Experiment: X-ray Spectra and the Charge of the Nucleus

Atomic Models and Spectra makes one of the strongest claims in the book. The elements are ordered not by their atomic weights, as chemistry had assumed for a century, but by a whole number that counts elementary charges on the nucleus; and the evidence for this is spectroscopic, drawn from radiation far outside the visible range. The chapter states the law, derives its slope from the hydrogenic level formula with no adjustable parameter, and stops there. It never says where the radiation came from, how anyone knew it was radiation at all, or how a wavelength shorter than a visible one by four powers of ten was measured in the first place.

This chapter supplies that chain. It is unusual among the experiment chapters of this treatise in that no single measurement carries the verdict: what is on trial is the whole instrument, and the instrument had to be built from nothing in eighteen years. Röntgen found the radiation and could say almost nothing about its nature. Barkla showed that it is transverse — hence a wave in the electromagnetic field of The Maxwell Equations and not the longitudinal aether pulse Röntgen had guessed — and that each element, struck hard enough, answers with a radiation of its own. Friedrich, Knipping and von Laue diffracted it from a crystal, which established in one photograph both that X-rays are waves of wavelength comparable to an atomic spacing and that a crystal is a three-dimensional periodic lattice. The Braggs turned that observation into a measuring instrument by reducing the diffraction condition to a reflection law and mounting the crystal on a divided circle. Moseley put the elements one after another into that instrument. Siegbahn then drove its accuracy to the point where the X-ray lines became a term system as sharp as the optical one.

The reader will find the six experiments below in that order, each with its apparatus, its procedure, its observations and its verdict. What they establish jointly is stated at the end (Section 76.7). Five of the six were recognised by a Nobel Prize — Röntgen with the first prize in physics ever awarded, then von Laue, the Braggs, Barkla and Siegbahn in a run of four consecutive years of X-ray work. Moseley, who is missing from that list, was killed at Gallipoli in 1915 at the age of twenty-seven, and the prize is not awarded posthumously.

Röntgen: a new kind of rays (1895)

The discovery was made on 8 November 1895 with apparatus that a dozen laboratories in Europe already possessed. What Röntgen added was the black cardboard shield and the willingness to look at a fluorescent screen he had no reason to expect to glow.

Apparatus

A Hittorf–Crookes discharge tube — a partially evacuated glass vessel with two electrodes — driven by a Ruhmkorff induction coil, the whole tube wrapped in a close-fitting shroud of black cardboard that passed no visible light. A screen coated with barium platinocyanide served as the detector; photographic plates in light-tight holders served as the recording detector. A darkened room. For the tests of the nature of the radiation: sheets of paper, wood, ebonite, aluminium, lead, platinum and other metals of graded thickness; prisms of water, carbon disulfide, ebonite and aluminium; polished surfaces; a strong magnet; and an electroscope.

Procedure

Run the discharge in the darkened room with the shrouded tube and observe the screen at increasing distances and orientations. Interpose absorbers of known material and thickness between tube and screen and compare the transmitted brightness. Attempt to refract the radiation with the prisms and to reflect it regularly from polished surfaces. Place the magnet across the path and look for a deflection. Bring a charged electroscope into the irradiated region. Expose plates behind absorbers of graded density, including a hand.

Observations and data

The screen fluoresces brightly whenever the discharge runs, at distances of the order of \(2\,\mathrm{m}\) from the tube and with the cardboard shroud in place; a sheet of paper, a bound book of about a thousand pages, deal boards, or thin sheets of aluminium interposed in the beam weaken but do not extinguish the effect, while a fraction of a millimetre of lead or platinum stops it. Transmission is governed chiefly by the mass of material traversed, and for equal masses the denser elements absorb more strongly. The radiation proceeds in straight lines from the spot on the tube wall struck by the cathode rays and casts sharp shadows; a hand held in the beam casts a shadow in which the bones stand out darker than the flesh. Photographic plates are blackened. Charged bodies in the irradiated air lose their charge. No regular refraction could be detected with any of the prisms and no regular reflection from any polished surface; a magnet across the path produced no deflection whatever [Roentgen:1895].

The absence of refraction is not a null result but a measurement, and it is worth extracting the number it contains.

