Question 1. Plot on a single graph the Lennard-Jones potential, Uu, using the parameter sets (i) a_i=2, e_i=2, (ii) G2=3, 6₂=3, and (iii) G₃=4 and 6₃=4. Please remember to label your axes properly.

Question 2: Plot on a single graph using the parameters G₂=3, 6₂=3: (i) the corresponding Lennard­Jones potential Uu, (ii) the repulsive term of this Uu potential (iii), the attractive term of Uu, and (iii) the derivative of the same Lennard-Jones potential function with respect to r,              dU_Li(r) /dr

Please remember to label your axes properly.

Question 3:

(i) Write the expression of the force fl_j corresponding to the Uu potential energy term.

(ii)  Derive the expression of the distance r_mi_n at which Uu has its minimum value, as a function of the parameters a and/or E.

(iii)  What is the value of P_LI(r_min) ?