Question

explain how ernest rutherfords gold-foil experiment showed that atom is mostly empty space

Answer 1

Rutherford bombarded the gold foil with alpha particles (Helium nuclei) and found that most of them would not deviate from the initial trajectory on passing through the foil. A very small part of the alpha particles, though, ended up reflected, changing the direction of propagation. This lead to the conclusion that in the atom there is a tiny positively-charged unit which repels the alpha particles which also have a positive charge.

The fact that almost all of the initial alpha particles are not deflected means that the atom is mostly empty space.