We can use the classical harmonic oscillator to think about molecular bonds. The HCl molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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We can use the classical harmonic
oscillator to think about molecular bonds. The
HCI molecule has a force constant k = 481
N/m. For the mass, use the reduced mass,
which is defined as µ = (m₁m₂)/(m₁+m₂).
a) Plot the potential energy of HCl from -1 to
1 Å. What happens to the curvature of the
potential as the force constant is varied? What
does this mean physically?
b) Plot position as a function of time for a total
energy of 6 x 10-20 J. What is the period of the
motion? How does the period change as the
force constant is varied? Explain why this
makes sense physically.
Transcribed Image Text:We can use the classical harmonic oscillator to think about molecular bonds. The HCI molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.
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