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By H. G. J. Moseley, M. A. *
Phil. Mag. (1913), p. 1024

p. 1024

In the absence of any available method of spectrum analysis, the characteristic types of X radiation, which an atom emits if suitably exited, have hitherto been described in terms of their absorption in aluminum.1 The interference phenomena exhibited by X-rays when scatted by a crystal have now, however, made possible the accurate determination of the frequencies of the various types of radiation. This was shown by W. H. and W. L. Bragg,2 who by this method analyzed the line spectrum emitted by the platinum target of an X-ray tube. C. G. Darwin and the author3 extended this analysis and also examined the continuous spectrum, which in this case constitutes the greater part of the radiation. Recently Prof. Bragg4 has also determined the wave-lengths of the strongest lines in the spectra of nickel, tungsten, and rhodium. The electrical methods which have hitherto been employed are, however, only successful where a constant source of radiation is available. The present paper contains a description of a method of photographing these spectra, which makes the analysis of the X-rays as simple as an other branch of spectroscopy. The author intends first to make a general survey of the principal types of high-frequency radiation, and then to examine the spectra of a few elements in greater detail and with greater accuracy. The results already obtained show that such data have an important bearing on the question

* Communicated by Prof. E. Rutherford, F.R.S. 1 Cf. Barkla, Phil. Mag. xxii, p. 396 (1911). 2 Proc. Roy. Soc. A. lxxxviii. p. 428 (1913). 3 Phil. Mag. xxvi. p. 210 (1913). 4 Proc. Roy. Soc. A. lxxxix. p. 246 (1913).


of the internal structure of the atom, and strongly support the views of Rutherford1 and of Bohr.2

Kaye3 has shown that an element excited by a stream of sufficiently fast cathode rays emits its characteristic X radiation. He used as targets a number of substances mounted on a truck inside an exhausted tube. A magnetic device enabled each target to be brought in turn into the line of fire. The apparatus was modified to suit the present work. The cathode stream was concentrated on to a small area of the target, and a platinum plate furnished with a fine vertical slit placed immediately in front of the part bombarded. The tube was exhausted by a Gaede mercury pump, charcoal in liquid air being also sometimes used to remove water vapor. The X-rays, after passing through the slit marked S in Fig. I,

emerged through an aluminum window 0.02 mm. thick. The rest of the radiation was shut off by a lead box which surrounded the tube. The rays fell on the cleavage face, C, of a crystal of potassium ferrocyanide which was mounted on the prism-table of a spectrometer. The surface of the crystal was vertical and contained the geometrical axis of the spectrometer.

1 Phil. Mag. xxi, p. 669 (1911). 2 Phil. Mag. xxvi, pp. 1, 476, & 857 (1913). 3 Phil. Trans. Roy. Soc. A. ccix, p. 123 (1909).


Now it is known1 that X-rays consist in general of two types, the heterogeneous radiation and characteristic radiations of definite frequency. The former of these is reflected from such a surface at all angles of incidence, but at the large angles used in the present work the reflexion is of very little intensity. The radiations of definite frequency, on the other hand, are reflected only when they strike the surface at definite angles, the glancing angle of incidence q, the wave-length l, and the "grating constant" d of the crystal being connected by the relation

nl = 2dsin q

[Reader's Note: Moseley labels this equation as (1).]

where n, an integer, may be called the "order" in which the reflexion occurs. The particular crystal used, which was a fine specimen with face 6 cm. square, was known to give strong reflexions in the first three orders, the third order being the most prominent.

If then a radiation of definite wave-length happens to strike any part P of the crystal at a suitable angle, a small part of it is reflected. Assuming for the moment that the source of the radiation is a point, the locus of P is obviously the arc of a circle, and the reflected rays will travel along the generating lines of a cone with apex at the image of the source. The effect on a photographic plate L will take the form of the arc of an hyperbola, curving away from the direction of the direct beam, With a fine slit at S, the arc becomes a fine line which is slightly curved in the direction indicated.

