An Approximate Law Of Energy Distribution In The General X-ray Spectrum(en)(4s) [PDF]

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unpublished work by Goodwin and Wilson of the Massachusetts Institute of Technology. In figure 2 the solid line shows the experimentally determined variation with the pressure of the overvoltage of nickel. Similar curves were found for mercury and lead. The dotted line shows the variation as calculated by Equation 2, using the overvoltage at one atmosphere as a basis for computing the values for the other pressures. The difference between these two curves may be explained by an increase of stirring at the lower pressures, since many more bubbles are produced per mol of gas. It appears quite probable, then, that the factor that determines the overvoltage of an electrode at any one pressure is the size of the gaseous nuclei that can cling to it. A number of observers have called attention to the fact that electrodes with low overvoltages are those that have large adsorptive powers. This adsorptive power is undoubtedly related to the attraction of an electrode for a gaseous nucleus. AN APPROXIMATE LAW OF ENERGY DISTRIBUTION IN THE GENERAL X-RAY SPECTRUM BY DAVID L. WEBSTER DEPARTMENT OF PHYSICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY Communicated by E. H. Hall, April 9, 1919

spectra of X-rays as ordinarily determined there are factors of abin sorption the anticathode, the glass of the tube, the reflecting crystal and the ionized gas, and of efficiency of reflection that are all functions of the frequency. Fortunately, except at the discontinuities of any of these absorptions, the unknown factors vary continuously with frequency, so that the measured intensities in the spectrum represent the energy distribution qualitatively, but by no means quantitatively. The problem of the present paper is to combine other available data in such a way as to find an approximate law of energy distribution, not involving unknown absorption factors, and avoiding also any a priori assumptions about the emitting mechanism. The data are incomplete and this work is merely a first approximation. For data we have (a) some graphs of intensity against potential at constant frequency (where the unknown factors are all constant in each graph), and (b) the total energy measurements by Beatty,' who made the absorption negligible by using a thin window and no crystal. Some of the intensity-potential graphs were obtained in the course of experiments for another purpose with a rhodium target by the author,2 and with platinum by the author and Dr. H. Clark,3 and others were obtained by taking points at the same wave length from intensity-wave length graphs drawn for tungsten by A. W. Hull,4 Hull and Rice5 and Ulrey,6 and for molybdenum by Hull. In the experiments on rhodium and platinum, the spectrometer was kept at a fixed wave length and the potential was changed between readings. In the



This with

gave directly a series of intensity-potential graphs that are represented fairly good accuracy by the law I(V,v)




(v) {(V Hv) + Hvp(v) 1-

where I (V, v)dv is the intensity in the frequency range dv per electron striking the target from potential V, and H is the ratio of Planck's h to the charge of the electron, and k(v), p(v) and q(v) are functions of v. Since p and q-are pure numbers they are independent of the arbitrary intensity unit, and can be determined wherever the data are available, though not very accurately because the term containing them is rather small. In the few data available for rhodium, p is of the order of 0.06 to 0.08 and q about 12 to 16, making pq about 1. The work on tungsten and molybdenum gives only a few points on each intensity potential graph, and because of the smallness of the exponential term and its disappearance at potentials large enough for really accurate intensity measurements, it is impossible to get an accurate test of this law except with more points than one can get from these graphs. But the data obtainable show that the relation between I and V is not far from linear, and the only definite curvature seems to be something of the type indicated by the above equation. In platinum, we have data scattered over the range from 1.33 to 0.43 A, but most of them rather rough. But to an accuracy of 20 or 30%, they seem to indicate constant values for both p and q, with p = 1/5 and q = 13, so that pq = 5/2. Fortunately the smallness of the p and q terms makes their influence on the determination of k also small, although the existence of the terms themselves may be of considerable theoretical importance. For the present, therefore, we shall include these terms in the calculation, but neglect any changes of p and q with v. An important point to be deduced from the graphs of 'intensity' against v is the fact that they are smooth and regular, so that k must have no discontinuities or sharp curvature in its graph against v. As a trial value we shall therefore assume first that k(v) kvn, with k and n both constant. The total energy is then =



1 I (V, v)dv k In4-1

EJ 0




C P x


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