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Why or how? The number of alpha particles deflected was small ... indicating the nucleus was small. The deflection of an even smaller amount of alpha particles almost straight back toward the emitting source proved that the nucleus was heavier than the alpha particle. According to previous atomic theory, the alpha particles should have all gone straight through the metal foil, with none deflected.

Math calculations based on the deflection pattern showed that the nucleus was repelling the alpha particles, that they were not actually hitting and bouncing off the nucleus... this showed that the nucleus was positively charged.

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Q: Why was existence of a tiny massive and positively charged nucleus was deduced from the observations?
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