The photographic plate was mounted on the spectrometer arm, and both the plate and slit were 17 cm. from the axis. The importance of this arrangement lies in a geometrical property, for when these two distances are equal the point L at which a beam reflected at a definite angle strikes the plate is independent of the position of P on the crystal surface. The angle at which the crystal is set is then immaterial so long as a ray can strike some part of the surface at the required angle. The angle q can be obtained from the relation 2q = 180° - SPL = 180° - SAL.

The following method was used for measuring the angle SAL. Before taking a photograph a reference line R was made at both ends of the plate by replacing the crystal by a lead screen furnished with a fine slit which coincided with the axis of the spectrometer. A few seconds' exposure to the X-rays then gave a line R on the plate, and so defined on it

1 Moseley and Darwin, loc. cit.


the line joining S and A. A second line RQ was made in the same way after turning the spectrometer arm through a definite angle. The arm was then turned to the position required to catch the reflected beam and the angles LAP for any lines which were subsequently found on the plate. The angle LAR was measured with an error of not more than 0°. D, by superposing on the negative a plate on which reference lines had been marked in the same way at intervals of 1°. In finding from this the glancing angle of reflexion two small corrections were necessary in practice, since neither the face of the crystal nor the lead slit coincided accurately with the axis of the spectrometer. Wavelengths varying over a range of about 30 per cent. could be reflected for a given position of the crystal.

In almost all cases the time of exposure was five minutes. Ilford X-ray plates were used and were developed with rodinal. The plates were mounted in a plate-holder, the front of which was covered with black paper. In order to determine the wavelength from the reflexion angle [theta] it is necessary to know both the order n in which the reflexion occurs and the grating constant d. n was determined by photographing every spectrum both in the second order and the third. This also gave a useful check on the accuracy of the measurements; d cannot be calculated directly for the complicated crystal potassium ferrocyanide. The grating constant of this particular crystal had, however, previously1 been accurately compared with d', the constant of a specimen of rock-salt. It was found that

Now W.L. Bragg2 has shown that the atoms in a rock-salt crystal are in simple cubical array. Hence the number of atoms per c.c.

N, the number of molecules in a gram-mol., = 6.05 x 1023 assuming the charge on an electron to be 4.89 x 10¯10; s, the density of this crystal of rock-salt, was 2.167, and M the molecular weight = 58.46.

1 Moseley and Darwin, loc. cit. 2 Proc. Roy. Soc. A. lxxxix. p. 248 (1913).


Table I


This gives d' = 2.814 x 10¯8 and d = 8.454 x 10¯8 cm. It is seen that the determination of wave-length depends on so that the effect of uncertainty in the value of this quantity will not be serious. Lack of homogeneity in the crystal is a more likely source of error, as minute inclusions of water would make the density greater than that found experimentally.

Twelve elements have so far been examined. The ten given in Table I were chosen as aforming a continuous series with only one gap. It was hoped in this way to bring out clearly any systematic results. The inclusion of nickel was of special interest owing to its was of special interest owing to its anomalous postition in the periodic system. Radiations from these substances are readily excited, and the large angles of reflexion make it easy to measure the wave-lengths with accuracy. Calcium alone gave any trouble. In this case, owing to the high absorption coefficient of the principal radiation-about 1200 cm¯1 in aluminium- the X-ray tube was provided with a window of goldbeaters's skin and the air between the crystal and the photographic plate displaced by hydrogen. The layer of lime which covered the surface of the metal gave off such a quantity of gas that the X rays substituted for zinc to avoid volatilization by the intense heat generated at the point struck by the cathode rays. Ferrovanadium (35 per cent. V) and ferro-titanium 23 per cent. Ti), for which I am indebted to the International Vanadium Co., proved convenient substitutes for the pure elements, which are not easily obtained in the solid form.

