A General Quantum Theory of the Wave-Length of Scattered X-rays

1924 ◽  
Vol 24 (2) ◽  
pp. 168-176 ◽  
Author(s):  
Arthur H. Compton

Energy may be removed from a beam of γ -rays traversing matter by two distinct mechanisms. A quantum of radiation may be scattered by an electron out of its initial direction with change of wave-length, or it may be absorbed completely by an atom and produce a photoelectron. The total absorption coefficient, μ, is defined by the equation d I/ dx = -μI, and is the sum of the coefficients σ and τ referring respectively to the scattering and to the photoelectric effect. For radiation of low frequency, such as X-rays, the photoelectric absorption is very much more important than the absorption due to scattering, and many experiments have shown that the photoelectric absorption per atom varies as the fourth power of the atomic number and approximately as the cube of the wave-length. For radiation of high frequency, such as the more penetrating γ -rays, the photoelectric effect is, even for the heavy elements, smaller than the scattering absorption; and, since the scattering from each electron is always assumed to be independent of the atom from which it is derived, it is most convenient to divide μ. defined above by the number of electrons per unit volume in the material and to obtain μ e the absorption coefficient per electron.


1984 ◽  
Vol 85 (2) ◽  
pp. 335-348 ◽  
Author(s):  
T. Ohkawa ◽  
H. Hashimoto
Keyword(s):  

1924 ◽  
Vol 23 (3) ◽  
pp. 313-317 ◽  
Author(s):  
G. E. M. Jauncey
Keyword(s):  

1924 ◽  
Vol 22 (3) ◽  
pp. 379-392 ◽  
Author(s):  
H. W. B. Skinner

1. Changes in the relative intensities of the lines in the fluorescentL-spectrum of Cerium excited by radiation of various wave-lengths have been observed.2. These results imply a change in the relative absorbing powers of the threeL-levels as the wave-length of the absorbed radiation diminishes from a value just below the absorption wave-length of theL-levels to a value considerably below. The absorbing power of theLI-level becomes increased relative to the absorbing powers of the otherL-levels as the wave-length diminishes. The results agree with those published by H. Robinson in a recent paper.3. These results imply a breakdown of the law that μ/λ3is a constant (where μ is the absorption coefficient of X-rays of wave-length λ) as applied to theindividual L-levels of an element.4. A comparison is made between the above results, and some results on the relative absorbing process of theL-levels obtained by Ellis and Skinner from β-ray spectra.


In the de Broglie theory of mechanics a moving particle behaves as a group of waves of wave-length = h √¯1 — v 2 / c 2 / m 0 v and phase velocity V = c 2 / v , where m 0 is the mass of the particle, v its speed and c the velocity of light. In the case of electrons of energy 10,000 to 40,000 volts, the corresponding wave­ lengths would be from 1·22 X 10 -9 to 0·66 X 10 -9 cms. These waves, there­ fore, should behave in many ways like hard X-rays, and, in particular, should show similar diffraction patterns when passed through crystals. Thus, accord­ing to the Bragg formula, if the rays are incident at an angle θ on a set of parallel planes, we should get reflection provided that 2 d sin θ = nλ,d being the spacing between the planes. To investigate these effects, a series of experiments, suggested and super­vised by Prof. G. P. Thomson, was begun in October, 1926. An account of these has already been published in ‘ Nature,’ but since then much more accurate work has been done. The experiments consisted in sending a beam of homogeneous cathode rays through a thin film at normal incidence and receiving them on a photographic plate. As shown below, the resultant pattern should be of the Hull-Debye-Scherrer type. Celluloid was chosen because it is comparatively easy to get films of the order of 500 Ă. U. thick. These were pre­pared by dissolving celluloid in amyl acetate. A little of the solution was dropped on water and the amyl allowed to evaporate. The celluloid which remained was removed on cardboard frames. It is essential that the films be thin enough to prevent blurring of the pattern by multiple scattering.


The agreement between the theories of the reflection of X-rays by solids and observations is discussed. Generally the observations so far obtained are not in close agreement with each other or with theory. The writers find that X-rays of wave-lengths 13·3 Å. (Cu Lα) and 44·7 Å. (C Kα) are reflected by glass, quartz and stainless steel at angles considerably greater than the calculated critical angles. The radiation from carbon has been focussed by a spherical mirror for an angle of incidence of 45°. The ratio of the intensity of the reflected to the incident beam, when X-rays from a carbon target are incident on a glass mirror, has been determined approximately by a photographic method and is found to agree with the Fresnel electromagnetic theory provided a higher absorption of the X-rays occurs than has been previously supposed. This evidence of reflection for angles of incidence greater than the critical angle, which is 6° for glass at a wave-length of λ = 44·7 Å., is confirmed by observations with a glass diffraction grating with which the λ = 44·7 Å. line has been observed for angles of incidence on a plane grating up to 19°. A new plane ruled grating spectrometer is described by means of which the C Kα line has been obtained with short exposures in all orders from the 18th negative to the 13th positive. Microphotometer curves of the wave-length distribution of the energy in the grating spectrum of carbon radiation are given, and these indicate that it consists almost entirely of the Kα line, λ = 44·7 Å. Using Rowland’s method of coincidences the wave-length λ C kα is found to be 44·7 5 Å. relative to λ Cu Lα = 13·32 Å.


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