Final answer:
The observation that some positively charged alpha particles bounced back from a gold foil during Rutherford's experiment indicates the presence of a small, dense, positively charged nucleus within the atom.
Step-by-step explanation:
The observation that indicates there is a small, dense, positively charged part in the center of an atom is that some positively charged particles bounce back from a gold foil. This was a key finding in the gold foil experiment conducted by Ernest Rutherford. When a beam of alpha particles, which are positively charged, was directed at a thin sheet of gold foil, most passed through but a few were deflected, and some even bounced back. This could only be explained by the existence of a positively charged nucleus at the center of gold atoms, which repelled the positively charged alpha particles upon close encounter.
Rutherford's experiment led to the conclusion that atoms have a nuclear model, with the majority of the mass and positive charge concentrated in a central nucleus, surrounded by a cloud of electrons. The bouncing of alpha particles directly back towards their source suggested the nucleus was both densely packed and contained a high positive charge, repelling the similarly charged alpha particles.