Deviations from Rutherford Scattering (DP IB Physics)

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.

Answer:

Step 1: Compare the relative charges of the nuclei

• The force between nuclei due to the electric repulsion is

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

• Gold has 79 protons, so 

• Aluminium has 13 protons, so 

• 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

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