1. There is a stable nuclear X, with mass number A and atomic number Z. Now let's separate all its nucleons to a free energy state with no matter what kind of method. The first thing we need to do is to estimate the minimum energy required for a successful seperation. We know that there is a strong interaction force acting among the nucleons, binding them tightly with a strong energy potential Ev. To separate all nucleons, the minimum energy to be provided should be equivalent to Ev if only considering this strong interaction. 1) Supposing that the strong interaction is a short range force and all nucleons interact with the same number of surrouding other nucleons, please infer that the energy potential Ev should be proportional to the mass number A. 2) Now consider that the nuclear has a spherical shape, that means for the nucleons at the spherical surface, there are fewer other nucleons surrouding it and interacting with it, compared to those nucleons within the sphere. Hence the energy potential in step 1) is an overestamation. We need correct it by considering the surface energy term Es. Now infer that Es should be proportional to A2/3 (reminder: the radius of the nuclear has an empirical dependence relationship on the mass number A). 3) If the strong interaction force is a long range force, meaning that any nucleon inside the nucleus can interact with all the rest nucleons, a. can you obtain the energy potential Ev triggered by this force as a function of A? b. In this situation, will you still need a surface correction term as stated in 2)? Why?