Interpretation

Röntgen's own conclusion was deliberately negative. The radiation is not cathode rays, because a magnet does not deflect it. It is not ultraviolet light, because it is not refracted, not regularly reflected, and could not be polarised by any means he tried. Lacking any positive evidence of transversality he suggested, tentatively, that the rays might be longitudinal waves in the aether. That guess was wrong, and it is the honest reason this chapter must continue: the question “what are X-rays?” was left open by the man who found them, and was closed by Section 76.2 and Section 76.3.

Primary references

[Roentgen:1895].

Barkla: characteristic radiation and the transversality of X-rays (1905–1911)

Barkla worked with an electroscope and an ionisation chamber, without ever resolving a spectral line, and settled two questions that resisted every more direct attack: whether X-rays are transverse, and whether the radiation an element emits belongs to the element.

Apparatus

For the polarisation experiment: an X-ray bulb giving a primary beam; a first scatterer — a block of a light element, paper or carbon, which scatters without appreciable absorption — placed in that beam; a second scatterer placed in the secondary beam that leaves the first at right angles; and an ionisation chamber with an electrometer, mounted so that it can be carried around the axis of the secondary beam while remaining at right angles to it.

For the characteristic-radiation experiments: the same primary bulb, with the beam falling on a radiator consisting of the element under test or one of its compounds; an ionisation chamber viewing the radiator at right angles to the primary beam; and a set of aluminium sheets of accurately known thickness to be interposed one at a time in the secondary beam.

Procedure

In the polarisation experiment, record the ionisation current produced by the twice-scattered beam as the chamber is carried around the axis of the once-scattered beam, and plot it against the azimuth.

In the absorption experiments, record the ionisation current as successive aluminium sheets are added, and read the mass absorption coefficient off the exponential decline. A radiation is called homogeneous when the decline is a single exponential over the whole range of thicknesses used. Repeat with radiator elements taken in order through the periodic table, and repeat each radiator with primary beams of different hardness, obtained by varying the tube.

Observations and data

The twice-scattered intensity is not the same in all azimuths: it passes through a maximum and a minimum ninety degrees apart, the maximum lying in the direction of the original primary beam. The modulation is partial rather than complete, as the finite apertures and the multiple scattering in the radiators require [Barkla:1905].

For radiators heavier than about calcium the secondary beam contains, besides the scattered primary, a component that is homogeneous. Its mass absorption coefficient in aluminium is a property of the radiator element and not of the primary beam; it decreases monotonically as one proceeds up the periodic table, so that heavier elements emit a more penetrating characteristic radiation. The component appears only when the primary beam is itself harder than the characteristic radiation it excites — there is a threshold — and for the heavier elements a second, much less penetrating homogeneous radiation appears alongside the first [Barkla:1908] [Barkla:1909]. Barkla named the more penetrating series K and the softer one L, choosing letters in the middle of the alphabet in case further series should be found on either side [Barkla:1911]. They were: M, N and O followed.

Interpretation

The polarisation result closed the question Röntgen had left open. X-rays are transverse, hence electromagnetic waves of The Maxwell Equations, and the aether pulse can be dropped. The characteristic-radiation result is the more consequential of the two for what follows. It says that the radiation carries the signature of the emitting atom, and therefore that a spectroscopy of the elements in this range is possible in principle. Barkla could rank the elements by absorption coefficient but could not attach a wavelength to any of them, because he had no dispersing element; his K and L are ordinal labels, not measurements. The instrument that converted his ordering into wavelengths arrives in the next two sections, and Moseley's law is the result of running it over Barkla's own K and L radiations. It is worth noticing that the monotone ordering Barkla found already contained Moseley's law in disguised form: absorption in aluminium increases steeply with wavelength, so “more penetrating for heavier elements” is “shorter wavelength for larger nuclear charge”.

Primary references

[Barkla:1905] [Barkla:1908] [Barkla:1909] [Barkla:1911].

Friedrich, Knipping and von Laue: diffraction by a crystal (1912)

The experiment was proposed on a guess and worked at once. Von Laue reasoned that if X-rays were waves of about the size of an atom, and if a crystal were a periodic array of atoms, then the crystal was a ready-made three-dimensional diffraction grating that nobody would have to rule. Neither premise was established at the time; the photograph established both together.

Apparatus

A gas X-ray tube; a lead-lined box carrying a series of pinhole apertures which cut from the emitted radiation a narrow pencil a fraction of a millimetre across; a crystal mounted on a goniometer at the exit of the collimator, so that a chosen crystallographic direction could be set parallel to the pencil; and photographic plates in light-tight holders placed behind the crystal, and in the first trials also to the sides and in front of it, to catch radiation scattered in any direction. The first crystal was copper sulfate, chosen because a good specimen was to hand; the decisive photographs were taken with zinc blende, which is cubic and of high symmetry.

