Arthur Compton

How to use this course

Arthur Compton is known for one formula, the shift in wavelength of X-rays scattered by electrons. The experiment behind it, done in St. Louis in 1922, persuaded most physicists that light quanta carry momentum as well as energy, seventeen years after Albert Einstein proposed them. Compton went on to measure X-ray wavelengths with ruled gratings, to show with a worldwide survey that cosmic rays are mostly charged particles, and, in the Second World War, to direct the laboratory where Enrico Fermi’s team built the first nuclear reactor and where the plutonium production reactors were designed.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The order follows his research: X-ray diffraction (1913–1919), the Compton effect (1919–1925), X-ray optics (1922–1925), cosmic rays (1930–1940) and nuclear fission (1941–1945).

Timeline

Wooster, 1892–1913

Arthur Holly Compton was born on 10 September 1892 in Wooster, Ohio. His father, Elias Compton, was a Presbyterian minister and professor of philosophy who became dean of the University of Wooster, a small Presbyterian college. His mother, Otelia Augspurger, was later named American Mother of the Year (1939). The household was devout, hard-working and ambitious for its children. All three sons earned Princeton doctorates and became college presidents or chancellors: Karl Taylor Compton led the Massachusetts Institute of Technology from 1930 to 1948, Wilson Compton the State College of Washington, and Arthur Washington University. Their sister Mary married a missionary educator, C. Herbert Rice, principal of Forman Christian College in Lahore.

As a young man Arthur was a keen amateur astronomer; he photographed Halley’s comet in 1910. He enrolled at the College of Wooster, where his father taught, and graduated with a BS in 1913. As a student he devised a method for demonstrating the Earth’s rotation with a ring of water in a tube, now called the Compton generator, around 1913.

Princeton, Minnesota, Westinghouse, 1913–1919

Compton followed Karl to Princeton, where he took an MA in 1914 and a PhD in 1916. His advisor was Hereward Lester Cooke. X-ray crystallography was only two years old: Max von Laue’s diffraction experiment dated from 1912, and William Henry and Lawrence Bragg had just built the first X-ray spectrometer. Compton’s thesis, published in 1917 as “The intensity of X-ray reflection, and the distribution of the electrons in atoms”, used measured reflection intensities to test models of where electrons sit in an atom. Lesson 04 explains the method.

In June 1916 he married Betty Charity McCloskey, whom he had met at Wooster. They had two sons, Arthur Alan, who joined the US Foreign Service, and John Joseph, who became a professor of philosophy at Vanderbilt University.

After one year teaching at the University of Minnesota (1916–17) he took a post as research engineer with the Westinghouse Lamp Company in East Pittsburgh, where he worked on the sodium-vapour lamp. During the First World War he also developed aircraft instruments for the Army Signal Corps. The industrial years gave him practical skill and an income, but he wanted to return to fundamental research.

Cambridge and St. Louis, 1919–1923

In 1919 Compton won one of the first National Research Council fellowships and spent a year at the Cavendish Laboratory in Cambridge, then directed by Ernest Rutherford. He was deeply impressed by Rutherford, Charles Galton Darwin and Arthur Eddington. Working with gamma rays, he found that the scattered radiation was softer, that is more easily absorbed, than the primary beam, and that the effect grew with scattering angle. Classical electromagnetic theory, in the form J. J. Thomson had given it, predicted scattered radiation of the same wavelength as the incident. Compton at first tried to explain the difference with a large, ring-shaped electron and with fluorescence.

In 1920 he became Wayman Crow Professor and head of the physics department at Washington University in St. Louis. There he repeated the experiment with X-rays, whose wavelengths he could measure directly with a Bragg crystal spectrometer. Over 1922 the data forced a new explanation, and by the end of that year he had it: a light quantum colliding with a single electron as one billiard ball strikes another. Lessons 05 and 06 tell the story. In 1923 he moved to the University of Chicago, where he stayed for twenty-two years.

