Physics • Year 12 • Module 8 • Lesson 11
The Nuclear Model of the Atom
Lock in the core vocabulary of Rutherford scattering, the three key experimental observations, and the nuclear model before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: alpha particle, nucleus, closest approach, atomic number, nuclear radius, Coulomb repulsion, plum pudding model, nuclear model, empty space, Geiger-Marsden experiment. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A helium nucleus (42He) carrying charge +2e; used as the projectile in Rutherford's scattering experiment. | |
| 1.2 | The tiny, dense, positively charged core of an atom; contains protons and neutrons and has diameter ~10−15 m. | |
| 1.3 | The minimum distance between an incoming alpha particle and the nucleus during a head-on collision, when all kinetic energy has been converted to electrical potential energy. | |
| 1.4 | The number of protons in a nucleus; defines which element the atom is. | |
| 1.5 | The quantity R given by R = R0 A1/3, where R0 ≈ 1.2 fm and A is the mass number. | |
| 1.6 | The electrostatic repulsion between two positively charged particles; responsible for deflecting alpha particles in scattering experiments. | |
| 1.7 | Thomson's model of atomic structure in which positive charge is spread evenly through the atom like a diffuse cloud, with electrons embedded inside like fruit in a pudding. | |
| 1.8 | Rutherford's model in which almost all mass is concentrated in a tiny positive nucleus with electrons orbiting at much larger distances (~10−10 m). | |
| 1.9 | The region between the nucleus and the orbiting electrons; why most alpha particles pass through gold foil undeflected. | |
| 1.10 | The 1909 investigation by Geiger and Marsden, directed by Rutherford, in which alpha particles were fired at a thin gold foil and a detector recorded the angles of deflection. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 In the Geiger-Marsden experiment, most alpha particles were deflected back by more than 90°. T / F
2.2 Large-angle scattering of alpha particles is consistent with Thomson's plum pudding model. T / F
2.3 The distance of closest approach gives an upper limit for the nuclear radius. T / F
2.4 The nuclear radius formula R = R0 A1/3 implies that nuclear density increases as A increases. T / F
2.5 Rutherford's nuclear model successfully explained why electrons in orbit do not spiral into the nucleus. T / F
2.6 The closest approach distance decreases if the alpha particle has a higher initial kinetic energy. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
empty space · energy conservation · gold · Marsden · nucleus · positive · scattering · upper limit
In 1909, Geiger and ___________ fired alpha particles at a thin ___________ foil under Rutherford's direction. The experiment, called alpha-particle ___________, revealed that atoms are mostly ___________, because most particles passed through undeflected. A small number bounced back at large angles, indicating the existence of a tiny, dense, ___________ core called the ___________. By applying ___________ to head-on collisions, Rutherford calculated the distance of closest approach, which is an ___________ on the nuclear radius.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What does the observation that most alpha particles pass straight through gold foil tell us about atomic structure?
4.2 Why does large-angle scattering of alpha particles require a concentrated, positively charged nucleus rather than diffuse positive charge?
4.3 What does the formula R = R0 A1/3 imply about the density of nuclei across different elements?
4.4 Why is the distance of closest approach an upper limit rather than the actual radius of the nucleus?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. "led to", "is explained by", "provides evidence for"). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: Geiger-Marsden experiment · large-angle scattering · nuclear model · empty space · closest approach · Coulomb repulsion.
6. Label the scattering outcomes
The diagram below shows three types of alpha-particle paths in the Geiger-Marsden experiment. For each labelled path (A, B, C), write the correct outcome name, an approximate frequency (most / some / very few), and the structural feature of the atom it reveals. 9 marks (3 per path)
| Path | Outcome name | Approximate frequency | Structural feature revealed |
|---|---|---|---|
| A | |||
| B | |||
| C |
Q1 — Term–definition match
1.1 alpha particle • 1.2 nucleus • 1.3 closest approach • 1.4 atomic number • 1.5 nuclear radius • 1.6 Coulomb repulsion • 1.7 plum pudding model • 1.8 nuclear model • 1.9 empty space • 1.10 Geiger-Marsden experiment.
Q2 — True / false with correction
2.1 False. Most alpha particles passed straight through with little or no deflection. Only approximately 1 in 8,000 were deflected by more than 90°.
2.2 False. Large-angle scattering is incompatible with Thomson's plum pudding model. A diffuse positive charge could only cause small deflections. Large-angle scattering requires a concentrated, dense positive nucleus (Rutherford's model).
2.3 True. The distance of closest approach is where the alpha turns around before actually reaching the nuclear surface, so it is an upper limit on the nuclear radius.
2.4 False. The formula implies that nuclear density is approximately constant for all nuclei. Since volume ∝ R3 ∝ A and mass ∝ A, density = mass/volume is approximately constant.
2.5 False. Rutherford's nuclear model could not explain this. Classical electromagnetism predicts that accelerating charges radiate energy, so orbiting electrons should spiral into the nucleus. Bohr's quantum model was needed to resolve this.
2.6 True. From rmin = k 2Ze2 / Ek, a higher kinetic energy gives a smaller closest approach distance.
Q3 — Cloze paragraph
In order: Marsden / gold / scattering / empty space / positive / nucleus / energy conservation / upper limit.
Q4.1 — Most particles pass straight through
Most alpha particles pass straight through because atoms are mostly empty space. The nucleus is tiny (~10−15 m) compared with the atomic radius (~10−10 m), so most alphas miss the nucleus entirely and pass through the vast empty region occupied by electrons.
Q4.2 — Why concentrated positive charge is needed
Only a concentrated positive charge can exert sufficient Coulomb repulsion at very short range to deflect an alpha particle by a large angle. In Thomson's diffuse model, the positive charge is spread over the whole atom (~10−10 m), so the repulsive force at any point is too small to cause large deflections. A tiny nucleus concentrates all the positive charge in a region ~10−15 m, producing an enormous force on alphas that pass close by.
Q4.3 — Nuclear density
The formula implies nuclear density is approximately constant for all nuclei. Since R ∝ A1/3, nuclear volume V ∝ R3 ∝ A. Nuclear mass is also proportional to A, so density = mass/volume ≈ constant. Nucleons are packed at the same density regardless of which element.
Q4.4 — Upper limit on nuclear radius
The distance of closest approach is the turning point where the alpha comes to rest momentarily before being repelled back. At this point the alpha is still outside the nuclear surface — Coulomb repulsion stops it before it reaches the actual nuclear surface. The real nuclear radius must therefore be smaller than rmin.
Q5 — Sample concept map
Correct maps should include arrows such as:
- Geiger-Marsden experiment — revealed → large-angle scattering
- large-angle scattering — led Rutherford to propose → nuclear model
- Coulomb repulsion — causes → large-angle scattering
- Coulomb repulsion — determines → closest approach
- Geiger-Marsden experiment — showed atoms contain → empty space
- nuclear model — explains → empty space
Award 1 mark per valid labelled arrow (minimum 6, maximum 6 marked).
Q6 — Label the scattering outcomes
Path A: Outcome — undeflected / straight-through. Frequency — most (~99.99%). Feature revealed — atoms are mostly empty space; the nucleus is tiny relative to atomic size.
Path B: Outcome — small-angle deflection. Frequency — some (a fraction of particles). Feature revealed — the positive charge is concentrated rather than uniform; a nearby pass to the nucleus causes a small repulsive deflection.
Path C: Outcome — large-angle scattering / back-scattering (>90°). Frequency — very few (~1 in 8,000). Feature revealed — the nucleus is very small, very dense, and carries a large positive charge capable of exerting enormous Coulomb repulsion.