Rutherford directed alpha particles from a decaying radioactive material to a piece of foil and observed the way in which these particles reflected and scattered. The only way the particular scattering made sense was if almost all the atomic matter was concentrated in a tiny volume situated at the atome center, the atomic nucleus.
ELI5 version:
If you close your eyes and throw tennis balls a vehicle you could probably figure out if if was a truck or a car or a motorcycle based on where the tennis balls ended up.
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