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I understand how they calculated a maximum radius for the gold atom nucleus. What I don't realize is how did they know that the alpha particle wasn't hitting the nucleus. I mean: if they had used particles with 2 times that kinetic energy, they would have obtained half the value for the radius of the nucleus. If they had used particles with less kinetic energy they would have obtained a bigger radius.

I think the solution to this problem would have to increase the kinetic energy until the particles actually hit the nucleus. But how would they know that?

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  • $\begingroup$ They would know because the cross-section would deviate from that given by the formula Rutherford derived for scattering from a $1/r^{2}$ potential (any $1/r^{2}$ potential, including gravity wells). At the time of the original experiment, they were using natural sources of alpha particles, with only a few available alpha energies. This fact was the driving forces behind the developments by Cockroft and Walton, and separately by Van de Graaff, to develop high energy particle accelerators. $\endgroup$ – Jon Custer Oct 5 '16 at 14:02
  • $\begingroup$ @Farcher - sorry, yes $1/r$ potential, $1/r^{2}$ force... $\endgroup$ – Jon Custer Oct 5 '16 at 15:55
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The theory depended on Coulomb's law being true - ${\rm force} \propto \frac {1 }{{\rm distance}^2}$.

Using the measured scattering distribution they could fit the experimental data to the theory and hence get the closest approach.

If the incoming $\alpha$ particles touch the nucleus, i.e. the strong nuclear force comes into play, then the measured large angle scattering would deviate from that expected for only the Coulomb interaction being present.

The onset of this deviation will give an estimate of the size of the nucleus.

In some later experiments with lighter nuclei the effect of the strong nuclear was seen.

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