Final answer:
Rutherford's gold foil experiment required extremely thin sheets to ensure alpha particles would mostly pass through without multiple scatterings, showing that atoms have a small, dense nucleus and are mostly space.
Step-by-step explanation:
In Rutherford's gold foil experiment, the use of extremely thin sheets was crucial for determining the structure of the atom. Gold was chosen for its property of being hammered into thin sheets, thus minimizing the number of atoms in the targets and maximizing the likelihood that alpha particles would encounter a single atom. The thinness ensured most alpha particles would pass right through, as the atom is mostly space, thus demonstrating that the atom is mostly empty with a very small, dense nucleus. If sheets were too thick, multiple scatterings could occur, preventing a clear understanding of the results.
The significance of the few deflections and the occasional backward scattering of alpha particles was that they indicated the presence of a dense center in the atom, contradicting the plum pudding model. This unexpected result led to the planetary model of the atom and the understanding that the nucleus is both very small and very dense.