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Vibrational motion of a diatomic molecule

An approximation for the potential energy of a KCl molecule is U=A[(R^7/8r^8)-(1/r)],
where R=2.67*10^-10m and A=2.31*10^-28J*m.

a. Using this approximation find the radial component of the force on each atom. Express your answer in terms of the variables A, R0 and r.

b.Find the equilibrium separation.

c. Find the minimum potential energy.

d. Use r=R+x
to show F= -(7A/R^3)

so that the molecule's force constant is k=7A/R^3

e. With both the K and CL atoms vibrating in opposite directions on opposite sides of the molecule's center of mass

(Mm/M+m)=3.06*10^-26kg

is the mass to use in calculating the frequency. Calculate the frequency of small-amplitude vibrations.

Solution Summary

The 3 pages file contain a detailed explanation how to expand teh radial potential and obtain the vibrational frequency of a diatomic molecule.

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