Procedure

Set the crystal in the pencil, expose the plate for a period of hours, and develop. Then rotate the crystal so that a symmetry axis lies along the pencil, and repeat. Compare the pattern with that obtained when the crystal is replaced by an amorphous body of similar absorbing power, and with that obtained when the crystal is displaced out of the beam.

Observations and data

The plate behind the crystal shows, in addition to the trace of the undeviated pencil, a set of discrete, sharp spots at well-defined angles. The spots are arranged about the central trace with the point symmetry of the crystal in the direction of the beam: with the pencil along a symmetry axis of zinc blende the pattern reproduces the symmetry of that axis. Rotating the crystal moves the spots as a rigid figure, and displacing the crystal out of the pencil extinguishes them all. An amorphous absorber in the same place gives a diffuse distribution and no spots [Friedrich:1912]. Von Laue's companion paper computes the directions of the maxima from a lattice model and reproduces the observed positions [vonLaue:1912].

Interpretation

One photograph settled two disputed questions in different fields. For physics, X-rays interfere, so they are waves, and their wavelength is of the order of an atomic spacing — which explains at a stroke why Röntgen found no refraction and no reflection with ordinary optics, and why Phenomenon 76.2 holds. For crystallography, the sharp maxima require the scatterers to sit on a lattice with long-range three-dimensional periodicity: the lattice hypothesis, until then an inference from the external shapes and cleavage of crystals, became a direct observation. Everything the treatise says about periodic solids in Phonons and Lattice Dynamics and Electrons in Solids: Band Theory rests on this measurement and on the industry of structure determination it founded.

Primary references

[Friedrich:1912] [vonLaue:1912].

The Braggs: the reflection law and the X-ray spectrometer (1913)

Laue's spots proved that X-rays are waves but were an awkward tool: a Laue photograph mixes all wavelengths and all lattice planes at once. The Braggs' contribution was to reorganise the same geometry so that one wavelength and one set of planes are isolated, and then to hang the whole arrangement on a divided circle. What had been a demonstration became an instrument, and every measurement in the two sections that follow was made with it.

Apparatus

An X-ray tube with a metal anticathode; a pair of lead slits defining a beam of small angular width; a cleaved crystal — rock salt in the first work, later calcite and mica — mounted on the table of a spectrometer with a divided circle; and, on an arm turning about the same axis, an ionisation chamber filled with a heavy gas so as to absorb the beam efficiently, connected to a quadrant electrometer. The crystal table and the chamber arm are geared or set so that when the crystal face makes a glancing angle with the incident beam, the chamber sits at twice that angle from the beam — the specular position.

Procedure

Set the crystal face at a small glancing angle and the chamber at the corresponding specular angle; record the ionisation current; advance both by a small step and repeat. The record of current against glancing angle is the spectrum of the tube as dispersed by that crystal face. Change the anticathode metal and repeat, to determine which features belong to the target and which to the crystal or the apparatus.

Observations and data

The current against glancing angle is a smooth continuous background on which sharp peaks stand out. The peaks come in families: within a family the glancing angles \(\theta_{n}\) satisfy \(\sin\theta_{n}=n\sin\theta_{1}\) for \(n=1,2,3,\dots\), so that a family is a single feature seen in successive orders. The angular positions of the families change when the anticathode metal is changed, and do not change when the crystal is exchanged for another face of the same crystal at the appropriate spacing; the peaks therefore belong to the target metal and are Barkla's characteristic radiations, now resolved and measurable [Bragg:1913a] [Bragg:1913b].

Interpretation

The spectrometer converts an angle read on a divided circle into a wavelength, absolutely, through Equation (76.6) and Equation (76.7). Three things follow immediately. Barkla's homogeneous radiations become spectral lines with wavelengths. The crystal becomes a monochromator, so that a structure determination can be run the other way round — known wavelength in, unknown spacings out — which is what the younger Bragg did for the alkali halides, diamond and much else, founding X-ray crystallography as a working science. And the incident wavelength of the Compton measurement of The Photon: Photoelectric and Compton Effects becomes a known quantity, which is what makes the shift there a measurement rather than an impression.

