Deviations from Rutherford Scattering
- In the Rutherford scattering experiment, alpha particles are fired at a thin gold foil
- Some of the alpha particles are found to come straight back from the gold foil
- This indicates that there is electrostatic repulsion between the alpha particles and the gold nucleus
- At the point of closest approach, r, the repulsive force reduces the speed of the alpha particles to zero momentarily
- At this point, the initial kinetic energy of an alpha particle, Ek, is equal to electric potential energy, Ep
- Then the alpha particle will be electrostatically repelled
The closest approach method of determining the size of a gold nucleus
- This experiment assumes that the alpha particles are only interacting through electrostatic repulsion
Deviations from Rutherford Scattering
- 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:
- 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
Alpha particles undergo scattering after being fired at a thin gold 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 foil of the same thickness.
Step 1: compare the relative charges of the nuclei
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- Gold has 79 protons, aluminium has 13 neutrons.
- The electric force between the nuclei is proportional to the charge, since,
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- Therefore the alpha particle will approach the aluminium nucleus to a much closer distance
Step 2: consider what causes deviation from Rutherford scattering
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- 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
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- The alpha particles gets closer to the aluminium nucleus, and the strong nuclear force affects them
- More deviation will be seen with aluminium foil than with gold foil
Exam Tip
- The greatest deviations from Rutherford scattering occur when the energy of the alpha particles is high and the radius of the target nuclei is small (meaning it has a small nucleon number)