Rutherford calculated that the radius of the nucleus is about 10^5 times less than the radius of the atom based on the observations of the deflected α-particles.
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Rutherford calculated the nucleus’s radius by observing the deflection of α-particles in his gold foil experiment. By analyzing the angles of deflection and applying principles of Coulomb’s law, he estimated the nucleus’s size to be about 10^5 times smaller than the atom’s radius.