Rutherford’s Gold Foil Experiment and Nucleus
Rutherford’s gold foil experiment, carried out by Hans Geiger and Ernest Marsden under Rutherford’s direction in 1909 and interpreted by Rutherford in 1911, showed that an atom has a tiny, dense, positively charged nucleus surrounded by mostly empty space. In brief: most alpha particles passed straight through a thin gold foil, a few were deflected by large angles and about 1 in 8,000 bounced almost straight back, which could only happen if the positive charge and most of the mass were concentrated in a very small region.
The experiment overturned the plum pudding model and led to the nuclear model of the atom, which is the foundation of modern atomic theory. This article explains how the experiment was set up, what was observed, how Rutherford interpreted the results, how large the nucleus is compared with the atom, a table of observations and conclusions, a worked scale calculation and the limits of the nuclear model.
How was the experiment set up?
Alpha particles are helium nuclei (two protons and two neutrons) with a charge of +2e, emitted by radioactive elements such as radium. In the experiment at the University of Manchester, a narrow beam of alpha particles from a radioactive source was directed at an extremely thin sheet of gold foil, only a few hundred atoms thick. A screen coated with zinc sulfide surrounded the foil, and it produced a tiny flash of light, a scintillation, wherever an alpha particle hit it. Geiger and Marsden counted the flashes at different angles by eye in a darkened room, which was tiring and required great patience.
What did the scientists observe?
- The great majority of alpha particles passed through the foil with little or no deflection.
- A small fraction was deflected through noticeable angles.
- A very small number, roughly 1 in 8,000 in the early measurements, were deflected by more than 90°, and some came almost straight back.
Rutherford later described the result as “almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you”.
How did Rutherford explain the results?
If the atom were a uniform sphere of positive charge, as in Thomson’s model, the electric force on an alpha particle would be weak and spread out, and the particles would pass with only small deflections. A backward bounce requires a strong force on a heavy, fast particle, which can only be produced by a very concentrated positive charge. Rutherford calculated in 1911 that the results fit an atom with a tiny central nucleus carrying most of the atom’s mass and all of the positive charge, with electrons far outside it.
Because a nucleus is so small, most alpha particles never come close to one and pass through the empty space. The few that approach a nucleus head-on are repelled by the strong electric force between the two positive charges, and they are scattered at large angles.
Observations and conclusions
| Observation | Conclusion |
|---|---|
| Most alpha particles pass straight through | Most of the atom is empty space |
| A few are deflected at small angles | They passed near positive charge, which repelled them |
| About 1 in 8,000 bounce back | The positive charge and mass are concentrated in a tiny, dense nucleus |
| Deflections depend on the gold atom’s charge | The charge of the nucleus equals the atomic number times e (later confirmed) |
What is the nucleus like?
The nucleus contains protons and neutrons, collectively called nucleons. It has a diameter of about 10−15 m (1 femtometer, fm) for the lightest nuclei to about 15 fm for the heaviest. The atom’s diameter is of the order of 10−10 m, so the nucleus is about 10,000 to 100,000 times smaller in diameter. More than 99.9% of the atom’s mass is in the nucleus, because a proton or neutron is about 1,840 times as heavy as an electron.
| Object | Typical diameter (m) |
|---|---|
| Atom (hydrogen to heavy atoms) | 1 × 10−10 to 5 × 10−10 |
| Nucleus of hydrogen (a proton) | about 1.7 × 10−15 |
| Nucleus of gold | about 1.4 × 10−14 |
| Electron | no measurable size (less than 10−18) |
Worked example: the scale of the atom
- Ratio of diameters. For an atom of 1.0 × 10−10 m and a nucleus of 1.0 × 10−15 m: 1.0 × 10−10 ÷ 1.0 × 10−15 = 1.0 × 105. The atom is about 100,000 times wider than its nucleus.
- Model scale. If the nucleus were a marble of 1 cm, the atom would have a diameter of 1 cm × 105 = 105 cm = 1 km.
- Ratio of volumes. Volume goes as the cube of the diameter, so the atom’s volume is (105)3 = 1015 times larger than the nucleus volume. That is a million billion.
- Fraction of mass. A carbon-12 atom has a mass of 12.000 u, and its 6 electrons contribute 6 × 0.000549 u = 0.00329 u. The electrons are 0.00329 ÷ 12.000 × 100% = 0.027% of the atom’s mass, so the nucleus makes up about 99.97%.
- Number passing through. If about 1 in 8,000 particles bounces back, then out of 80,000 particles about 10 would be reflected.
What problems did the nuclear model have?
According to classical physics, an electron orbiting a nucleus is accelerating and should radiate energy continuously, spiraling into the nucleus in a tiny fraction of a second. Atoms would not be stable. The model also did not explain why elements emit light only at particular wavelengths. These problems were addressed in 1913 by Niels Bohr, who combined the nuclear atom with the ideas of quantum theory.
What happened after 1911?
In 1913, Henry Moseley showed that the charge on the nucleus (the atomic number) is the basis for the order of elements in the periodic table. In 1919, Rutherford produced the first artificial nuclear reaction by bombarding nitrogen with alpha particles and identified the proton. In 1932, James Chadwick discovered the neutron. Rutherford had received the Nobel Prize in Chemistry in 1908 for his work on radioactivity, before the gold foil work was complete.
Which mistakes are common?
Mistake 1: Saying that Rutherford discovered the proton and the neutron in the gold foil experiment
The experiment showed the nucleus. The proton was identified in 1919 and the neutron by Chadwick in 1932.
Mistake 2: Believing that the electrons were observed
The experiment did not detect electrons. They are so light that they do not deflect alpha particles noticeably.
Mistake 3: Thinking that the atom is mostly nucleus
The nucleus contains almost all of the mass but only a tiny fraction of the volume.
Mistake 4: Describing the foil as being made of a single layer of atoms
The foil was thin, but it contained hundreds of layers of atoms. Most particles pass through all of them.