# Rutherford's Gold Foil Experiment: how did they stablished a minimum radius

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?

• 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. – Jon Custer Oct 5 '16 at 14:02
• @Farcher - sorry, yes $1/r$ potential, $1/r^{2}$ force... – Jon Custer Oct 5 '16 at 15:55

The theory depended on Coulomb's law being true - ${\rm force} \propto \frac {1 }{{\rm distance}^2}$.
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.