3. The interaction between neutral atoms can be approximated with the Lennard- Jones potential 0 12 a 6 U=4[(;) -(:)l where U is potential energy, 7' is the interatomic distance, and e and or are positive constants. a) What are the dimensions of e and or? Express your answer in terms of prod- ucts LaTbMC, 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 arbitrarily large separations (7* >> a). c) Find the value, 7' 2 T6, for which U is a minimum. d) What is the minimum value of U? e) Consider the expansion of U (1') in powers of 7' around 1' 2 re (1(7)%U(Te)+g(rre)+%k(rre)2+-~ nd 9 and k