••• A simple analytic function that can be used to approximate the potential energy of the...

••• A simple analytic function that can be used to approximate the potential energy of the two atoms in a diatomic molecule is the Morse potential

where A, R0, and S are positive constants, with R0≫ S. (a) Sketch this function for 0 ≤ R < ∞. (b) In terms of A, R0, and S, write down the bond length and binding energy of a molecule whose potential energy is given by (12.42). (c) Write down the first three terms of the Taylor series for U(R) about R0 (see Appendix B) and show that they give the parabolic approximation (12.25). (d) Show that the force constant k is 2A/S2.