A Determination ofhefrom the Short Wave-Length Limit of the Continuous X-Ray Spectrum

Two precision determinations of the short wave-length limits of the continuous x-ray spectrum have been made, one in the region of 10,000 volts, the other in the region of 20,000 volts by the method of isochromats under very steady applied voltage. The two crystal spectrometer was used as a monochromator. The $K{\beta }_2$ line of molybdenum and the $L{\beta }_1$ line of tungsten were used for setting the monochromator. The experimental technique is fully described. A thin window tube with a nickel target coated with tungsten by evaporation was used as the x-ray source. The effect of the finite resolution of the two crystal spectrometer, its behavior as a function of wave-length, and the pitfalls resulting from the "tails" of the spectral window as defined by the selective bicrystalline reflection are carefully considered. The advantage of using a thin layer target of high atomic number on a back support of lower atomic number in order to minimize the danger from these pitfalls is explained. Arguments for the applicability of a correction to the measured voltage for the work function of the cathode are presented. All effects such as the finite resolution of the spectrometer tending to render the voltage threshold for a given wave-length setting less well defined are here called for brevity "smearing effects" and five different new methods of "desmearing" the isochromats or of locating the thresholds are considered. The presence of a hitherto unsuspected knee in the isochromat within a few volts of the quantum limit is shown to render inapplicable the only method so far in use for locating the threshold voltage, the "method of the projected tangent," which is also shown to contain other objectionable pitfalls. The experiment permits of determining either $\frac{h}{e}$ or $\frac{e}{h^{\frac{3}{4}}}$ according to whether we assume the ruled grating wave-lengths of x-rays to be correct or make no such assumption but include the data from selective x-ray crystal reflection, crystal density, molecular weight and the Faraday constant as part of the computation. By these respective methods we obtain $\frac{h}{e}=1.3762\mathrm{}\pm 0.0003\times {10}^{-17\mathrm{}}$; $\frac{e}{h^{\frac{3}{4}}}=2.0720\mathrm{}\pm 0.0004\times {10}^{10}$. These results agree with those of Kirkpatrick and Ross and those of Schaitberger on the same experiment with deviations which are small compared to the disagreement with two other entirely different experiments for determining functions of $e$ and $h$. This discrepancy on the Birge-Bond diagram already emphasized by Birge is carefully discussed and possible causes for it are considered. Two possible objections to the present experiment are raised and we believe successfully disposed of. The practical impossibility of blaming this discrepancy on the short wave-length limit experiment is, we believe, convincingly proven by our results.