The famous experiment of Geiger and Marson found that when they shot alpha particles at a very thin sheet of gold foil, a few of the alpha particles – about one in twenty thousand – were reflected by the foil rather than merely deflected. As Rutherford said later:
It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you. (Ernst Rutherford, ‘The Development of the Theory of Atomic Structure’, in Background of Modern Science, edited by J. Needham and W. Pagel, Cambridge University Press, Cambridge, 1938, pp. 61-74.)
This remark of Rutherford’s shows the utterly revolutionary nature of the discovery: no one expected to see alpha particles rebound off gold, and yet it was conceivable. Rutherford realized that the experiment refuted J.J. Thomson’s model of the atom, and he replaced it by his own model of the atom.
This was the beginning of nuclear science.
It also happens to fit exactly within Popper’s method of falsificationism.