Rutherford's Gold Foil Experiment: How Bouncing Alpha Particles Revealed the Nucleus

Rutherford’s gold foil experiment was really a series of experiments by Hans Geiger and Ernest Marsden at the University of Manchester, from 1909 to 1913. They fired alpha particles at thin metal and counted where they landed. Nearly all went straight through or were turned by about a degree, but about one in eight thousand bounced back from a metal plate. No atom of spread-out charge could do that. In 1911 Ernest Rutherford explained it: almost all of an atom’s mass, and its positive charge, sits in a minute centre. We now call it the nucleus.

The atom everybody believed in

In March 1904 J. J. Thomson, Cavendish Professor of Experimental Physics at Cambridge, described atoms as “a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification”. The corpuscles are what we call electrons. The picture has a nickname Thomson never used, the plum pudding: the electrons are the plums, the positive charge is the pudding.

The important thing about such an atom is what it lacks. Its positive charge is spread thinly through the whole sphere, so nowhere inside is the electric force very strong.

The probe was the alpha particle. In 1908, at Manchester, Rutherford and Thomas Royds trapped alpha particles in a sealed glass tube, passed a spark through it and saw the spectrum of helium. Today we would say an alpha particle is a helium nucleus, two protons and two neutrons. The same year Rutherford won the Nobel Prize in Chemistry, “for his investigations into the disintegration of the elements, and the chemistry of radioactive substances”.

Alpha particles are fast and heavy. In his 1911 paper Rutherford took their speed as 2.09 × 10⁹ centimetres per second, about 20,900 kilometres a second, and an alpha particle is about 7,300 times heavier than an electron. Fired into a plum-pudding atom, it should barely notice. The light electrons cannot turn it, and the spread-out positive charge only nudges it. As Rutherford put it, Thomson’s structure “does not admit of a very large deflexion of an α particle in traversing a single atom”.

Counting flashes in the dark

Rutherford came to Manchester in 1907, and his assistant there was the German physicist Hans Geiger. To see a single alpha particle, they let it hit a screen coated with zinc sulphide. Each hit makes a tiny flash of light, a scintillation. In a darkened room, you count the flashes through a microscope, one by one. It is slow work. Rutherford wrote to the American physicist Henry Bumstead in July 1908:

Geiger is a demon at the work of counting scintillations and could count at intervals for a whole night without disturbing his equanimity. I damned vigorously and retired after two minutes. — Rutherford to H. Bumstead, 11 July 1908

Geiger found that alpha particles passing through thin metal were scattered only a little, “of the order of one degree”, in Rutherford’s words. Then, as Rutherford told it many years later, Geiger asked whether young Marsden, whom he was training, ought to begin a small research. Ernest Marsden was an undergraduate, 20 years old in 1909. Rutherford’s answer: “Why not let him see if any α-particles can be scattered through a large angle?” He added: “I may tell you in confidence that I did not believe that they would be.”

Memory is not perfect. Marsden later remembered Rutherford’s words as “See if you can get some effect of alpha-particles directly reflected from a metal surface.” Either way, it was a long shot.

One in eight thousand: what the gold foil experiment found

The set-up in Geiger and Marsden’s paper is simple. A conical glass tube full of radium emanation, the gas we call radon, is closed by a thin mica window. A lead plate stands between the tube and a zinc sulphide screen, so no alpha particle can reach the screen directly. The screen can only light up if something sends particles back from a metal plate placed in front of the tube. When they put the plate in place, “scintillations were at once observed”.

Heavy metals sent back far more than light ones. Per minute: gold 67, platinum 63, aluminium 3.4. Then they counted carefully, against a source of known strength:

Stacks of thin gold foils showed that it was not a surface effect. Some alpha particles, they wrote, “can be turned within a layer of 6 x 10⁻⁵ cm. of gold through an angle of 90°, and even more”. To bend them that sharply with a magnet would take “the enormous field of 10⁹ absolute units”, a billion gauss. The paper reached the Royal Society on 19 May 1909. In 1911 Rutherford summed up their gold result this way: about 1 in 20,000 alpha particles were turned through an average angle of 90 degrees by a gold foil about 0.00004 centimetres thick.

In 1936, in a lecture at Cambridge, Rutherford remembered Geiger coming to him “in great excitement” to say that they had got some of the alpha particles coming backwards. Then came the line everyone quotes:

It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. — Rutherford, lecture at Cambridge, 1936, printed in Background to Modern Science (1938)

The lecture was printed in 1938, after Rutherford’s death, rewritten by J. A. Ratcliffe from a stenographer’s notes, “keeping as closely as possible to Lord Rutherford’s own words”. Marsden, for his part, remembered reporting the result himself. The surprise is the same in both accounts.

A minute massive centre: the nucleus

Rutherford thought about it for almost two years. His key step, in the same lecture: “On consideration I realized that this scattering backwards must be the result of a single collision”. Many small nudges could not add up to a U-turn often enough. One encounter had to do it, and for one encounter to turn back a fast, heavy particle, the atom’s positive charge and almost all its mass had to be packed into a tiny space. “It was then that I had the idea of an atom with a minute massive centre carrying a charge.” Most alpha particles miss that centre by far and fly straight on; the very few heading almost straight at it are turned right round. The video animates both kinds of path.

Early in 1911 he told the Manchester Literary and Philosophical Society, and in May 1911 the full paper appeared in the Philosophical Magazine: “it seems simplest to suppose that the atom contains a central charge distributed through a very small volume”.

How small? In his calculation, an alpha particle heading straight for the centre of a gold atom is stopped and turned back about 3.4 × 10⁻¹² centimetres from it, while the atom’s radius is of the order of 10⁻⁸ centimetres, roughly 3,000 times further out. He put gold’s central charge at about 100 units of electric charge. Today we know it is 79: gold is element number 79.

The theory made predictions anyone could check: how the count of scattered particles should change with the angle, the thickness of the foil, the central charge and the speed of the alpha particles. In 1913 Geiger and Marsden built an apparatus whose microscope turned round the foil, to angles of 150 degrees, and the predictions held. Soon the central charge had the name we use today.

An atom that is almost all empty space, with a minute, massive, charged centre, found by counting flashes in the dark. And that’s how we found out.

Twenty years later the same zinc sulphide flashes, at the Cavendish Laboratory, showed lithium nuclei splitting and checked Einstein’s most famous equation: read where E=mc² comes from.