Plate XXII shows the spectra in the third order placed approximately in register. Those parts of the photographs which represent the same angle of reflexion are in the same vertical line. The actual angles can be taken from Table I. It is to be seen that the spectrum of each element consists of two lines. Of these the stronger has been called a in the table, and the weaker b. The lines found on any of the plates besides a and b were almost certainly all due to impurities. Thus in both the second and third order the cobalt spectrum shows Nia very strongly and Fea faintly. In the third order the nickel spectrum shows Mna2 faintly. The brass spectra naturally show a and b both of Cu and of Zn, but Znb2 has not yet been found. In the second order the ferro-vanadium and ferro-titanium spectra show very intense third-order Fe lines, and the former also shows Cua3 faintly. The Co contained Ni and 0.8 per cent. Fe, the Ni 2.2 per cent. Mn,


and the V only a trace of Cu. No other lines have been found, but a search over a wide range of wave-lengths has been made only for one or two elements, and perhaps prolonged exposures, which have not yet been attempted, will show more complex spectra. The prevalence of lines due to impurities suggests that this may prove a powerful method of chemical analysis. Its advantage over ordinary spectroscopic method lies in the simplicity of the spectra and the impossibility of one substance masking the radiation from another. It may even lead to the discovery of missing elements, as it will be possible to predict the position of their characteristic lines.

It will be seen from Table I, that the wave-lengths calculated from the two orders are in good agreement. The third lated from the two orders are in good agreement. The third order gives the stronger reflexion, and as the angles dealt with are the larger these results are the more accurate. The similarity of the different spectra is shown by the fact that the two lines a and b remain approximately constant, not only in relative intensity but also in relative wave-length. The frequency of b increases, however, slightly faster than that of a. The same two lines a strong and b weak constitute the rhodium spectrum examined by Bragg1, and they are obviously in some way closely related. One or two photographs taken with the radiation from platinum gave results in good agreement with those obtained by the electrical method, and no trace of the elaborate system of bands described by de Broglie2 in the reflexion from rocksalt was encountered. The three lines found by Herveg3 in the reflexion from selenite doubtless represent part of the Pt spectrum in the second order. The actual breadth of the lines and certain minute details in their structure will not be considered here, as discussion would take too much space and more experiments are needed. The only other element examined was tantalum. In this case the radiation belongs to the L series, and the spectrum consists of a strong line of wave-length 1.525 x 10¯8 cm., two others of less intensity at 1.330 and 1.287 x 10¯8 cm., and probably some very faint lines also.

A discussion will now be given of the meaning of the wave-lengths found for the principal spectrum-line a. In Table I. the values are given of the quantity EQUATION


We will now examine the relation EQUATION more closely. So far the argument has relied on the fact that Q is a quantity which increases from atom to atom by equal steps. Now Q has been obtained by multiplying v1/2 by a constant factor so chosen as to make the steps equal to unity. We have, therefor, EQUATION where k is a constant. Hence the frequency v varies as (N-k)2. If N for calcium is really 20 then k=1.

There is good reasion to believe that the X-ray spectra with which we are now dealing come from the rinnermost ring of electrons 3. If these electrons are held in equilibrium by mechanical forces, the angular velocity w with which they are rotationg and the radius r of their orbit are connected by EQUATION where sn is a small term arising from the influences of the n electons in the ring on each other , and s2=0.25, s4=0.96, s6=1.83, s8=2.81. In obtaining this simple expression the very small effect of other ourside rings has been neglected. If then, as we pass from atom to atom, the number of electrons in the central ring remains unaltered, EQUATION remains constant; but these experiments have shown that EQUATION is also constant, and therefore EQUATION is constant.

For the types of radiation considered by Bohr, provided the ring moves from one stationary state to another as a whole, and for the ordinary transverse vibrations of the ring, provided the influence of outerings can be nelected, v is proportional to w.

This gives W3/2r3 and therefor mwr2, the angular momentum of an electron, the same for all the different atoms. Thus we


have an experimental verification of the principle of the constancy of angular momentum which was first used by Nicholson 4, and is the basis of Bohr's theory of the atom.

It is evident that k=sn. If then k=1 it is suggested that the ring contains 4 electrons, for s4=0.96.

We are now justified in making a quantitave comparison between the frequency of a and that of the fundamental radiation from such a ring calculated from the theory of Bohr.

We have obtained the experimental result, EQUATION. On his theory, makng the assumption that the ring moves as a whole from stationary state 2 to state 1, the frequency of the principal radiation emitted is EQUATION, where e is the charge on an electron, m its mass, and h Planck's constant.

