The nuclear model of the atom

The nuclear model of the atom says that an atom has a tiny, positively charged nucleus at its centre, which holds almost all of the atom's mass, with negatively charged electrons around it and mostly empty space in between. Ernest Rutherford proposed it in 1911 to explain the results of the alpha particle scattering experiment, and it replaced the plum pudding model.

What is the nuclear model of the atom?

The nuclear model of the atom describes an atom like this:

• A nucleus at the centre, made of protons and neutrons, with an overall positive charge.
• The nucleus is tiny: its radius is less than 1/10,000 of the radius of the atom.
• Almost all of the atom's mass is in the nucleus.
• Electrons are arranged at different distances from the nucleus, called energy levels or shells.
• Most of the atom is empty space.

Atoms have a radius of about 1 × 10⁻¹⁰ m, so a nucleus has a radius of less than 1 × 10⁻¹⁴ m. To picture the scale: if an atom were the size of a 100 m football stadium, its nucleus would be smaller than 1 cm across, about the size of a pea on the centre spot.

How the model of the atom changed

The model of the atom is a good example of science changing its mind when new evidence turns up. Each model explained the experiments of its time, until an experiment came along that it could not explain.

The plum pudding model

In 1897 J. J. Thomson found that atoms contain electrons: tiny particles with a negative charge. Atoms are neutral overall, so there had to be positive charge somewhere to balance the electrons. The plum pudding model put it everywhere: the atom was a sphere of positive charge, with the negative electrons sitting in it like fruit in a pudding.

In this model the mass and the positive charge are spread evenly through the whole atom. That detail is what the alpha particle scattering experiment tested.

The alpha particle scattering experiment

In 1909 Hans Geiger and Ernest Marsden, working with Rutherford in Manchester, fired alpha particles at a very thin sheet of gold foil. It is also called the alpha scattering experiment, the gold foil experiment, or the Geiger and Marsden experiment.

How the experiment worked

• A radioactive source gave out alpha particles: fast, positively charged particles made of 2 protons and 2 neutrons, about 7,300 times the mass of an electron.
• The alpha particles were aimed at gold foil. Gold was used because it can be hammered into an extremely thin sheet.
• The apparatus was kept in a vacuum, because air absorbs alpha particles after a few centimetres.
• A detector (a screen that gave a tiny flash of light when an alpha particle hit it, viewed through a microscope) was moved around the foil to count the alpha particles scattered at each angle.

Results of the alpha scattering experiment

If the plum pudding model were right, the thinly spread positive charge would only nudge the heavy, fast alpha particles, and they would all go through with tiny deflections. Most did. But a few were deflected through large angles, and a very small number bounced straight back. Rutherford said it was as if you had fired a fifteen-inch shell at a piece of tissue paper and it had bounced back and hit you.

Only a tiny, massive, positively charged centre could turn an alpha particle round, so Rutherford concluded that the mass of the atom is concentrated in a small nucleus and that the nucleus is charged. This nuclear model replaced the plum pudding model.

Match each result to what it tells you in this question from the Atomic Structure course.

After Rutherford: Bohr, protons and neutrons

Rutherford's model left a problem: it did not say where the electrons were or why they did not spiral into the nucleus. In 1913 Niels Bohr adapted the nuclear model by suggesting that electrons orbit the nucleus at specific distances. The theoretical calculations agreed with experimental observations, and these orbits are the energy levels, or shells, used today.

Later experiments showed that the positive charge of any nucleus could be divided into a whole number of smaller particles, each with the same positive charge. These particles were named protons. Then in 1932 James Chadwick found evidence for the neutron, a particle with no charge in the nucleus, about 20 years after the nucleus became an accepted idea. You can build atoms from protons, neutrons and electrons in the Atom Builder.

Plum pudding model vs nuclear model

Distance of closest approach (A-level)

At A-level you can use the scattering experiment to estimate the size of a nucleus. An alpha particle aimed straight at a nucleus slows down as the repulsion grows, stops, and turns back. At the turning point all its kinetic energy has become electric potential energy:

Here Q₁ = 2e is the alpha particle's charge, Q₂ = Ze is the nucleus's charge, and d is the distance of closest approach. The nucleus must be smaller than d, or the alpha particle would have hit it.

Example: a 5.0 MeV alpha particle and a gold nucleus

Gold has Z = 79. First convert the energy to joules: 5.0 × 10⁶ × 1.60 × 10⁻¹⁹ = 8.0 × 10⁻¹³ J. Then rearrange for d, with ε₀ = 8.85 × 10⁻¹² F m⁻¹:

So a gold nucleus has a radius of less than about 4.5 × 10⁻¹⁴ m, which is thousands of times smaller than the atom. AQA A-level Physics covers Rutherford scattering qualitatively in 3.8.1.1 and this closest approach estimate in 3.8.1.5.

Common mistakes

• Saying "most alpha particles bounced back". Most went straight through. Only a very small number bounced back.
• Linking a result to the wrong conclusion. Passing straight through shows empty space; it says nothing about charge.
• Forgetting the charge. The deflections show the nucleus is positive, because like charges repel.
• Saying Rutherford discovered the neutron. Chadwick did, in 1932.
• Calling the plum pudding model "Rutherford's model". It was Thomson's. Rutherford's is the nuclear model.
• Thinking alpha particles hit the nucleus. They are repelled by it before they touch it.

Practice questions

1. What did the discovery of the electron lead to?
2. In the alpha particle scattering experiment, what does the fact that most alpha particles passed straight through the foil tell you?
3. Why did some alpha particles bounce back?
4. Give two differences between the plum pudding model and the nuclear model.
5. An atom has a radius of 1.5 × 10⁻¹⁰ m. Use the fact that a nucleus is less than 1/10,000 of the atom's radius to give an upper limit for the radius of its nucleus.

Answers: 1) The plum pudding model. 2) Most of the atom is empty space. 3) They came close to a tiny nucleus that holds most of the mass and is positively charged, and were repelled. 4) Any two: in the nuclear model the positive charge is concentrated in the nucleus rather than spread out; the mass is in the nucleus rather than spread out; most of the atom is empty space. 5) 1.5 × 10⁻¹⁰ ÷ 10,000 = 1.5 × 10⁻¹⁴ m.

Practise with a short timed paper

The model of the atom comes up in GCSE Physics, GCSE Chemistry and Combined Science. The daily GCSE Physics Higher and GCSE Combined Science Higher papers are short timed papers of 8 questions, with a new one every day.

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