Absolute Wave-Lengths of the Copper and ChromiumK-Series

Abstract

In the measurement of x-ray wave-lengths by ruled gratings two principal difficulties have been discussed which may account for the difference observed between the wave-lengths determined by this method and those determined by using crystal gratings. They are, the periodic error in the grating, and the geometrical divergence of the x-ray beam. It is now shown that the effect of the periodic error can be determined by a study of the intensities of the optical ghost lines. For a good quality optical grating it has been found that the error in x-ray wave-lengths due to the periodic error in the grating is thus of no importance. By using a suitable disposition of apparatus the effect of the geometrical divergence of the x-ray beam can be made as small as desired. Thus it is concluded that ruled gratings can be used for precise wave-length measurements of x-ray spectra.In the present experiment the two parallel plate method has been used for determining the angles of incidence and diffraction. Five glass gratings of different grating spaces and ruled on two ruling engines have been used. The results from the various gratings on the same wave-length have agreed satisfactorily. No consistent variations of any type were observed. The final results from 172 sets of plates are given in the following tables. From these results the true grating space of a calcite crystal is $d=3.0359\ifmmode\pm\else\textpm\fi{}0.0003$ A. Using this value of the grating constant, Planck's constant as determined by Duane, Palmer and Yeh is, $h=6.573\ifmmode\pm\else\textpm\fi{}0.007\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ erg\ifmmode\cdot\else\textperiodcentered\fi{}sec. $\frac{e}{m}$ can be determined from the dispersion of x-rays by using the absolute wave-length of an x-ray spectrum line. The mean of the values of the dispersion as given by Stauss and Larsson gives $\frac{e}{m}=1.769\ifmmode\times\else\texttimes\fi{}{10}^{7}$ e.m.u.${\mathrm{g}}^{\ensuremath{-}1}$. The values of these constants are independent of any imperfection in the crystal. If the crystal lattice is assumed to be perfect we then have Avogadro's number, $N=6.019\ifmmode\times\else\texttimes\fi{}{10}^{23}$ mol. per mole, and the charge on the electron $e=4.806\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ e.s.u. Using this value of $e$, and $d$ as above, we find Planck's constant $h=6.623\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ erg\ifmmode\cdot\else\textperiodcentered\fi{}sec.