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Physics 1911

The Scattering of α and β Particles by Matter and the Structure of the Atom

Ernest Rutherford

An atom is mostly empty space, its mass and charge packed into a tiny central nucleus.

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In depth · the introduction

Fire tiny bullets at a thin sheet of gold and almost all sail through — but a stubborn few come bouncing straight back, and that is how we found the atom's core.

The big idea

At the start of the twentieth century everyone pictured the atom as a soft, even ball of positive charge with electrons dotted inside — a kind of plum pudding. Rutherford's team tested it by shooting α particles (fast, heavy, positively charged specks) at a gold foil only a few thousand atoms thick.

A pudding-like atom should let every particle pass with at most a tiny nudge. Instead, a small number were deflected enormously — some came almost straight back. The only way to throw a fast, heavy particle backwards is to hit something small, hard and intensely charged. Rutherford concluded that nearly all of an atom's mass and all of its positive charge sit in a minute core at the centre, with the electrons far outside and almost everything in between being empty space.

How it came about

At the University of Manchester, Rutherford set Hans Geiger and a young student, Ernest Marsden, to count faint flashes as α particles struck a screen — patient, eye-straining work done in the dark. In 1909 Marsden checked, almost as an afterthought, whether any particles came back toward the source. To everyone's astonishment, a few did.

Rutherford turned the surprise over for more than a year. He later said it was “quite the most incredible event that has ever happened to me in my life — almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” By 1911 he had the mathematics: a single close pass by a concentrated central charge could fling an α particle backwards, and the numbers of particles at each angle followed a precise rule he could write down.

Why it mattered

This is the moment the atom got a centre. The nuclear picture replaced the featureless pudding and became the foundation of all later physics of matter — leading directly to Bohr's model two years later, and eventually to the discovery of the proton, the neutron, and nuclear energy. It also established a method that still drives discovery: to learn what something is made of, shoot particles at it and study how they scatter.

A way to picture it

Imagine rolling marbles across a dark room toward a hidden object, over and over, and recording which way each one bounces. Most roll straight through, telling you the room is mostly empty. But every so often one ricochets sharply back — and from how often that happens, and at what angles, you can work out that there is a small, hard, heavy peg somewhere in the middle, even though you never see it directly. The α particles are the marbles; the nucleus is the peg.

Interactive Rutherford scattering: an α particle approaches a small positively charged nucleus from the left; a slider sets how nearly head-on the shot is, bending the path more and more — a near miss barely turns, a near-direct hit is flung almost straight back. A toggle switches the target between a gold and an aluminium nucleus.

Where it sits

A century earlier, Dalton had revived the idea that matter is made of atoms, and J. J. Thomson had just found the electron — but the atom was still imagined as a soft, structureless blob. Rutherford gave it architecture: a hard centre and a vast empty surround. Yet his nuclear atom should have collapsed in an instant under classical physics; it was Niels Bohr who, in 1913, used the new quantum ideas to make the orbiting electrons stable. From Rutherford's core run the lines to the proton, the neutron, and the entire scattering method that later laid bare the quarks inside.

The original document
Original source text
E. Rutherford · Philosophical Magazine, Series 6, 21 (1911): 669–688
§ 1 — The problem
It is well known that the α and the β particles suffer deflexions from their rectilinear paths by encounters with atoms of matter.
Rutherford opens by separating two ideas. A particle may be turned a little by each of many atoms it passes — he calls this “compound” scattering — or it may be turned through a considerable angle by a single close encounter, which he calls “single” scattering. The accepted Thomson atom, with its positive charge spread thinly through the whole sphere, could only ever give the gentle, compound kind.
But Geiger and Marsden had just found something the spread-out atom could not explain — a few α particles turned right around. Rutherford quotes their result:
If the high velocity and mass of the α-particle be taken into account, it seems surprising that some of the α-particles, as the experiment shows, can be turned within a layer of 6 × 10⁻⁵ cm. of gold through an angle of 90°, and even more.
§ 2 — A single encounter
It seems reasonable to suppose that the deflexion through a large angle is due to a single atomic encounter, for the chance of a second encounter of a kind to produce a large deflexion must in most cases be exceedingly small.
A simple calculation shows that the atom must be a seat of an intense electric field in order to produce such a large deflexion at a single encounter.
Rutherford then treats the α particle and the atom's charge as points obeying the inverse-square law, and works out the hyperbolic orbit. The geometry ties the deflexion angle to how nearly head-on the shot is, and predicts that the number of particles scattered at an angle φ should vary as cosec⁴(φ/2) — falling off steeply, but never to zero, so that very large angles, though rare, are not forbidden.
[ … ]
§ 4 — The structure of the atom
Considering the evidence as a whole, it seems simplest to suppose that the atom contains a central charge distributed through a very small volume, and that the large single deflexions are due to the central charge as a whole, and not to its constituents.
He is careful about what the experiment can and cannot show: the sign of the central charge is left open (a positive or a negative core of the same magnitude would scatter the α the same way), and its magnitude comes out roughly proportional to the atomic weight. The word “nucleus” does not yet appear — that name, and the identification of the central charge with the atomic number, came in the two years that followed.
University of Manchester · April 1911