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Let f be the fraction of the detected alpha particles that were deflected through large angles...

Let f be the fraction of the detected alpha particles that were deflected through large angles (greater than 90 degrees). Would careful measurement of f would allow Rutherford to estimate the size of the nucleus of the gold atoms?

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Yes, by careful measurement of fraction of particles scattered at greater angle (more than 90) would give size of nucleus. Since the positive charge and the mass of gold atom are concentrated in a small fraction of the total volume and then deriving mathematical equations for the scattering would predict that the number of -particles scattered through a given angle should be proportional to the thickness of the foil and the square of the charge on the nucleus,

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