The numerical agreement between these two constants v0 and EQUATION is known to be very close, while Bohr's explanation of the Balmer series for hydrogen assumes them to be identical. This numerical agreement between the experimental values and those calculated from a theory designed to explain the ordinary hydrogen spectrum is remarkable, as the wave-lengths dealt with in the two cases differby a factor of about 2000. The assumption that the whole ring takes part in the radiation introduces, however, a grave difficulty from energy considerations, while no explanation of the faint line b has been forthcoming. Probably further experiments will show that the theory needs some modification.

The results hitherto obtained for the radiations of the L series are too meagre to justify any explanation. As before, the line of longest wave-length is the most prominent, a result similar to that found in ordinary light-spectra. The wave-lengths found for this line in the case of tantalum and platinum suggest that possibly the frequency is here EQUATION Here N and sn are unknown, but it is evident from the periodic system that NPT-NTA=5, while probably sn remains the same for all elements in the same column.

Phil. Mag. (1914), p. 703.

The first part of this paper dealt with a method of photographing X-ray spectra, and included the spectra of a dozen elements. More that thirty other elements have now been investigated, and simple laws have been found which govern the results, and make it possible to predict with confidence the position of the principal lines in the spectrum of any element from aluminum to gold. The present contribution is a general preliminary survey, which claims neither to be complete nor very accurate....

The results obtained for radiations belonging to Barkla's K series are given in table I, and for convenience the figures already given in Part I. are included. The wave-length l has been calculated from the glancing angle of reflexion q by means of the relation nl = 2d sinq, where d has been taken to be 8.454 x 10¯8 cm. As before, the strongest line is called a and the next line b. The square root of the frequency of each line is plotted in Fig. 3, and the wavelengths can be read off with the help of the scale at the top of the diagram.

[N.B. - Fig. 3 is included at the very end of this file since, in order to make it readable on-screen, I had to make it rather large, as in a 163K GIF. John Park]

Table I
  a line
l x 108 cm
QK N Atomic
b line
l x 108 cm
Aluminum 8.364 12.05 13 7.912
Silicon 7.142 13.04 14 6.729
Chlorine 4.750 16.00 17 -------
Potassium 3.759 17.98 19 3.463
Calcium 3.368 19.00 20 3.094
Titanium 2.758 20.99 22 2.524
Vanadium 2.519 21.96 23 2.297
Chromium 2.301 22.98 24 2.093
Manganese 2.111 23.99 25 1.818
Iron 1.946 24.99 26 1.765
Cobalt 1.798 26.00 27 1.629
Nickel 1.662 27.04 28 1.506
Copper 1.549 28.01 29 1.402
Zinc 1.445 29.01 30 1.306
Yttrium 0.838 38.1 39 -------
Zirconium 0.794 39.1 40 -------
Niobium 0.750 40.2 41 -------
Molybdenum 0.721 41.2 42 -------
Ruthenium 0.638 43.6 44 -------
Palladium 0.584 45.6 46 -------
Silver 0.560 46.6 47 -------

The spectrum of Al was photographed in the first order only. The very light elements give several other fainter lines, which have not yet been fully investigated, while the results for Mg and Na are quite complicated, and apparently depart from the simple relations which connect the spectra of the other elements.

Table II
  a line
l x 108 cm
QL N Atomic
b line
l x 108 cm
f line
l x 108 cm
g line
l x 108 cm
Zirconium 6.091 32.8 40 --- --- ---
Niobium 5.749 33.8 41 5.507 --- ---
Molybdenum 5.423 34.8 42 5.187 --- ---
Ruthenium 4.861 36.7 44 4.660 --- ---
Rhodium 4.622 37.7 45 --- --- ---
Palladium 4.385 38.7 46 4.168 --- 3.928
Silver 4.170 39.6 47 --- --- ---
Tin 3.619 42.6 50 --- --- ---
Antimony 3.458 43.6 51 3.245 --- ---
Lanthanum 2.676 49.5 57 2.471 2.424 2.313
Cerium 2.567 50.6 58 2.366 2.315 2.209
Praseodymium (2.471) 51.5 59 2.265 --- ---
Neodymium 2.382 52.5 60 2.175 --- ---
Samarium 2.208 54.5 62 2.008 1.972 1.893
Europium 2.130 55.5 63 1.925 1.888 1.814
Gadolinium 2.057 65.5 64 1.853 1.818 ---
Holmium 1.914 58.6 66 1.711 --- ---
Erbium 1.790 60.6 68 1.591 1.563 ---
Tantalum 1.525 65.6 73 1.330 --- 1.287
Tungsten 1.486 66.5 74 --- --- ---
Osmium 1.397 68.5 76 1.201 --- 1.172
Iridium 1.354 69.6 77 1.155 --- 1.138
Platinum 1.316 70.6 78 1.121 --- 1.104
Gold 1.287 71.4 79 1.092 --- 1.078