X-ray reflection and the electrons in atoms

For the general reader. X-rays bouncing off a crystal reinforce one another only at special angles, set by the spacing of the atomic layers. How strong each reflection is depends on how the electrons are spread through each atom. Compton’s doctoral thesis was one of the first attempts to read the shape of atoms from these strengths.

The path difference between rays reflected from adjacent planes is \(2d\sin\theta\); constructive interference requires a whole number of wavelengths.

Form factor and structure factor

A single free electron scatters X-rays with amplitude set by the Thomson formula (Lesson 07). An atom with electron density \(\rho(\mathbf r)\) scatters with amplitude multiplied by its form factor, the Fourier transform of the density at the scattering vector \(\mathbf q\), with \(|\mathbf q|=4\pi\sin\theta/\lambda\):

For a unit cell with atoms at fractional positions \((x_j,y_j,z_j)\), the reflection with Miller indices \((hkl)\) has structure factor

If the electrons were concentrated at the nucleus, \(f\) would equal \(Z\) at all angles and intensities would fall off only through polarization and thermal factors. Compton argued, from measured intensities of rock-salt reflections, that the electrons must be spread over distances comparable to the atomic spacing, so that \(f\) falls with angle.

The Compton effect

For the general reader. When X-rays bounce off the electrons in a block of carbon, some come out with a longer wavelength than they went in with, and the change depends only on the angle. Waves cannot do this, but particles can: a quantum of light that knocks an electron aside loses some energy, and lower energy means longer wavelength. Compton’s 1923 paper treated the collision exactly like one between two balls and got the shift right.

Derivation with four-momenta

Let \(k,k'\) be the photon four-momenta and \(p,p'\) the electron’s, with \(p=(mc,\mathbf 0)\). Conservation gives \(p'=p+k-k'\). Squaring, with \(p^2=p'^2=m^2c^2\) and \(k^2=k'^2=0\),

With \(k=(E/c,\mathbf k)\), the Minkowski products are \(p\cdot k=mE\), \(p\cdot k'=mE'\), and \(k\cdot k'=(EE'/c^2)(1-\cos\theta)\). Hence

and with \(E=hc/\lambda\) this is the Compton formula. The shift does not depend on the wavelength or on the material, only on the angle.

The experiment

Compton sent molybdenum K\(\alpha\) X-rays (\(\lambda=0.711\) Å) onto a graphite block and analysed the scattered rays with a calcite crystal spectrometer and ionization chamber at several angles. At each angle he saw two lines: one at the original wavelength and one shifted by close to \(\lambda_C(1-\cos\theta)\), about 0.024 Å at \(90^\circ\). The unshifted line comes from scattering by electrons tightly bound to the atom, so that the whole atom takes up the recoil; replacing \(m\) by the atomic mass makes the shift negligible. Peter Debye published the same quantum analysis independently in Physikalische Zeitschrift in 1923, within weeks of Compton.

Recoil electrons and the reality of the photon

For the general reader. Compton’s formula could only be right if each scattered photon came with a recoiling electron, at a definite angle, at the same instant. In 1924 Niels Bohr and colleagues proposed a theory in which energy was conserved only on average, which would remove the need for photons. Experiments by Walther Bothe and Hans Geiger, and by Compton and Alfred Simon, tested this directly in 1925, and the photon won.

Derivation. Transverse momentum balance gives \(p_e\sin\varphi=(E'/c)\sin\theta\); longitudinal balance gives \(p_e\cos\varphi=E/c-(E'/c)\cos\theta\). Dividing, \(\cot\varphi=(E/E'-\cos\theta)/\sin\theta\). Substituting \(E/E'=1+\varepsilon(1-\cos\theta)\) gives \(\cot\varphi=[(1-\cos\theta)(1+\varepsilon)]/\sin\theta=(1+\varepsilon)\tan(\theta/2)\).

Duane’s objection

William Duane at Harvard could not at first reproduce the shifted line and argued that it came from secondary radiation in the apparatus. The two argued at the American Physical Society meeting of December 1923 and again at the British Association meeting of 1924. Later in 1924 Duane’s group found the shifted line and he withdrew his objection.

