Vibration of a Covalently Bond

Vibration of a Covalently Bonded Molecule many diatomic (two-atom) molecules are bound together by covalent that are much stronger than the van der Waals interaction. Examples include H., 0 €¢€¢ and N2€¢ Experiment shows that for many such molecules, the interaction can be described by a force of the form

Where A and b are positive constants, r is the center-to-center separation of the atoms, and Ro is the equilibrium separation. For the hydrogen molecule (H,), A = 297 X lO-8 N. b = 1.95 X l0 m-1, and Ro = 7.4 X to-11 m. Find the force constant for small oscillations around equilibrium. (Hint: Use the expansion for ex given in Appendix B.) Compare your result to the value given in Exercise 13.40.

Solution:

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