Final answer:
Ernest Rutherford used the gold foil experiment and Coulomb's law to estimate the size of the nucleus, indicating a tiny, dense center within the atom with immense density.
Step-by-step explanation:
Ernest Rutherford used the principles of classical mechanics and Coulomb's law to estimate the size of the nucleus. By analyzing the scattering of helium-4 nuclei off gold-197 nuclei, and observing the angles at which they were deflected, he concluded that the nucleus was very small and dense. The key experiment leading to this discovery is famously known as the gold foil experiment.
Rutherford's findings revolutionized atomic theory, introducing the concept of the nuclear atom with a dense center containing most of the atom's mass. This discovery indicated that atoms have a size of about 10-10 m, with nuclei being approximately 100,000 times smaller, at about 10-15 m, suggesting a density on the order of 1015 g/cm³ for gold. Such a high density implied the existence of powerful forces within the nucleus, later understood as the strong nuclear force.