Bohr–Kramers–Slater and the coincidence tests

In 1924 Niels Bohr, Hendrik Kramers and John Slater proposed that atoms interact with radiation through a virtual field, with energy and momentum conserved only statistically. Recoil electrons and scattered photons would then be uncorrelated in time and direction. Bothe and Geiger in Berlin used two counters and found coincidences in time between recoil electrons and scattered quanta. Compton and Simon in Chicago photographed recoil electrons and the tracks of secondary electrons ejected by scattered photons in a Wilson cloud chamber, and found the angles agreed with the formula above. Bohr accepted that the proposal was refuted. Both experiments were completed in 1925, months before the new quantum mechanics of Werner Heisenberg appeared.

Cross-sections: Thomson to Klein–Nishina

For the general reader. How likely is an X-ray to be scattered, and in which direction? At low energies classical physics gives a clean answer, the Thomson formula. Compton’s experiments showed this fails at high energies, where scattering becomes weaker and more forward. In 1929 Oskar Klein and Yoshio Nishina derived the exact quantum answer from Paul Dirac’s theory of the electron.

As \(E\to0\), \(E'/E\to1\) and the bracket becomes \(2-\sin^2\theta=1+\cos^2\theta\), recovering Thomson. At high energies \(E'/E\) is small at large angles, so backward scattering is suppressed and the total cross-section falls roughly as \((mc^2/E)\ln(2E/mc^2)\). Compton’s measured absorption coefficients for hard X-rays and gamma rays were among the first evidence that scattering decreases with energy.

X-ray optics: total reflection and ruled gratings

For the general reader. X-rays pass almost straight through matter, and for years it seemed they could not be reflected or focused like light. Compton showed in 1922–23 that at very shallow angles a polished surface reflects X-rays completely. That made it possible, in 1925, to diffract X-rays from an ordinary ruled grating, whose spacing is known by construction, and so to measure X-ray wavelengths absolutely. The result fed back into the value of the electron’s charge.

Sketch. A free electron driven at angular frequency \(\omega\) gives a dielectric constant \(\epsilon=1-\omega_p^2/\omega^2\) with \(\omega_p^2=n_ee^2/(\varepsilon_0m)\). Then \(n\approx1-\omega_p^2/(2\omega^2)\), which equals the expression above. Snell’s law with glancing angles gives \(\cos\theta=n\cos\theta'\); total reflection begins when \(\cos\theta_c=n\), and \(1-\theta_c^2/2=1-\delta\).

Gratings and the value of e

With Richard Doan in 1925, Compton diffracted X-rays from a speculum-metal grating ruled with lines of known spacing, at glancing angles below \(\theta_c\). For incidence and diffraction measured from the grating surface, the grating equation is

This gave X-ray wavelengths independent of any crystal. Crystal spacings had been computed from the density and Avogadro’s number, that is, from Millikan’s \(e\). When later measurements, notably by John Bearden, compared grating and crystal wavelengths, they disagreed by a few parts in a thousand. The discrepancy was resolved by revising \(e\) upward and correcting the viscosity of air used in the oil-drop experiment.

The world cosmic-ray survey

For the general reader. Robert Millikan believed cosmic rays were very energetic light. If instead they were charged particles, the Earth’s magnetic field would turn the weaker ones away from the equator. Compton organized measurements across the globe and found the intensity really did fall toward the magnetic equator. Within a year others showed more particles came from the west than from the east, so the particles were mostly positive.

Jacob Clay had reported lower ionization near the equator on sea voyages to Java in 1927–28, but the result was disputed. Compton planned a systematic survey for 1932. He and collaborators carried identical ionization chambers on expeditions that, according to his National Academy memoir, ranged from about 46° S to 68° N, at sea level and on mountains. Plotted against geographic latitude the data scattered; plotted against geomagnetic latitude, measured from the axis of the Earth’s dipole field, they fell on one curve, flat at high latitudes and dipping toward the magnetic equator.

