Physics 1923

A Quantum Theory of the Scattering of X-Rays by Light Elements

Arthur H. Compton

An X-ray bouncing off an electron grows longer, like a billiard ball losing speed — light carries momentum as a particle.

Choose your version

In depth · the introduction

Shine X-rays at a block of carbon and the rays bounce back a different colour — and that small change settled a twenty-year argument about whether light is a wave or a particle.

The big idea

For a century light had been understood as a wave, and waves don't change their colour when they bounce. Yet when Arthur Compton fired X-rays at matter, the scattered rays came back “softer” — stretched to a slightly longer wavelength — and the more sharply they were deflected, the more they stretched.

His explanation was to treat the X-ray not as a wave but as a particle: a tiny bullet of light that carries momentum. When it hits an electron it knocks the electron flying, exactly like one billiard ball striking another, and bounces away with less energy — which for light means a longer wavelength. He could even write down the formula: the stretch depends only on the angle of the bounce, and on nothing else. The experiment matched the formula. Light, it turned out, hits like a thing.

How it came about

Einstein had suggested back in 1905 that light comes in packets, but for two decades most physicists treated that as a useful trick rather than a literal truth — the wave theory was simply too successful to abandon. Compton, working at Washington University in St. Louis, had been puzzling over an oddity in scattered X-rays that the wave theory could not explain.

Around 1922 he made the leap of giving each X-ray packet a definite momentum and treating its encounter with an electron as a straightforward collision. The numbers fell out cleanly, and his careful spectrometer measurements on graphite confirmed them. The Dutch physicist Peter Debye reached the same formula independently at almost the same moment. When others soon photographed the recoiling electrons flying off in step with the scattered rays, the case was closed. Compton received the Nobel Prize in 1927.

Why it mattered

This was the experiment that made the photon real. The photoelectric effect had hinted that light delivers energy in lumps, but Compton showed that light also carries momentum and recoils in collisions — behaving, in every mechanical sense, like a particle. After Compton you could no longer wave away the light quantum as a calculating convenience. Light is somehow both wave and particle at once, and accepting that paradox was the doorway into modern quantum mechanics, which arrived just two years later.

A way to picture it

Think of a game of pool. The cue ball (the X-ray) rolls in and strikes a resting ball (the electron). The cue ball can't pass through — it glances off, and the ball it hit rolls away carrying some of the speed. The cue ball leaves slower than it arrived. For light, “slower” isn't quite right — light always travels at light speed — so it sheds energy a different way: by stretching to a longer wavelength. And just as in pool, a glancing hit barely changes anything while a head-on collision robs the most speed, the X-ray's stretch is smallest for a slight deflection and largest when it bounces straight back. Use the tool below to aim the bounce and watch the wavelength grow.

Where it sits

Compton's collision is a hinge in the story of light. Behind it stand Planck (1900) and Einstein (1905), who first proposed that light comes in quanta, and Bohr (1913), who put quanta inside the atom; beside it stands the photoelectric effect, the other proof of the photon. In front of it stand de Broglie (1924), who turned Compton's logic around to give matter a wavelength, and Heisenberg, whose 1927 uncertainty principle uses the very recoil Compton discovered — the unavoidable kick a photon gives the electron you try to look at. Compton's measurement is the moment the particle of light stopped being a hypothesis and became a fact you could weigh.

The original document

Original source text

Arthur H. Compton · Physical Review, Series 2, vol. 21, no. 5, pp. 483–502 · May 1923 · Washington University, St. Louis

The problem — scattered X-rays come back “softer”

On the wave theory of light, an X-ray passing through matter should set the electrons oscillating at its own frequency, and they should re-radiate at exactly that frequency: the scattered ray ought to have the same wavelength as the incident ray, with an intensity falling off with angle as J. J. Thomson's classical formula prescribes. Yet measurements — Compton's own among them — showed that the scattered radiation was consistently “softer” (longer in wavelength, more easily absorbed) than the primary beam, and that this softening grew steadily as the scattering angle increased. Classical electrodynamics had no room for such a shift.

The hypothesis — one quantum strikes one electron

Compton breaks with the wave picture and treats the X-ray as a quantum carrying energy hν and momentum h/λ. He pictures it making a single relativistic elastic collision with one free electron, like one billiard ball striking another, and imposes conservation of energy and of momentum on the pair. The recoiling electron carries off energy and momentum; the scattered quantum, left with less of both, must emerge with a lower frequency — a longer wavelength.

The result

Working the conservation equations through, the increase in wavelength depends only on the scattering angle θ — not on the incident wavelength, and not on the scattering material: Δλ = (h/mₑc)(1 − cos θ). The constant h/mₑc, the Compton wavelength, equals 0.0243 Å (2.43 pm). The shift vanishes straight ahead (θ = 0) and reaches its maximum, twice the Compton wavelength, for back-scattering (θ = 180°).

The test — molybdenum X-rays on graphite

Compton scattered the molybdenum Kα line (about 0.71 Å) from a block of graphite — carbon being a “light element” whose electrons are loosely bound — and measured the wavelengths of the scattered rays with a Bragg crystal spectrometer at a series of angles. At each angle the spectrum showed a shifted (“modified”) line beside an unshifted one, and the displacement of the modified line grew with angle exactly as the formula required, reaching about 0.024 Å at 90°. His verdict was plain:

This remarkable agreement between our formulas and the experiments can leave but little doubt that the scattering of X-rays is a quantum phenomenon.

[ … ]

The paper closes by drawing the consequence its title only hints at: scattering is not a wave gently re-radiating, but a corpuscle of radiation, with definite energy and momentum, deflecting a single electron — direct evidence for the reality of the light quantum.

Arthur H. Compton · Washington University, St. Louis · 1923