Final answer:
Rutherford's experiment showed that alpha particles could be scattered at large angles due to Coulomb interactions with small, dense gold nuclei. While the fraction of particles scattering greater than 14.5° from a gold foil can be estimated using Rutherford's scattering formula, precise fraction calculation requires specific formula or data not provided in the context of the student's question.
Step-by-step explanation:
The student's question relates to Rutherford's gold foil experiment and involves concepts of nuclear physics. In the experiment, Rutherford and his team discovered that a small fraction of alpha particles were scattered at large angles after interacting with the dense gold nuclei. This observation contrasted with the expected behavior based on the then-accepted atomic model of a uniform distribution of mass and charge within the atom. The scattering was a result of the Coulomb interaction between the positively charged alpha particles and the gold nuclei.
To estimate the fraction of 5 MeV alpha particles scattered at angles greater than 14.5° from a gold foil, Rutherford's scattering formula or a simulation based on this formula would normally be used. These methods take into account the charge of the alpha particle, the charge and mass of the gold nucleus, the density of the gold, and the thickness of the foil. However, without the complete scattering calculation formula or detailed cross-section data within the context of this problem, providing a precise fraction is not possible.
The key point from Rutherford's findings is that the gold nuclei must be very small and massive compared to the rest of the atom, which consists of mostly empty space. The surprising result that a non-negligible fraction of alpha particles could be scattered at such large angles was critical evidence leading to the revision of the atomic model to include a dense, central nucleus surrounded by a cloud of electrons.