Primary references

[Bragg:1913a] [Bragg:1913b].

Moseley: the high-frequency spectra of the elements (1913–1914)

Moseley took the finished instrument and did the obvious thing that nobody had done: he put the elements through it one after another, in order, and looked at the sequence rather than at any one spectrum. The law he found, and its derivation from the hydrogenic level formula, are stated in Atomic Models and Spectra and are not repeated here; what follows is the measurement.

Apparatus

A Bragg-type crystal spectrometer with a crystal of potassium ferrocyanide, recording photographically rather than by ionisation chamber so that a whole spectrum is captured in one exposure. The essential addition was to the source: inside the evacuated tube ran a small trolley carrying a dozen target elements in a row, drawn along by a thread led out through a seal, so that one element after another could be brought into the cathode-ray beam without letting the tube up to air. Wavelengths were referred to the known spacing of the crystal.

Procedure

Bring a target into the beam, expose the plate through a chosen range of glancing angles, advance the trolley, and expose the next element on the same plate so that neighbouring elements appear side by side and can be compared directly. Measure the positions of the lines on the developed plate, reduce them to glancing angles, and convert to wavelength with Equation (76.6). Identify in each spectrum the strong pair of lines belonging to Barkla's K series, and for the heavier elements the group belonging to the L series.

Observations and data

Every element examined shows the same small number of strong lines, and the lines move steadily and by regular steps as one passes from element to element along the plate. Plotting the square root of the frequency of the strongest K line against the ordinal number of the element in the periodic table gives a straight line, of a slope that the hydrogenic formula reproduces without adjustment; the same holds, with a different slope, for the L series. The first paper covered the range from calcium to zinc; the second extended it from aluminium to gold, using the K series for the lighter half of the range and the L series for the heavier [Moseley:1913] [Moseley:1914]. Between aluminium and gold the sequence of ordinal numbers is unbroken except at three places, corresponding to elements not then known and later found.

Interpretation

The consequences are structural rather than numerical. The periodic table acquires an exact ordinal parameter, so the three weight inversions that had embarrassed it since Mendeleev cease to be anomalies and become confirmations: the X-ray spectra put argon before potassium, cobalt before nickel and tellurium before iodine, which is the chemically correct order in every case. The number of elements between any two is fixed, so the count of missing elements ceases to be a matter of opinion; Moseley's range left exactly three gaps below gold, which is exactly what was later filled. The number of rare-earth elements, contested for decades, is likewise settled by counting the gaps in their L spectra. And the nuclear model of the atom acquires its missing parameter: after Moseley an element is specified by an integer \(Z\), the atomic weight being a separate and, as Nuclear Forces and Nuclear Structure shows, a compound quantity. The isotope — same \(Z\), different weight — becomes intelligible in the same stroke.

Primary references

[Moseley:1913] [Moseley:1914]. The independent scattering determination of the nuclear charge is [Chadwick:1920], resting on [Rutherford:1911]; the hypothesis tested is [vandenBroek:1913].

Siegbahn: precision X-ray spectroscopy (1916–1925)

Moseley's lines were sufficient for counting but not for anatomy. What looked like one line at his resolution is generally a group, and the groups are what a theory of the many-electron atom actually has to predict. Siegbahn spent a decade rebuilding the spectrometer around that requirement.

Apparatus

A vacuum spectrograph: the whole path from anticathode to plate is evacuated, so that soft radiation is not absorbed in air and the range of the instrument extends far beyond the K lines of the heavy elements. A demountable, water-cooled tube with interchangeable anticathodes, run at high load to obtain usable intensity in a narrow line. Precisely ruled circles carrying cleaved crystals of accurately known spacing — calcite, gypsum, sugar and mica were used for different ranges. Narrow slits and long crystal-to-plate distances for high dispersion. Photographic recording with comparison lines on the same plate. In the later work, ruled concave gratings used at grazing incidence, which measure a wavelength against a ruling interval and so make no assumption whatever about crystal structure.

Procedure

Photograph the spectrum of each anticathode element, measure the line positions against the comparison lines with a travelling microscope, reduce them to glancing angles, and convert to wavelength through Equation (76.6) with the tabulated crystal spacing. Repeat with different crystals to test for systematic error in the spacings. Separately, measure selected lines with the grazing-incidence grating and compare the two wavelength scales.

