WITH A BRIEF STATEMENT OF THEIR BEARING ON THEORIES OF THE STRUCTURE OF ATOMS AND THE MECHANISM OF RADIATION*

BY WILLIAM DUANE

PROFESSOR OF BIO-PHYSICS, HARVARD UNIVERSITY

The following tables contain wave-lengths in X-ray spectra that have been measured recently by means of crystal spectrometers (Bragg spectrometers).

The equation

λ

=

2d X sin 0

(1)

gives the wave-length, λ, where @ is the angle made by the incident beam of X-rays with the reflecting planes of the crystal, and d is the perpendicular distance between two successive planes.

Most of the wave-lengths have been measured by means of crystals of rock salt (NaCl), or calcite (CaCO3). The usually accepted value of d for rock salt (100 planes) is:

Some discussion has arisen as to the probable value of d (100 planes) for calcite. A. H. Compton (Physical Review, June, 1918, p. 430) gives the value:

d = 3.0281 X 10-8 cm.

which Uhler estimates (Physical Review, July, 1918, p. 39) to be correct to within about 0.0016. Using corrections suggested by Birge (Physical Review, Oct., 1919, p. 361) and by Ledeux

* This monograph is the first 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.

Lebard and Dauvillier (C. R., Nov. 24, 1919) the value of d for calcite:

E = electro-chemical equivalent of silver per E. M. U.

The most recent direct comparison of d for calcite with d for rock salt by means of X-rays themselves has been made by Siegbahn (Phil. Mag., June, 1919, p. 601). Assuming that for rock salt:

The weight of opinion seems to incline toward calcite as a more uniform, and therefore, a better crystal than rock salt for making accurate wave-length measurements.

Since an X-ray wave-length can be measured with much greater precision than that indicated by the probable error in the value of d for either calcite or rock salt, the writer for some years has been accustomed to calculate the wave-lengths measured in his laboratory by means of the grating space for calcite:

If the value of d ultimately selected (by international agreement, for instance) differs from this, all these wave-lengths can be changed easily in the required ratio.

Two kinds of X-radiation have been recognized: general, or continuous spectrum X-rays and characteristic X-rays. The wave-lengths of the characteristic X-rays depend upon the atomic number of the chemical element used as a target in the X-ray

tube (Moseley, Phil. Mag., Dec., 1913, p. 1024, and April, 1914, p. 703). The general X-radiation contains all wave-lengths down to a certain well-defined minimum, the value of which depends upon the difference of potential, V, applied to the X-ray tube, in accordance with the Planck-Einstein quantum equation:

Ve = hv = h=

(Duane and Hunt, Phys. Rev., Aug., 1915, p. 166).

(2)

In 1913 W. H. Bragg tested the quantum law as applied to characteristic X-rays, the wave-lengths of which had actually been measured. He used Whiddington's estimates of the voltages, V, required to produce the characteristic X-rays.

In 1914 the writer made some experiments to test the law in the case of the general radiation. In these experiments a fairly constant measured voltage was applied to the X-ray tube, and the average (or effective) wave-length was determined by measuring the coefficient of absorption of the rays in aluminium, and by calculating the wave-length from the known relation between the

two.

The experiments showed in each case that Ve had the same order of magnitude as hv.

Measurements of h by means of the limiting values of the wavelengths in the general X-radiation have been made as follows: (Millikan's value of e = 4.774 X 10-10 E. S. U. has been used in the computations.)

Four kinds of wave-lengths (and vibration frequencies) may be regarded as associated with each series of characteristic X-rays: (a) Critical ionization wave-lengths. (b) Critical absorption wave-lengths.

(c) The wave-lengths in the emission lines of the series. (d) The quantum wave-lengths.

(a) A critical ionization wave-length characteristic of a chemical element is a wave-length such that, if the element is present in a gas through which X-rays pass, X-rays of shorter wave-length than the critical value ionize the gas more strongly than X-rays

of longer wave-length do. The increase in ionization may be ascribed to an increase in the emission of high speed electrons from the atoms of the chemical element due to the passage of X-rays across them.

(b) A critical absorption wave-length characteristic of a chemical element is a wave-length such that, if the element lies in the path of the X-rays, it absorbs the X-rays of shorter wave-length than the critical value to a greater extent than it does X-rays of longer wave-length.

(c) Each series of X-rays contains a number of emission lines of different wave-lengths.

(d) A quantum wave-length is a wave-length such that, if it is substituted in the quantum equation (2), it gives the energy of the electron (or voltage applied to the X-ray tube) required to produce the series of X-rays with which it is associated.

It has been known for some time that all of these four kinds of characteristic wave-lengths that belong to the same X-ray series lie together in the same region of the X-ray spectrum.

Recent improvements in the methods of measuring wave-lengths have made it possible to prove (A) that a critical ionization wavelength characteristic of a chemical element (iodine, for example) equals the critical absorption wave-length characteristic of the same element (and associated with the same series) to within less than one-tenth of one per cent (Duane and Hu, Phys. Rev., Oct., 1918, p. 3721); (B) that the shortest wave-length in the K series of X-rays exceeds the critical absorption wave-length associated with the same series by a fraction of one per cent (one-fourth of one per cent for rhodium, and one-half of one per cent for tungsten) (Duane and Hu, Loc. Cit., and Duane and Stenström, Nat. Acad. Proc., Aug., 1920); and (C) that the quantum wave-length for the K series (of rhodium, for instance) is a fraction of one per cent shorter than the shortest emission wave-length in the K series (Webster, Phys. Rev., June, 1916, p. 599). This means that, according to (B), the quantum wave-length coincides with the corresponding critical absorption wave-length to within the limits of error of the measurements. Webster has also determined two of the quantum wavelengths in the L series (of platinum) (Phys. Rev., June, 1917, p. 571), and these lie close to two of the three critical absorption wavelengths in the same series.

It has been found by experiment that within the limits of experimental error the differences between the K critical absorption

frequency and the L critical absorption frequencies equal, respectively, the frequencies of the a lines in the K series, and that the difference between the K critical absorption frequency and one of the M critical absorption frequencies equals the frequency of the line in the K series (Duane and Shimizu, Phys. Rev., July, 1919, p. 67; Duane and Stenström, Nat. Acad. Proc., Aug., 1920).

The following values of the emission and absorption wavenumbers illustrate these laws. The K and L critical absorption wave-numbers, Ka, La1, La2 and Las, have been computed from the wave-lengths for tungsten contained in Tables 2 and 3. The K emission wave-numbers Ka1, Kα2, Ka3 and K3 have been computed from the wave-lengths for tungsten contained in Table 8. The M critical absorption wave-number, Ma,, has been estimated from the data in Tables 4 and 13.

It has been found by experiment, also, that several (not all) of the lines in the L series have emission frequencies equal to the differences between the critical absorption frequencies in the L series and those in the M series (Duane and Patterson, Nat. Acad. Proc., Sept., 1920).

The following wave-numbers illustrating this have been computed from the data for uranium and thorium, contained in Tables 3, 4 and 11:

Lines corresponding to some of the differences between critical absorption frequencies have not been observed. The vacancies are indicated by dots in the table.

Several pairs of lines in the emission spectra of a chemical element appear to have the same frequency difference (Kossel, Sommerfeld, Swinne, etc.). For instance: (a) the difference in frequency between the a1 and a lines in the K series equals that between the