Compton presented his results at the end of 1932. Millikan, whose earlier measurements had shown little latitude dependence, disputed them publicly, and the newspapers made it a duel. Further measurements, including Millikan’s own group’s, confirmed the effect within a year. In 1933 Thomas Johnson, and independently Luis Alvarez working with Compton in Mexico City, found the west-to-east excess that identified the primaries as mainly positive. They are now known to be mostly protons, with helium and heavier nuclei.

The chain reaction and plutonium

For the general reader. When a uranium nucleus splits, it releases two or three neutrons that can split other nuclei. If on average more than one of them goes on to cause another fission, the reaction grows. Compton’s laboratory in Chicago showed this could be controlled, and used the neutrons to turn uranium-238 into a new element, plutonium, that could fuel a bomb.

A fraction of about 0.65 % of fission neutrons in uranium-235 are emitted with delays of seconds to a minute. Keeping \(k\) just above 1 using prompt neutrons alone makes the effective generation time long enough for control rods to respond. On 2 December 1942, under the west stands of Stagg Field, Fermi’s team withdrew the cadmium control rod of Chicago Pile-1, a lattice of natural uranium and uranium oxide in graphite, and measured a self-sustaining reaction with \(k\) just above 1.

Making plutonium

Plutonium-239 fissions with slow neutrons like uranium-235 but, being a different element, can be separated chemically rather than by isotope separation. The Metallurgical Laboratory designed the X-10 pilot reactor at Clinton (Oak Ridge), Tennessee, and the production reactors at Hanford, Washington, whose plutonium was used in the Trinity test and the Nagasaki bomb.

The Metallurgical Laboratory and the bomb, 1941–1945

Compton received the Nobel Prize in Physics in 1927, shared with C. T. R. Wilson, whose cloud chamber had photographed the recoil electrons. Through the 1930s he led the Chicago department, ran the cosmic-ray programme with a group that at various times included Alvarez, Pierre Auger and Ernest Wollan, and wrote with Samuel Allison the standard text X-Rays in Theory and Experiment (1935). He served as president of the American Physical Society (1934) and of the American Association for the Advancement of Science (1942).

In 1941 Vannevar Bush asked him to chair a National Academy of Sciences committee on the military value of uranium. Its reports helped persuade the government to commit to a bomb. In December 1941 he was put in charge of the work on the chain reaction and plutonium production, and early in 1942 he concentrated it at Chicago under the name Metallurgical Laboratory, bringing in Fermi and Leo Szilard from Columbia and Eugene Wigner from Princeton. In mid-1942 he gave J. Robert Oppenheimer responsibility for fast-neutron and bomb-design studies, the group that grew into Los Alamos. After Chicago Pile-1 went critical, he telephoned James Conant with a coded message that the Italian navigator had landed in the new world.

As director of the Metallurgical Project he oversaw the reactors at Argonne, Clinton and Hanford. In 1945 he served with Fermi, Oppenheimer and Ernest Lawrence on the Scientific Panel advising Secretary of War Henry Stimson’s Interim Committee. The panel reported in June 1945 that it could propose no technical demonstration likely to end the war and saw no alternative to direct military use. Many Met Lab scientists disagreed; at Compton’s request Farrington Daniels polled them in July 1945, and Compton forwarded the results. He defended the decision for the rest of his life, most fully in Atomic Quest (1956). He received the Medal for Merit for his war work.

Chancellor, believer and legacy, 1945–1962

In 1945 Washington University in St. Louis chose Compton as its ninth chancellor, and he was inaugurated in 1946. He expanded its research and raised it toward national standing. He stepped down in 1954 to become Distinguished Service Professor of Natural Philosophy, and in 1961 planned to divide his time as professor-at-large between Washington University, the University of California at Berkeley and the College of Wooster.

Religion was central to his life. He was an elder of the Second Presbyterian Church in St. Louis and wrote and spoke often on science and faith. In The Freedom of Man (1935) he argued that quantum indeterminacy leaves room for human free will, a view he developed into a two-stage model in which chance proposes and choice decides. He was also active in movements for international understanding and in Christian service organizations.

