Determination of Elementary Charge E from Measurements of Shot-Effect.

Probability fluctuations in thermionic emission (shot effect).—Schottky first pointed out that if the electrons evaporate independently of each other, probability fluctuations of current are to be expected. These fluctuations were observed and roughly measured by Hartmann. Measurements have now been made, using a much higher frequency (750×${10}^3$) and a reliable arrangement for measuring the small r.m.s. voltages (od order ${10}^{-4\mathrm{}}$) due to the effect. The method involves the measurement of the alternating current excited in a tuned circuit by the probability variations in the electron current through a vacuum tube (radiotron, UV 199), the Schottky equation for the mean square current being $\overline{J^2}=\frac{i_{0}e}{2RC}$ where $i_0$ is the thermionic current, $R$ and $C$ the resistance and capacity of the tuned circuit and $e$ the electronic charge. To measure the current, it is amplified by a known amount (using a special 4 stage amplifier) and is rectified so that its r.m.s. value may be determined with a d.c. meter. It is important that the rectifier be used only in the range in which it gives a current proportional to the square of the impressed voltage. The tuned circuit picks out a narrow band of frequencies present in the fluctuations, and since the amplification is not the same for frequencies slightly different from the resonance frequency, correction is made for this by a factor $F$, for which a mathematical expression is derived and values are obtained by integration or summation. Calibration of the amplifier is avoided by substituting, after each reading of the amplified and rectified shot-current, a measured pure sine voltage across the terminals of the tuned circuit, which is adjusted to give the same rectified current as the effect. Calling this $v_1$ the actual mean square shot voltage $\overline{v_0^{}{}_{}{}^2}=\frac{v_1^{}{}_{}{}^2}{F}$ and $\overline{J^2}=\frac{Cv_1^{}{}_{}{}^2}{\mathrm{LF}}$ where $L$ is the inductance of tuned circuit. It was found that with currents limited by space charge, the observed effect might be only 20 per cent of the theoretical; but with currents limited only by temperature, the agreement was within one per cent. The effect may therefore be used to study the effect of space charge on electronic evaporation.