The Geiger-Marsden experiment successfully demonstrated the existence of the nucleus and put limits on its size using the scattering of alpha particles from gold foils. Assume that the alpha particles were fired with a speed about 5.00% of the speed of light.
a) Derive the upper bound of the radius of the nucleus in terms of the speed of the alpha particle that is scattered in the backward direction.
b) Calculate the approximate radius of the gold nucleus using the result from part (a).