Explain how the observation that a small fraction of alpha particles in the Geiger–Marsden experiment were deflected through angles greater than 90° led to the conclusion that the positive charge of an atom is concentrated in a small, dense nucleus.

IB DP Physics Standard Level (2023 syllabus) — E.1 Structure of the atom · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

In the Geiger–Marsden experiment, a beam of alpha particles was directed at a thin gold foil. Whilst the vast majority passed through with little or no deflection, approximately 1 in 8000 alpha particles were deflected through angles greater than 90°.

Model answer (4 marks)

Large‑angle deflections of the α particles require a very large electrostatic repulsive force, which can only be produced if the positive charge of the gold atom is concentrated in a very small region. The Coulomb force is inversely proportional to the square of the distance between charges, so a small separation gives a very intense electric field and a large force on the α particle. The fact that only about 1 in 8000 particles are deflected through angles greater than 90° shows that this small, highly charged region occupies only a tiny fraction of the atom’s volume – most particles miss it and pass straight through. Finally, the α particle is almost brought to rest and reversed, meaning the nucleus must be massive and dense so that it does not recoil appreciably during the collision.

Examiner tips

  • Mention Coulomb force and its distance dependence
  • Explain why only a small fraction of particles are deflected
  • Show that the nucleus must be dense to avoid recoil

Common mistakes

  • Saying the charge is spread out over the whole atom
  • Forgetting to link the large force to a small distance
  • Not explaining why the nucleus must be dense

Mark scheme (4 marks)

  1. Large-angle deflections require a large electrostatic (Coulomb) repulsive force acting on the alpha particle.
  2. Such a large force is only possible if the positive charge is concentrated in a very small region (nucleus), producing an intense electric field at close range.
  3. The rarity of large deflections indicates that the nucleus occupies only a tiny fraction of the atom's volume, so most alpha particles pass far from it and are undeflected.
  4. The nucleus must also be dense (massive) because the alpha particle is brought almost to rest and reversed in direction, implying the nucleus does not recoil significantly.

Key terms in this question

alpha particle · nucleus

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