=

A theory by which the relative intensities of spectral lines may be calculated has been suggested by Sommerfeld (Atombau und Spektrallinien, Chapter 6). He applied the quantum laws to orbits that do not lie in the same plane. He assumed that the integral equation pdq Th holds for each of the three coordinates of an electron moving in an orbit, the plane of which may be inclined at an angle to a fixed direction in the atom. It appears from the theory that the plane can have any one of several positions, and that the number of these positions depends upon the value of associated with the angular (but not the radial) coordinate of the electron. On the assumption that each position of the plane is equally probable the theory gives a method of estimating the relative intensities of spectral lines, for, if is large, there are more positions that the plane of the orbit can occupy, and therefore a greater chance for transfers from that orbit to take place.

According to a theory of Bohr's one of the positions of the plane is dynamically impossible, which changes somewhat the estimate of relative intensity.

If we apply the theory to the a lines in the K series of X-rays we find that according to it the ratio of the intensity of a1 to that

3 2 of a is either or The actual ratio determined from ionization 2 1'

curves for rhodium and tungsten (Duane and Hu, Duane and Shimizu) is 2.0.

Applied to the two a lines in the L series the theory gives or

3 2 as the ratio of their intensities, whereas from measurements on ionization curves for tungsten (Duane and Patterson) the ratio appears to be 10.

In general the theory of radiation discussed in this summary seems to represent a great many details of X-ray spectra with considerable precision and accuracy. In some cases, however, it does not in its present form agree with the facts.

No satisfactory explanation both of the production of secondary corpuscular rays and of such phenomena as interference has been given by one and the same theory, without making a number of special hypotheses.

INTENSITY OF EMISSION OF X-RAYS AND THEIR* REFLECTION FROM CRYSTALS

BY BERGEN DAVIS, Professor of Physics, Columbia University

The decrease of electron velocities on penetrating the target...

424

Spectra in different directions and polarization of X-rays..

445

* This monograph is the second of a series which when complete will form the report of a committee of the Division of Physical Sciences of the National Research Council. This committee on X-ray spectra consists of the following members: William Duane, Harvard University, Chairman; Bergen Davis, Columbia University; A. W. Hull, General Electric Research Laboratory; D. L. Webster, Leland Stanford Junior University.

INTENSITY OF EMISSION OF X-RAYS AND THEIR
REFLECTION FROM CRYSTALS

BY BERGEN Davis

TOTAL EMISSION OF ENERGY FROM X-RAY TUBES

From the very beginning after the discovery of Röntgen rays there was great interest in and discussion of the new phenomenon. While the possibility that the new radiations might be corpuscular in nature was given much consideration, the consensus of opinion among physicists was that they were not corpuscular but of the nature of electromagnetic waves or pulses emitted from the target at the impact of the cathode rays. This view was early formulated by Sir George Stokes. Whatever might be the nature of the radiation, it must be energy in some form and many attempts were made to detect this energy and to measure it.

This résumé will be divided into two parts. The one concerning itself with the less accurate experiments with the gas-filled X-ray tube and the unsatisfactory sources of high potential available at that time. The other will consider those later investigations un-. dertaken after the development of the hot filament tubes of the Coolidge type and the electron rectifying tubes that are now so effective in X-ray experiments.

Earlier Experiments

Only a cursory view will be taken of those earlier measurements of X-ray energy. The phenomenon was so new, the conditions for the production and regulation of the radiation so little understood that the results necessarily cannot now be considered as accurate.

The principal sources of error were of two kinds: (a) the high potential source for exciting the tubes. In the earlier work on X-rays, the usual source of high potential was the induction coil operated by some form of interrupter as the mechanical break, the mercury turbine and later the Wehnelt electrolytic interrupter. These methods gave such variable voltage impulses, that it was difficult to measure accurately either this variable voltage or the still more variable current passing through the tube. (b) The other great source of inconstancy was the gas-filled tube. Both the potential and current depended not on the apparatus but on the vacuum conditions in the tube. To keep this constant or to regulate it was a matter of great difficulty.