In the spectra from yttrium onwards only the a line has so far been measured, and further results in these directions will be given in a later paper. The spectra both of K and of Cl were obtained by means of a target of KCl, but it is very improbable that the observed lines have been attributed to the wrong elements. The a line for elements from Y onwards appeared to consist of a very close doublet, an effect previously observed by Bragg in the case of Rhodium.

The results obtained for the spectra of the L series are given in Table II and plotted in Fig. 3. These spectra contain five lines, a, b, g, d, e, reckoned in order of decreasing wave-length and deceasing intensity. There is also always a faint companion a' on the long wave-length side of a, a rather faint line f between b and g for the rare earth elements at least, and a number of very faint lines of wave-length greater than a. Of these, a, b, f, and g have been systematically measured with the object of finding out how the specturm alters from one element to another. The fact that often values are not given for all these lines merely indicates the incompleteness of the work. The spectra, so far as they have been examined, are so entirely similar that without doubt a, b, and g at least always exist. Often g was not included in the limited range of wave-lengths which can be photographed on one plate. Sometimes lines have not been measured, either on account of faintness or of the confusing proximity of lines due to impurities....


In Fig. 3 the spectra of the elements are arranged on horizontal lines spaced at equal distances. The order chosen for the elements is the order of the atomic weights, except in the cases of A, Co, and Te, where this clashes with the order of the chemical properties. Vacant lines have been left for an element between Mo and Ru, an element between Nd and Sa, and an element between W and Os, none of which are yet known, while Tm, which Welsbach has separated into two constituents, is given two lines. This equivalent to assigning to successive elements a series of successive characteristic integers. On this principle the integer N for Al, the thirteenth element, has been taken to be 13, and the values of N then assumed by the other elements are given on the left-hand side of Fig. 3 This proceeding is justified by the fact that it introduces perfect regularity into the X-rays spectra. Examination of Fig 3. shows that the values of n1/2 for all the lines examined both in the K and the L series now fall on regular curves which approximate to straight lines. The same thing is shown more clearly by comparing the values of N in Table I with those of

n being the frequency of the line and no the fundamental Rydberg frequency. It is here plain that QK = N - 1 very approximately, except for the radiations of very short wave-length which gradually diverge from this relation. Again, in Table II a comparison of N with

where n is the frequency of the La line, shows that QL = N - 7.4 approximately, although a systematic deviation clearly shows that the relation is not accurately linear in this case.

Now if either the elements were not characterized by these integers, or any mistake had been made in the order chosen or in the number of places left for unknown elements, these regularities would at once disappear;. We can therefore conclude from the evidence of the X-ray spectra alone, without using any theory of atomic structure, that these integers are really characteristic of the elements. Further, as it is improbable that two different stable elements should have the same integer, three, and only three, more elements are likely to exist between Al and Au. As the X-ray spectra of these elements can be confidently predicted, they should not be difficult to find. The examination of keltium would be of exceptional interest, as no place has been assigned to this element.

Now Rutherford has proved that the most important constituent of an atom is its central positively charge nucleus, and van den Broek has put forward the view that the charge carried by this nucleus is in all cases an integral multiple of the charge on the hydrogen nucleus. There is every reason to suppose that the integer which controls the X-ray spectrum is the same as the number of electrical units in the nucleus, and these experiments therefore give the strongest possible support to the hypothesis of van den Broek. Soddy has pointed out that the chemical properties of the radio-elements are strong evidence that this hypothesis is true for the elements from thallium to uranium, so that its general validity would now seem to be established.