Page:Design and Calibration of a New Apparatus to Measure the Specific Electronic Charge.pdf/5

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I. The Theory of the Experiment.

1.0 General Introduction.

For many years the specific electronic charge $(e/m)$ has been a subject of considerable interest to physicists. It remains today the most uncertain of the important physical constants, the best value being the least-squares value of DuMond & Cohen^[1] who give

$e/m=(1.758897\pm .000032)\times 10^{7}e.m.u./gr.$

as of 1950. The best direct measurement is the 1937 one of Dunnington^[2] who quotes

$e/m=(1.7597\pm .0004)\times 10^{7}e.m.u./gr.$

It is true that superior accuracy has been obtained by indirect measurements, for example the experiments of Thomas, Driscoll & Hipple^[3] who give

$e/m=(1.75890\pm .00005)\times 10^{7}e.m.u./gr.$

All such indirect experiments, however, measure $e/m$ for bound electrons and are subject to inaccuracies in associated physical constants from which $e/m$ must be derived. Then too, a derived value of any physical constant is not suitable for a least-squares adjustment of the atomic constants^[1]. Clearly therefore, a new and more accurate free electron, i.e. deflection, direct value for $e/m$ is highly desirable.

Now any deflection method for measuring $e/m_{o}$ depends upon measuring the velocity of an electron, $v$, which has fallen through a known potential difference, $V.$ Application of the relativistic energy equation

$eV=m_{o}c^{2}(1-v^{2}/c^{2})^{-{\frac {1}{2}}}-m_{o}c^{2}$

where $c$ is the velocity of light, will then yield $e/m_{o}$.

The present method is similar in principle to that of

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1. J.W.M. DuMond & E.R. Cohen, unpublished report of the N.R.C.
2. F.G. Dunnington, Phys. Rev. 52, 475, (1937)
3. H.A. Thomas, R.L. Driscoll, & J.A. Hipple, Phys. Rev. 78,787, (1950)