•• (Section 12.6) The potential energy of the two atoms in HCl can be approximated by the...

•• (Section 12.6) The potential energy of the two atoms in HCl can be approximated by the Morse potential (12.42) (Problem 1) with

 A = 4.57 eV, R0 = 0.127 nm, S = 0.0549 nm

(a) Plot the potential energy U(R) for 0 ≤ R ≤ 0.3 nm. (Restrict the vertical axis to the range −5 ≤ U ≤ 5 eV.) (b) What are the bond length and binding energy for HCl? (You may ignore the zero-point vibration.) (c) What is the force constant k for HCl? [See Problem 1(d).] (d) Plot the SHO well (12.25) that approximates U(R) near R0. Superpose this plot on your previous one.

Problem 1

••• 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.