12.2.3 Deviations from Rutherford Scattering

• Rutherford's alpha scattering experiment originally assumed that the alpha particles are only interacting through electrostatic repulsion
  • However, if the energy of the alpha particles exceeds 27.5 - 28 MeV, then they will be close enough to interact with the nucleus via the strong nuclear force

• The Rutherford formula describes this as it states that as the angle of scattering angle increases, the number of alpha particles scattered at that angle sharply decreases

• Where:
  • N = number of alpha particles
  • θ = angle of scattering
• Rearranging this equation shows that it should be the case that:

• Where:
  •  k = a constant
• Experimental data bears this out, suggesting that the Rutherford formula is correct
• A number of assumptions are made in deriving this formula, with the main one being that the only force we need to consider is the electric force
• Deviations from Rutherford scattering are evidence of the strong nuclear force 

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

Worked Example

Step 1: Compare the relative charges of the nuclei

• • Gold has 79 protons, aluminium has 13 protons.
  • The electric force between the nuclei is proportional to the charge, since,

• • Therefore the alpha particle will approach the aluminium nucleus at a much closer distance

Step 2: Consider what causes deviation from Rutherford scattering

• • Deviations from Rutherford scattering occur when forces apart from the electric force between the nuclei are at play
  • At much smaller distances the effect of the strong nuclear force will be felt

Step 3: Deduce the solution

• • The alpha particles get closer to the aluminium nucleus, at a distance the strong nuclear force begins to act
  • More deviation will be seen with aluminium foil than with gold foil

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