The Measurement of X-Ray Wavelengths by Large Ruled Gratings

A plane ruled grating was placed between the crystals of a precision double crystal spectrometer for the determination of the diffraction angles and the absolute wavelengths of x-ray lines. This arrangement has two important advantages: (1) A large grating surface is employed and (2) the ionization chamber method for recording intensities permits an accurate location of the peak of the diffracted lines. The gratings were 75 mm long and were ruled with 100 and 300 lines per mm, respectively. The results on the copper $K\alpha$ line (1.54A) are in good agreement with previous ruled grating measurements. The differences between the ruled grating and crystal wavelengths as obtained by Backlin, Söderman and the writer have been recalculated using as the "true" value of the calcite grating constant $d=3.02810A$ and the most recent determinations of the calcite diffraction angles. There is excellent agreement among the various observations and the difference between the grating and crystal values is independent of wavelength. The results of two independent methods of measuring x-ray wavelengths are included and these agree with the ruled grating values. Calculations of the "true" grating constant of calcite $d$, Avogadro's number $N$, the charge on the electron $e$, and Planck's constant $h$ were made. Some of the difficulties encountered if these values of $e$ and $h$ are used are pointed out.