that they carry the very large current of amperes, and that they move with the very high velocity of 10" cm/see. If N is the number of corpuscles striking a surface in unit time, m the mass of the corpuscles; then supposing the corpuscles to rebound from the surface with a velocity equal to
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Journal of Chemical Educofion
that with which they impinge against it, the momentum communicated to the surface in unit time is 2Nm10LD. If e is the charge carried by a corpuscle, then Ne is the current carried by the rays, in our case lo-' in absolute measure. Hence, the momentum communiertted to the surface per second is equal to 2 m/e 10' dynes or, as m/e = lo-', to 2 X lo-' dynes. This is equivalent to s. difference of pressure, on the two sides of a vane 1 cmZinares of one-five-hundred-millionthpart of an atmosphere; an effect altogether too small to explain the movement of a, body such as that represented in Figure 163 (Crookes tube). This movement is probably due to an effect similar to that observed in a radiometer, as the impact of the cathode rays will make one side of the vanes much hotter than the other. Starkel has shown that when the vanes are arranged 80 that the radiometer effectis eliminated, the mechanical effect is exceedingly small-in his experiments, where the current carried by the cathode rays was lo-' amperes and the potential difference 10,000 volt-certainly less than lo-' dynes.
The effect in the Crookes paddle-wheel tube is therefore the same as in the light radiometer and should be interpreted in the same way. Excellent discussions of this latter effect may be found in most common textbooks on the kinetic theory of gases. A complete discussion is given in "Kinetic Theory of Gases," (E. H. Kennard, McGraw-Hill Book Company, Inc., 1938). Briefly, the radiometer effect is due to the tendency of the gas to creep over a surface from a cold to a hot region. In a simple vane radiometer, the gas will creep around the edges toward the center of the heated or bombarded side. This effect tends to increase the gas concentration on the heated side somewhat and result in a slight excess pressure on this side, thus repelling the radiometer vane. This tends to produce a revolution away from the bombarded side, so that the bombarded side recedes from the bombarding particles. Thus it seems clear that the paddle-wheel Crookes tube should not be interpreted in terms of straight momentum transfer but in terms of the radiometer effect as has been thoroughly explored early in the developments of this instrument, as indicated above. However, since almost no chemistry courses discuss the radiometer effect, i t is apparent that the paddle-wheel Crookes tube should now be largely removed from any such course.
' STARKE,H., Ann., 308,101 (1900).
