Rutherford conducted the experiment that showed that atoms were mostly made up of empty space.
Rutherford done an experiment in which he allowed alpha particle to bombard on gold foil . Which shows that the atom is mostly empty space with a tiny, dense, positively-charged nucleus. Based on these results, Rutherford proposed the nuclear model of the atom.
The observations made by Rutherford led him to conclude that: A major fraction of the α-particles bombarded towards the gold sheet passed through the sheet without any deflection, and hence most of the space in an atom is empty.
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