Observations and data

Each of Barkla's series resolves into a group of components: the K group into a close doublet and further lines, the L group into a set that requires three distinct L levels to explain it, the M group into a set requiring five. Every measured line frequency is a difference of two terms drawn from a table belonging to the element, so that the combination principle familiar from optical spectra holds here as well; the terms are the K, L\(_{1}\)–L\(_{3}\), M\(_{1}\)–M\(_{5}\) levels and their successors. The absorption edges measured in the same instrument fall at the term values themselves, just above the emission lines of the corresponding series, which identifies each term as the energy required to remove an electron from that level. Line wavelengths are reproducible to a few parts in ten thousand and better, which is what makes such an analysis possible at all [Siegbahn:1919] [Siegbahn:1925].

The comparison of the crystal scale with the grating scale exposed a systematic discrepancy of about two parts in a thousand. It was traced not to either instrument but to Equation (76.7): the crystal spacings had been computed with the value of \(N_{\mathrm{A}}\) then current, which rested in turn on the value of the elementary charge then current. Siegbahn's X unit, defined by reference to a crystal spacing, is therefore not exactly \(10^{-13}\,\mathrm{m}\), and X-ray wavelengths quoted in it must be corrected by that factor before being compared with anything measured optically.

Interpretation

Two results of lasting consequence come out of this work. The first is that the inner structure of the atom is directly readable. The multiplicities one, three, five are not fitted to the data; they are the counts of distinct inner levels, and any theory of the atom must reproduce them — as the quantum numbers of Atoms and Molecules and the spin-orbit coupling of Angular Momentum and Spin do. The identification of terms with absorption edges makes each of these levels a measurable binding energy, which is the quantity the excitation threshold of Phenomenon 76.4 had been signalling since Barkla.

The second is methodological, and it is the reason the discrepancy above is reported here rather than buried. A wavelength scale built on Equation (76.7) inherits every uncertainty in \(N_{\mathrm{A}}\), so an X-ray wavelength was never a purely spectroscopic quantity: it was tied to a mass, a density and a counting constant. That is no longer a limitation, since \(N_{\mathrm{A}}\) is exact by definition in the present SI (Measurement, SI Units, and the Theory of Errors); but the episode is a clean example of a systematic error that no amount of repetition inside one method can reveal, and that only an independent method — here the ruled grating — can expose.

Primary references

[Siegbahn:1919] [Siegbahn:1925].

What the X-ray spectra established

Taken in order, the six experiments make a single argument, and it is worth setting the conclusion down without hedging.

There exists a penetrating radiation emitted where fast electrons are stopped (Phenomenon 76.1). It is a transverse wave (Phenomenon 76.3), hence a solution of the field equations of The Maxwell Equations, with a frequency so far above every atomic resonance that matter is very nearly transparent to it and its refractive index is barely below one (Phenomenon 76.2). Its wavelength is comparable to the spacing of atoms in a solid, which both crystal diffraction (Phenomenon 76.5) and the reflection law built on it (Phenomenon 76.6) make measurable in absolute units. Each element, struck hard enough, emits a characteristic radiation of its own (Phenomenon 76.4), resolvable into a term system with a definite inner-shell structure (Phenomenon 76.8). And the integer that orders those spectra is the charge on the nucleus (Phenomenon 76.7).

The last statement is the one that reorganised chemistry. Before Moseley the periodic table was an empirical arrangement whose ordering principle — atomic weight — was known to fail in at least three places and whose length was unknown. After Moseley the table is indexed by an integer with a physical meaning, the number of protons in the nucleus, and the failures of the weight ordering are explained rather than tolerated: weight is a nuclear quantity that depends on neutron number as well, and two samples of one element may differ in it. Nuclear Forces and Nuclear Structure takes that up. What matters here is that the identification was not an interpretation placed on the data but a measurement, made twice by unrelated means — a spectroscopic plate and a count of scattered alpha particles — and agreeing.

It should be said plainly that this chapter also records how much can be achieved without a theory. Barkla ranked the elements correctly by a property he could not name, using an electroscope and a stack of aluminium foil. Von Laue's photograph settled a question in crystallography with a piece of zinc blende and a photographic plate. Moseley's decisive instrument was a spectrometer and a trolley pulled by a thread. In each case the quantum theory that explains the result arrived afterwards, and in Barkla's and von Laue's cases the discoverer guessed wrongly about the mechanism while being entirely right about the fact. The facts are what this treatise records; the explanations are checked against them, not the other way round.