Question B1 a) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A) av Aas A2/3 - ac Z(Z-1) A1/3 ΠΑ (A-2Z)² A +8(Z, A). Give a discussion of the origin of the last term in this expression. b) Starting from the Pauli exclusion principle, justify the asymmetry term in the SEMF. c) Derive an expression for the constant in the Coulomb term in the SEMF, ac, based on the electrostatic formula for the potential energy of a sphere radius R with charge Q, E 3 Q2 5 4περ R Use your formula to estimate the theoretical value of ac and compare it to its measured value. d) Show that the values of N where the minimum mass value roughly occurs when A = N+Z is constant is given by You may neglect the 5 term. N 2a+acA2/3 A 4a+acA2/31 Use this to argue whether heavy nuclei have more neutrons or more protons. How would this change if the Coulomb term was zero?

Question B1 a) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A) av Aas A2/3 - ac Z(Z-1) A1/3 ΠΑ (A-2Z)² A +8(Z, A). Give a discussion of the origin of the last term in this expression. b) Starting from the Pauli exclusion principle, justify the asymmetry term in the SEMF. c) Derive an expression for the constant in the Coulomb term in the SEMF, ac, based on the electrostatic formula for the potential energy of a sphere radius R with charge Q, E 3 Q2 5 4περ R Use your formula to estimate the theoretical value of ac and compare it to its measured value. d) Show that the values of N where the minimum mass value roughly occurs when A = N+Z is constant is given by You may neglect the 5 term. N 2a+acA2/3 A 4a+acA2/31 Use this to argue whether heavy nuclei have more neutrons or more protons. How would this change if the Coulomb term was zero?