X-rays and the Subatomic World

Danny Bankman
February 24, 2016

Submitted as coursework for PH241, Stanford University, Winter 2016


Fig. 1: The x-ray region of the electromagnetic spectrum and applications. (Source: "Wikimedia Commons")

X-rays have numerous practical applications in our everyday lives, including medical imaging, airport security, and structural analysis. It is undeniable that x-rays have played a major role in keeping us healthy and safe in the past century, since their discovery by Röntgen in 1895. [1-2] However, the utility of x-rays is not limited to the macroscopic scale. In more subtle ways than casting a shadow, x-rays have shaped our understanding of biology, chemistry, and physics down to the subatomic scale.

X-rays as a measurement tool owe their versatility to the region of the electromagnetic spectrum in which they reside (Fig. 1). With subnanometer wavelengths, x-rays can be used to probe the atomic structure of crystals and complex biomolecules, notably the DNA double helix. [3] In order to generate photons of such high energy, electrons must undergo energetic transitions within the atom. Characterizing the spectra of these emitted photons allowed Moseley to see into the internal structure of the atom, generating results that supported the theory of the atomic nucleus, which had been previously proven by Rutherford, Geiger, and Marsden. [4-7] The narrow wavelength of x-rays permits the characterization of nanoscale structures, and the high energy per photon (in the keV range) renders many macroscopic structures transparent.

Fig. 2: Röntgen's lab at the University of Würzburg, Germany. (Source: "Wikimedia Commons")

The First X-Rays

X-rays were discovered by Professor Wilhelm Röntgen at the University of Würzburg, Germany, in 1895. [2] At the time, Röntgen had intended to study cathode rays (electron beams), and to do so constructed a transformer capable of delivering 35,000V pulses between electrodes inside a low pressure gas tube. Today, a student of electronics traditionally receives stern warning about the dangers of dissecting a cathode ray tube even when it is turned off, due to the residual charge stored on capacitors with voltages in the kilovolt range. Röntgen suffered from no such fear of high voltage. Working alone in the dark (Fig. 2) on the night of November 8, 1895, Röntgen noticed a student's doodle of the letter "A" on a sheet of paper in platinocyanide solution glowing on the table. Röntgen quickly realized that because the sheet of paper was too far a distance from the tube for cathode rays to reach, the glowing must have been due to some other form of excitation. He wrote: "For brevity's sake I shall use the expression 'rays'; and to distinguish them from others of this name I shall call them 'X- rays'." [1]

During the following weeks, Röntgen took three x-ray images that set the stage for a century of applications. First, he took an x-ray photograph of his wife Bertha's hand, revealing the bones in her fingers. During the 15 minutes of exposure, she unfortunately received a lifetime dose of radiation. Second, Röntgen imaged his hunting rifle, revealing a small structural flaw for the first time without destroying the object under examination. Third, he imaged a closed wooden box of weights for a torsion scale, revealing the contents of the box without opening it. Röntgen summarized his findings in an article to be published on New Year's Day. On January 16th, an article about his recent results appeared in the New York Times. In 1901, Röntgen won the first Nobel Prize in physics, and donated all prize money to the University of Würzburg to be used as scholarships for students.

Fig. 3: Henry Moseley in the Balliol-Trinity College Laboratories at Oxford University soon after his graduation. (Source: "Wikimedia Commons")

Moseley's Law

The high voltages necessary for Röntgen's cathode ray experiments sent electrons hurtling towards a copper anode with energies in the keV range, enough to dislodge an electron in the innermost orbital of the copper atom with binding energy equal to 8.979 keV. This triggers a cascade of energetic transitions among outer electrons to refill the inner shell. The original energy level of the "falling" electron together with the energy level of the vacancy it fills dictates the energy of the photon emitted by the transition. The energy levels accessible to electrons depend on the number of protons in the nucleus of the atom, a number which uniquely specifies its elemental identity. One such characteristic energy transition of the copper atom, known as Cu Kα, releases photons of wavelength 0.15418 nm, in the x-ray region of the electromagnetic spectrum.

