A Precision Measurement at 24 500 Volts of the Conversion Constant λν

Abstract

A precision determination of the wavelength in x-units (Siegbahn scale) at the quantum limit of the continuous spectrum from a tungsten target sealed-off x-ray tube operating under an accurately stabilized and measured applied voltage, ${V}_{H}=24498.7\ifmmode\pm\else\textpm\fi{}1.1$ absolute volts (emu) is described. This experiment, often loosely described as a measurement of $\frac{h}{e}$, is, in the present state of our knowledge of the general physical constants, more properly to be referred to as a determination of the conversion constant ${V}_{A}{\ensuremath{\lambda}}_{s}$ between x-ray wavelengths and quantum energy in electron volts. If ${V}_{A}={V}_{H}+{V}_{w}$ is the sum of the absolute applied voltage ${V}_{H}$ and the work function ${V}_{w}$ of the tungsten cathode emitter and if ${\ensuremath{\lambda}}_{s}$ is the quantum limit wave-length on the Siegbahn scale expressed in kilo x-units (kx-units), then ${V}_{A}{\ensuremath{\lambda}}_{s}=(\frac{h}{e}){c}^{2}{(\frac{{\ensuremath{\lambda}}_{g}}{{\ensuremath{\lambda}}_{s}})}^{\ensuremath{-}1}{10}^{8}$, wherein $h$ is Planck's constant in erg sec, $e$ is the electronic charge in absolute cgs electrostatic units, $c$ is the velocity of light in cm ${\mathrm{sec}}^{\ensuremath{-}1}$, and $\frac{{\ensuremath{\lambda}}_{g}}{{\ensuremath{\lambda}}_{s}}$ is the conversion factor from wavelengths measured on the Siegbahn nominal scale in x-units to absolute wavelengths in milliangstrom units (${10}^{\ensuremath{-}11}$ cm). Using the method of isochromats, the value obtained in this experiment, with the 2-meter focusing curved quartz crystal spectrometer for the monochromator was ${V}_{A}{\ensuremath{\lambda}}_{s}=12370.02\ifmmode\pm\else\textpm\fi{}0.63$ emu\ifmmode\cdot\else\textperiodcentered\fi{}kx-units, the error \ifmmode\pm\else\textpm\fi{}0.63, a relative error of 51 parts per million, being our estimated standard deviation. A comparison with other determinations of this type is given. This value has been used as one of some thirteen precision data of eight different types in DuMond and Cohen's recent least-squares adjustment (November, 1952) to determine the "best" values of five fundamental constants: $\ensuremath{\alpha}$, the fine structure constant; $c$, the velocity of light; $e$, the electronic charge; $N$, Avogadro's number; and $\ensuremath{\lambda}=(\frac{{\ensuremath{\lambda}}_{g}}{{\ensuremath{\lambda}}_{s}})$, the above mentioned wavelength conversion factor; and to obtain from these a large number of other useful constants.

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