(a) (b) In 1956 a breakdown of the Rutherford formula for the differential scattering cross section was observed experimentally by Farewell et al. In the figure is the observed dependence (Ex) for a particular scattering angle 8 of a-particles from a 289Pb target (data points and solid trend line) which shows disagreement in comparison to the predicted by the Rutherford classical Coulomb scattering model (dashed line). Scattered a particles at 60 in relative units a on 20 Pb target 20 25 30 35 40 a particle energy, Eg, in MeV ii. i. Explain the reason for the breakdown of the Rutherford scattering formula. Use the graph to extract an approximate value for the critical energy E. Show how this can be used for an estimation of the nuclear radius. Compare your result with an empirical radius of half density R/2 = (1.2 fm) 4/3 and comment on the possible reasons for the discrepancy. The probability that a radioactive atom will decay in one hour is 5 x 10-. Assume that you have a sample containing 1 mol of these atoms. i. Calculate the half-life of this radio-isotope. ii. How many radioactive atoms will remain in the sample after 1 day?