An early investigation of total emission was that of Dorn.1 The energy of the emitted rays was measured by the heat developed by their total absorption in strips of metal, the amount of heat being measured by the expansion of the strips. The total energy emitted from the tube in the form of X-rays varied from 0.85 X 10-5 to 3 X 10-5 gram cal. per second.

2

Another investigation of interest is that of M. Wien. The efficiency of X-ray emission was determined in this case. The target was so arranged that the heat produced by the impact of the cathode rays could be measured by a calorimetric method. The energy emitted was measured by absorbing it in both a thermopile and a bolometer. The potential across the tube was maintained about 59000 volts. The ratio of X-ray energy to the energy of the cathode rays was about 1.1 X 10-3 to 1.3 X 10-3. Using these results Wien attempted to calculate the pulse length of the X-rays and obtained a value of 1.15 X 10-10 cm. We now know that the shortest waves emitted by a tube at 59000 volts are about 2.3 X 10-9 cm. in length.

E. Carter3 found an efficiency of 1.07 × 10-3. The efficiency increased with increasing atomic weight of the target.

E. Angerer1 obtained an efficiency of 2 X 10-3. The efficiency increased with increasing voltage.

Other attempts were made to measure the efficiency by means of the ionization produced by the X-rays. Among others might be mentioned the experiments of Rutherford and McClung" and Eve and Day."

The dependence of the total emission on the atomic weight of the anticathode was investigated by Kaye. The intensity of Xray emission was measured by an ionization method. The tube was so arranged that a number of metals placed on a carrier could be moved into place and bombarded by the cathode rays. The conditions as to current and voltage were kept as constant as possible throughout. The result indicated that the intensity was proportional to the atomic weight of the metal forming the target. An improvement in the means of studying total emission was made in 1913 by R. T. Beatty. The principal object in this research was to ascertain how the intensity of the X-rays depended on the velocity of impact of the cathode electrons against the target. Homogeneous cathode rays were obtained by drawing the nonhomogeneous rays out into a spectrum and allowing the rays of a

8

given velocity to pass through a small hole and strike the target. The X-rays were emitted through a thin partition into a long ionization chamber containing methol iodide. The chamber was sufficiently long to permit of the complete absorption of the X-rays. The intensity was found to be proportional to the fourth power of the velocity of the cathode rays. It was also proportional to the atomic weight of the target. The intensity was found to increase more rapidly in some cases at the velocity at which the characteristic rays are produced. This was notably the case with copper. The following relation was found to hold.

X =

.58A84, where A is the atomic weight of the target and B = v/c, and X = energy emitted as X-rays. He deduces the following relation between the X-ray energy and the cathode ray energy N.

X/N = 2.54 X 10-4 A 2.

Later Experiments

In recent years X-ray research has been placed on a new plane of accuracy by the development of new apparatus and the discovery of new phenomena.

(a) The invention of the new type of X-ray tube known as the Coolidge tube was one of these great improvements. This tube permits of the accurate control of the potential and current through the tube, each independent of the other. This was quite impossible with the gas-filled tube.

(b) The improvements in the methods of producing high vacua together with the perfection of the tungsten filament as a source of thermo-electrons resulted in the development of very efficient electron valve tubes for the rectification of high potentials. One of the most successful of these is the kenotron developed by the General Electric Company.

(c) The discovery by M. Lane of the diffraction (reflection) of X-rays by crystals and the application of this discovery in the Xray spectrometer by W. H. Bragg marks a new departure in X-ray research.

One of the earliest investigations using the standard Coolidge X-ray tube with a tungsten target was that of Rutherford. The emission at three voltages, 48, 64 and 96 kilovolts was compared. The radiated energy was found to be nearly proportional to the