- #1

BlueDevil14

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## Homework Statement

Many diatomic (two-atom) molecules are bound together by covalent bonds that are much stronger than the van der Waals interaction. Experiment shows that for many such molecules, the interaction can be described by a force of the form

[itex]F_{r} = A[ e^{- 2b( r - R_0 )} - e^{ - b(r - R_0 )}][/itex]

where A and b are positive constants, r is the center-to-center separation of the atoms, and R_0 is the equilibrium separation. For the hydrogen molecule, [itex]A = 2.97 * 10^{ - 8} {\rm N}, b = 1.95 \times 10^{10} {\rm m}^{ - 1}, \text{and } R_0 = 7.4 \times 10^{ - 11} {\rm m}.[/itex]

Find the force constant for small oscillations around equilibrium

Hint: Use the Taylor series expansion for e^x

i.e. [itex]e^{x}=1+x+\frac{x^{2}}{2}...[/itex]

## Homework Equations

Hooke's Law: F=-k*x

## The Attempt at a Solution

I assume that the displacement for Hooke's Law is r/2 from the equation. We know force as a function of r already, and everything else is constant. The question is more math related, because I do not remember how to simplify this

*at all*.