He died of a cerebral haemorrhage in Berkeley on 15 March 1962, aged 69, and was buried in Wooster.

Legacy

• The photon: the Compton effect and the coincidence experiments made light quanta with momentum part of physics, and prepared the ground for quantum mechanics.
• Everyday physics: Compton scattering shapes X-ray imaging, radiotherapy dose, gamma-ray detectors and the Compton camera; inverse Compton scattering is central to high-energy astrophysics and the Sunyaev–Zel’dovich effect.
• Units: the Compton wavelength \(h/mc\) is a fundamental length for any particle.
• Cosmic rays: the latitude survey established that the primaries are charged.
• Nuclear energy: the laboratory he founded became Argonne National Laboratory, and the reactors he oversaw were the first of their kind.
• Honours: NASA’s Compton Gamma Ray Observatory (1991–2000) bears his name, as does a lunar crater shared with his brother Karl.

Connections

People linked to Arthur Compton across this collection. A name without a link has no page here yet. See Arthur Compton in the network of all 337 lives →

Teachers and advisors

• Hereward Lester Cooke 1916

Students

• Luis Alvarez 1936

Influenced by

• Albert Einstein
• Ernest Rutherford 1919-1920

Colleagues and collaborators

• C. T. R. Wilson 1927
• Enrico Fermi 1942-1945
• J. Robert Oppenheimer 1942-1945
• Peter Debye 1923
• Alfred W. Simon 1925
• Eugene Wigner 1942-1945
• Leo Szilard 1942-1945
• Richard L. Doan 1925
• Samuel K. Allison

Rivals

• Peter Debye 1923
• Robert Millikan 1932-1933
• William Duane 1923-1924

Family

• Karl Taylor Compton

Also mentioned in this life

• Amedeo Avogadro
• Niels Bohr
• Paul Dirac
• Arthur Eddington
• Joseph Fourier
• Benjamin Franklin
• Hans Geiger
• Edmond Halley
• Werner Heisenberg
• J. J. Thomson
• Felix Klein
• Lawrence Bragg
• Hendrik Antoon Lorentz
• Hermann Minkowski
• Max von Laue

Fields

• cosmic rays 3 lives
• nuclear physics 13 lives

On CoursesHub

• Nuclear Physics

Sources and further reading

Biography

1. Arthur Compton, Wikipedia.
2. Arthur H. Compton, biographical, NobelPrize.org.
3. S. K. Allison, Arthur Holly Compton 1892–1962, Biographical Memoirs of the National Academy of Sciences.
4. A. H. Compton, Atomic Quest: A Personal Narrative, Oxford University Press, 1956.
5. R. S. Shankland (ed.), Scientific Papers of Arthur Holly Compton: X-Ray and Other Studies, University of Chicago Press, 1973.
6. AIP Center for History of Physics, Compton’s selected papers.

Physics

1. A. H. Compton, The intensity of X-ray reflection, and the distribution of the electrons in atoms, Physical Review 9 (1917) 29–57.
2. A. H. Compton, A quantum theory of the scattering of X-rays by light elements, Physical Review 21 (1923) 483–502.
3. P. Debye, Zerstreuung von Röntgenstrahlen und Quantentheorie, Physikalische Zeitschrift 24 (1923) 161–166.
4. A. H. Compton and A. W. Simon, Directed quanta of scattered X-rays, Physical Review 26 (1925) 289–299.
5. A. H. Compton, X-rays as a branch of optics, Nobel lecture, 1927.
6. O. Klein and Y. Nishina, Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac, Zeitschrift für Physik 52 (1929) 853–868.
7. A. H. Compton, A geographic study of cosmic rays, Physical Review 43 (1933) 387–403.
8. A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment, Van Nostrand, 1935.
9. R. H. Stuewer, The Compton Effect: Turning Point in Physics, Science History Publications, 1975.
10. Compton scattering, Wikipedia.