Long-Wavelength X-Rays

M. E. Holweck. Recherches expérimentales sur les rayons X de grande longueur d’onde.

Annales de Physique XVII, p. 5, (1922).

The braking of a body under the action of electrons falling upon it and moving with velocity \(v\), in addition to the characteristic radiation, gives another kind of white light, decomposable and of continuous spectrum.

The distribution of energy among the wavelengths of this spectrum follows a law analogous to the law of radiation of a black body, with the difference that this spectrum is sharply bounded on the side of short waves. Einstein, for this minimum wavelength \(\lambda_0\), gives the formula:

\[ h\nu=\frac{1}{2}mv^2=eV, \]

where \(\nu=\dfrac{c}{\lambda_0}\), which is well confirmed experimentally also in the region of X-radiation of the tube by Coolidge’s work and by Blake and Duane’s work. The maximum of energy in this spectrum falls in the region near \(\lambda_0\). For the absorption coefficient of the residual rays of the spectrum, after preliminary absorption of 90% of its energy, and for rays of the same wavelengths separated by dispersion, results of one and the same order of magnitude were obtained. The author transfers the method of residual rays, whose validity has been established for ordinary X-rays, to the rays of that region of the spectrum which he is investigating.

The apparatus—the vacuum tube—was made of brass and glass; exhaustion was carried out by a Gaede molecular pump; a discharge tube connected to the apparatus served as an indicator of the degree of rarefaction; it gave no glow when fed by an induction coil with a spark of 15 cm, so that it could be assumed that the pressure in the apparatus was below \(10^{-5}\) cm Hg. A tungsten hairpin, 0.02–0.03 cm in diameter—the cathode—was heated by two springy current-carrying rods, which made it possible to bring to the cathode an anode to fractions of a millimeter from the point of contact. The anode had various forms. A metal diaphragm with a row of holes 0.08 cm in diameter, covered with a thin sheet of collodion (weighing 1 cm\(^2\), \(2 \cdot 10^{-5}\) g), separated the vacuum tube from the ionization chamber, or, as in some experiments, from the electroscope. The collodion sheet placed on the diaphragm withstood a pressure difference of 5 cm Hg and was opaque to cathode rays.

The absorption of the examined rays by gases was studied by the author on the basis of the following considerations: let \(I_0\) be the intensity of the radiation entering the ionization chamber—

measure; at depth \(x\) the intensity will be \(A_x=A_0e^{-\mu\rho x}\), where \(\mu\) is the total coefficient of absorption of the rays at normal pressure, \(\rho\) is the actual pressure in fractions of normal. The ionization current in the layer at depth \(x\) and \(x+dx\) will be: \(J=kA_x\mu\rho\,dx=k\mu\rho A_0e^{-\mu\rho x}dx\), where \(k\) is a constant coefficient. The ionization current in a condenser of depth \(a\) will be:

\[ J=\int_0^a k\mu\rho A_0e^{-\mu\rho x}\,dx=kA_0\left(1-e^{-\mu\rho a}\right); \]

since the limiting ionization current \(J_\infty\), corresponding to complete absorption, will be \(kA_0\), then \(J=J_\infty(1-e^{-\mu\rho a})\). Hence it is clear that, in order to determine \(\mu\), it is possible to vary either \(a\) or \(\rho\). The values of \(\mu\) obtained for \(O\) by both methods agree very well.

A study of the dependence of \(\frac{\mu}{\rho}\) on wavelength for nitrogen led to the following results: in the region \(40\,\text{\AA}<\lambda_0<100\,\text{\AA}\) (rays from \(300\)–\(123\ \mathrm{V}\)) \(\frac{\mu}{\rho}\) follows the law: \(\frac{\mu}{\rho}=0.7\lambda^{2.72}\); for rays from \(300\)–\(1200\ \mathrm{V}\), \(\frac{\mu}{\rho}\) remains constant. This region is ascribed by the author to the characteristic radiation of the \(K\) series of carbon in Celluloid. \(\frac{\mu}{\rho}\) for \(O\) and \(H\) as a function of \(\lambda\) can be expressed thus: \(\left(\frac{\mu}{\rho}\right)_O=0.9\lambda^{2.5}\) and \(\left(\frac{\mu}{\rho}\right)_H=4.2\lambda^{2.5}\), from eight observations for \(O\) in the region \(40\)–\(100\,\text{\AA}\) and from two observations for \(H\). Thus it may be said that the rays studied are absorbed according to a law analogous to that for rays with wavelengths 100 times greater. De Broglie theoretically arrived at the same result. The fact that the exponent of \(\lambda\) in the formulas for \(\frac{\mu}{\rho}\) is not 3 but 2.5 is explained by the author by the imperfection of the residual-ray method, and he concludes that the physical properties of the rays he investigated differ in no way from the properties of ordinary X-rays.

A study of \(\frac{\mu}{\rho}\) for Celluloid leads to the establishment of proportionality of the changes in \(\frac{\mu}{\rho}\) to \(\lambda^{2.5}\) for rays with wavelengths \(40\,\text{\AA}<\lambda<80\,\text{\AA}\). Beginning with \(80\,\text{\AA}\), \(\frac{\mu}{\rho}\) increases ever more slowly, passes through a maximum at \(\lambda=320\,\text{\AA}\), and then decreases, to become constant for rays from \(300\)–\(1200\ \mathrm{V}\), probably owing to the selective absorption of the carbon \(K\) series.

The principal results of the work are as follows: X-radiation has been extended to the middle of the ultraviolet region obtained by Millican (\(510\)–\(160\,\text{\AA}\), Millican, The Astrophysical Journal, vol. LII, no. 1, July 1920; Physical Review, vol. XII, no. 2, 1918); the laws of absorption of \(H\), \(O\), \(N\) rays with \(40\,\text{\AA}<\lambda<100\,\text{\AA}\) have been determined; the law of absorption in Celluloid for rays \(10\,\text{\AA}<\lambda<1000\,\text{\AA}\) has been determined; a maximum of absorption in this region has been established.

Of the numerous projected works in the field of X-rays with long wavelengths—works which the author lists at the end of the article—some have already been completed during printing: the absorption curve in \(N\) has been extended to \(\lambda=140\,\text{\AA}\); it has been established that the absorption of the investigated rays has no molecular character; the method used has been checked for rays whose wavelength could be determined from the phenomenon of diffraction; it has been established that the maximum of the radiation energy falls in the region near \(\lambda\), and thereby the regularity of the application of the residual-ray method has been confirmed. Finally, it should be noted that experiments with the diffraction of the rays obtained by the author are, according to his conclusion, on the way to realization.

Vl. Karapetian.