In the decades following Röntgen's discovery, the inner structure of the atom was hot a subject of debate. In 1911, Professor Ernest Rutherford at the University of Manchester published a paper which proved the theory of the atomic nucleus backed by data collected by researchers Geiger and Marsden. [5-7] The now famous gold foil experiment showed that the distribution of scattering angles of alpha particles by atoms in a thin foil was not consistent with the theory that an atom's positive charge is distributed uniformly throughout its radius. If the positive charge were distributed uniformly, the alpha particles would have undergone many scattering events, which probabilistically lead to small scattering angles. Rather, Geiger and Marsden observed several large (greater than 90 degree) scattering angles that should have occurred with vanishingly small probability had the theory of uniformly distributed positive charge been correct. Rutherford found that the significant frequency of large scattering angles fit with a model of the atom containing a central charge surrounded by a cloud of electrons in void space.

In 1910, Henry Moseley (Fig. 3) joined Professor Rutherford's group with a passion for X-rays. Taking inspiration from William L. Bragg's 1912 work on x-ray diffraction, Moseley created an experimental setup for photographing the line spectra of x-rays emitted by metals under excitation by electron beams. By examining the spectra of the transition metals along the fourth period of the periodic table, Moseley found that as he moved from one element to the next, a quantity which he called Q scaled proportionally to the square root of the frequency of the element's Kα line. He wrote: "While, however, Q increases uniformly the atomic weights vary in an apparently arbitrary manner, so that an exception in their order does not come as a surprise. We have here a proof that there is in the atom a fundamental quantity, which increases by regular steps as we pass from one element to the next. This quantity can only be the charge on the central positive nucleus, of the existence of which we already have definite proof." [4] Moseley formalized his results with a Rydberg-like equation, which predicted the frequency of the line spectra emitted by any element, in terms of the atomic number, the energy levels of the transition, and a "screening factor" which accounted for the net charge seen looking at the positive nucleus surrounded by a partial cloud of negative electrons. Today, this equation is known as Moseley's Law.

When World War I broke out, Moseley insisted on taking a combat role in the British Army's Royal Engineers. At the age of 27, he was killed in action at the Battle of Gallipoli. Following Moseley's death, the American physicist Robert Millikan wrote: "In a research which is destined to rank as one of the dozen most brilliant in conception, skillful in execution, and illuminating in results in the history of science, a young man but twenty-six years old threw open the windows through which we can now glimpse the subatomic world with a definiteness and certainty never even dreamed of before. Had the European war had no other result than the snuffling out of this young life, that alone would make it one of the most hideous and most irreparable crimes in history."

© Danny Bankman. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] G. Barker, Röntgen Rays: Memoirs by Röntgen, Stokes, and J.J. Thomson, ed. by G. F. Barker (Harper and Brothers, 1898), p. 3.

[2] G. Farmelo, "The Discovery of X-rays," Scientific American 273, No. 5, 86 (November 1995).

[3] R. E. Franklin and R. G. Gosling, "Evidence For 2-Chain Helix in Crystalline Structure of Sodium Deoxyribonucleate," Nature 172, 156 (1953).

[4] H. Moseley, "The High-Frequency Spectra of the Elements," Phil. Mag. 26, 156 (1913).

[5] E. Rutherford, "The Scattering of α and β Particles by Matter and the Structure of the Atom," Phil. Mag. 92, 379 (Reprint 2012).

[6] H. Geiger and E. Marsden, "The Laws of Deflexion of α Particles Through Large Angles," Phil. Mag. 25, 604 (1913).

[7] B. Webber and E. Davis, "Commentary on: 'The Scattering of α and β Particles by Matter and the Structure of the Atom'," Phil. Mag. 92, 399 (2012).