A grain of green light carries too little energy to feel. A grain of gamma light from caesium carries three hundred thousand times as much, and a detector can hear every one arrive.
Chapter 12 · Beyond the visible
The Hardest Light
Light from inside the nucleus of an atom. Counting it one grain at a time, again, and catching it bouncing off an electron like a ball.
Look first
Counting, again
In chapter 5 the lamp was turned down until light arrived one detection at a time, and it took a very sensitive detector to register each one. Gamma rays need no such care. Caesium-137, a common laboratory source, sends out gamma rays of 662 keV, each with about 300,000 times the energy of a grain of green light. When one is absorbed in a crystal of sodium iodide, the crystal gives a flash of visible light bright enough for a photomultiplier to measure. The brighter the flash, the more energy the gamma ray left behind.
So a gamma detector does two things at once: it counts each grain, and it weighs it. Sort the flashes by brightness and you get a spectrum, built one count at a time. Start the source and watch it grow.
0 gamma rays counted
Press start.
computed Counts sorted by energy, in bins 5 keV wide.
Four features grow out of the noise. A tall, narrow peak at 662 keV, where the whole gamma ray was absorbed. A broad shelf to the left of it that stops at a sharp edge near 480 keV. A small hump near 190 keV. And a narrow peak at 32 keV, from X-rays given off by the barium atom that caesium becomes. The shelf, the edge and the hump all come from one event, seen from different sides.
Commit to a prediction
A head-on bounce
A 662 keV gamma ray meets a loose electron and bounces straight back the way it came, as a ball bounces off a wall.
What energy does the gamma ray keep?
The same spectrum, finished and labelled.
Now the spectrum reads like a sentence. A gamma ray that bounces off an electron inside the crystal and escapes leaves only the electron’s share behind, anywhere from nothing up to the head-on case, 662 − 184 = 478 keV: that is the shelf and its edge. A gamma ray that bounces back off the shielding behind the source, and then is absorbed in the crystal, arrives carrying what a head-on bounce leaves it, about 184 keV: that is the hump.
Why the first guesses made sense
Light carries a push
If you chose all of it, you were reasoning from everything this exhibition has shown about light as a wave. A wave that sets an electron shaking is re-radiated at the same frequency, which is why a mirror does not change colours. For visible light that is very nearly true.
But light also carries momentum, its energy divided by the speed of light. Treat a gamma ray as a particle with that much push, and the bounce is a collision: energy and momentum must both balance, as they do for billiard balls. Whether the electron takes a little or a lot depends on how the gamma ray’s energy compares with the electron’s own mass-energy, 511 keV. For green light, 2.25 eV, the ratio is tiny: a ping-pong ball against a bowling ball, bouncing back almost unchanged. For a 662 keV gamma ray it is larger than one: closer to two snooker balls, and the electron takes most of it.
If you chose none, you were right that a head-on collision gives the target the most, and wrong only in thinking it could take everything: the gamma ray cannot stop, because something must carry its momentum backward.
The bench
Bounce any light off an electron
Choose the energy of the incoming light and the angle it bounces through. The arrows show the momenta to scale: the incoming light, the outgoing light, and the electron’s recoil, which closes the triangle. The polar plot shows where scattered light tends to go: evenly forward and back at low energies, more and more forward as the energy rises.
The collision
A case you have not seen
Why nobody saw it sooner
Arthur Compton found this effect in 1923 with X-rays, and noticed something striking about it: the change in wavelength depends only on the angle, never on the wavelength itself. Bounced through a right angle, any light gets longer by the same 2.4 picometres.
Now take green light, 550 nm, and bounce it straight back off a free electron.
What share of its energy does it lose?
The same law covers both. Bounced straight back, any light gets longer by about five picometres. That more than triples the wavelength of a caesium gamma ray, and adds a hundred-thousandth to green light’s. That is why light looked like a pure wave for a century after Young: its push was always there, but at the energies anyone could see it was far too small to notice. It took X-rays, with wavelengths only thirty times the shift, to make the particle side of light impossible to ignore.
What you can now say
Light arrives in grains that carry energy and a push. At gamma-ray energies each grain is large enough to count and weigh, and when one bounces off an electron the two share energy and momentum like colliding balls.
The wavelength grows by the same few picometres whatever the light, which is huge for a gamma ray and invisible for green light.
For the determined reader: the Compton formula, Klein and Nishina, and the limits
The collision
A photon of energy E has momentum E/c. Conserving energy and momentum with an electron at rest, of rest energy mc2 = 511.0 keV, gives
E′ = E / (1 + (E/mc2)(1 − cosθ)), λ′ − λ = (h/mc)(1 − cosθ), h/mc = 2.426 pm
At θ = 180° the electron receives the most it can, the Compton edge, E · 2ε/(1 + 2ε) with ε = E/mc2: 477 keV for caesium’s 662 keV.
Where the light goes
Oskar Klein and Yoshio Nishina worked out in 1929 how likely each angle is, from Dirac’s new theory of the electron: dσ/dΩ = (re2/2) P2(P + 1/P − sin2θ), with P = E′/E and re = 2.818 fm. At low energy it reduces to the classical result for a wave shaking an electron, the same forward and back; at high energy it leans forward. Its total, at 662 keV, is per electron, about 39% of the low-energy value.
Where this stops
Electrons in atoms are bound, not free; for gamma rays the difference is small, and for visible light it is everything, since a bound electron in glass or air does not recoil on its own. The detector is schematic: the shares of photopeak, single-scatter and backscatter events depend on the crystal’s size and the shielding, and real spectra also show multiple scatters and pile-up. The energies of every feature are exact.
A third kind of ray, and a ball of light
In 1900, studying radium in Paris, Paul Villard found a radiation that a magnet could not bend and that passed through layers of lead that stopped the other rays. Ernest Rutherford, who had already named the first two kinds of radioactivity alpha and beta, called it gamma. In 1914 he and Edward Andrade showed it could be diffracted by a crystal: it was light, with a wavelength smaller than an atom.
Einstein had proposed in 1905 that light comes in quanta, and for nearly twenty years most physicists, including Planck and Bohr, would not believe it. In 1923 Arthur Compton, at Washington University in St Louis, scattered X-rays from molybdenum off a block of graphite and measured their wavelength with a crystal spectrometer. The scattered rays were longer, by an amount that grew with the angle exactly as a collision between two particles would require. He received the Nobel Prize in 1927. After Compton, light’s push was no longer a matter of opinion.
Where this explanation stops
The whole spectrum
This room has walked from Jansky’s 14.6 metres to caesium’s 1.9 picometres: nearly thirteen factors of ten, all of it the same kind of thing as the green light in the first room. At the long end, light behaves as a wave so plainly that telescopes must be the size of the Earth. At the short end, it behaves as a particle so plainly that it can be counted, weighed and bounced. In the middle, where our eyes are, it does both, and we needed every chapter to see it.
Light bends around a pinhole like a wave and knocks an electron aside like a ball. What kind of thing can do both?
End of the second room
Added to your notebook
Light arrives in grains that carry energy and a push. When a gamma ray bounces off an electron, the two share energy and momentum like colliding balls.
What kind of thing can be both a wave and a ball?