who said atoms contain mostly empty space

The scientist who said that atoms contain mostly empty space was Ernest Rutherford. Rutherford's gold foil experiment in 1909 led him to conclude that an atom has a small, dense, positively charged nucleus at its center, with electrons orbiting around it at relatively large distances. Most of the atom's volume is empty space, which explained why most alpha particles passed through the foil with little deflection while a few were deflected at large angles. This discovery fundamentally changed the atomic model by disproving the earlier "plum pudding" theory and establishing the concept of the nuclear atom.