I need detailed explanation for my hw problem.

3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U(T) = D(e2a(rrg) _ 26a(rre)) where "r is the interatomic distance, are is the equilibrium bond distance, D is the dissociation energy (a constant), and a, is a positive constant. a) What are the dimensions of are, D, and 0,? Express your answer in terms of products LaTch, where L is length, T is time, M is mass, and a, b, and c are rational numbers. b) What is the value of the potential at arbitrarely large separations (T > are). c) Find the value of r for which U is a minimum. d) What is the minimum value of U? e) Show that for very small displacements 59 = (r 73,)