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IBPhysicsHLRevision NotesNuclear & Quantum PhysicsStructure of the AtomDeviations from Rutherford Scattering (HL)

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First exams 2025

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Deviations from Rutherford Scattering (HL) (HL IB Physics)

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Katie M

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Katie M

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Deviations from Rutherford Scattering

  • Rutherford's scattering experiment predicted that
    • As the scattering angle increases, the number of alpha particles scattered at that angle decreases
  • This was found to be correct at low to moderately high energies
  • However, at very high energies (>27.5 MeV) significant deviations from Rutherford's predictions were observed
  • Instead of the number decreasing at the expected rate, the number of alpha particles being back-scattered sharply decreases to zero

12-2-3-rutherford-scattering-deviation-ib-hl

The observed back-scattering from alpha particles strongly deviates from the predicted relationship based only on electromagnetic repulsion at 27.5 MeV

  • Rutherford's alpha scattering experiment originally assumed that the alpha particles only interact through electrostatic repulsion
  • However, if the energy of the alpha particles exceeds 27.5 MeV, then they will be close enough to interact with the nucleus via the strong nuclear force
  • Factoring in the interactions due to the strong nuclear force explains the scattering pattern observed in the experimental results
  • Therefore, deviations from Rutherford scattering provide evidence for the strong nuclear force

5-1-6-strong-nuclear-force-coulomb-repulsion-comparison

Very high-energy alpha particles can get close enough to the nucleons that the effect of the strong nuclear force becomes significant

Worked example

Alpha particles undergo scattering after being fired at a thin gold begin mathsize 16px style Au presubscript 79 presuperscript 197 end style foil. The gold is then replaced to make a comparison.

Describe the predicted difference in the scattering pattern when the foil is replaced with aluminium Al presubscript 13 presuperscript 30 foil of the same thickness.

Answer:

Step 1: Compare the relative charges of the nuclei

  • The force between nuclei due to the electric repulsion is

F space equals space k fraction numerator q Q over denominator r squared end fraction space space space space space rightwards double arrow space space space space space space r squared F space equals space k q Q

  • Therefore, the charge of a nucleus is proportional to the square of the distance between it and an alpha particle

Q space proportional to space r squared

  • Gold has 79 protons, so Q subscript g o l d end subscript space equals space plus 79 e
  • Aluminium has 13 protons, so Q subscript a l u m i n i u m end subscript space equals space plus 13 e
  • Therefore, an alpha particle will get closer to the nucleus with less charge i.e. the aluminium nucleus than the gold nucleus

Step 2: Predict the patterns and deviations from Rutherford scattering

  • Deviations from Rutherford scattering occur when alpha particles get close enough for the strong nuclear force to begin to become more significant than the electric force 
  • At very small separations (<1.5 fm) the effect of the strong nuclear force becomes significant
  • Alpha particles will be able to get closer to aluminium nuclei at lower energies than the gold nuclei
  • Therefore, alpha particles will be less affected by electric repulsion and able to get close enough for interactions with the strong nuclear force
  • Hence, more deviation will be seen with aluminium foil than with gold foil

Examiner Tip

Make sure you can explain when the greatest deviations from Rutherford scattering will occur i.e.

  • When the alpha particles have high energies
  • The target nuclei have a low nucleon number

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.