1. (20 points total). Consider the Morse potential given by U(R) D[1-e-A-R)] = Fix the three potential parameters as follows: D-102.5 kJ/mol; B - 2.85 ', and Ro = 2.1 A. a) (5 points) Plot U(R) as a function of R, for R-0 to R-6. Be sure to use enough points to generate a smooth curve. b) (5 points) Using derivatives, derive an expression for the minimum of U(R), Re [Note: visual estimation from the plot will not receive credit). c) (5 points) What is the value of U(R.)? d) (5 points) Using derivatives, find an expression for the force constant k for the harmonic approximation to the potential near its minimum, as a function of the parameters D, B, and Ro