Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Question
Chapter 14, Problem 14.62E
Interpretation Introduction
Interpretation:
Whether the deviations come out from an ideal harmonic oscillator are probably seen at low energies or high energies is to be stated.
Concept introduction:
A system, the displacement of which from the equilibrium location corresponds to a restoring force, denoted by F is known as harmonic oscillator. This restoring force is directly proportional to the displacement, x.
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11. (
Draw the potential energy as a function of x. On top of the potential function, draw horizontal
lines corresponding to the ground and first two excited quantum mechanical state energies of
this system. Label the lines with their respective "v labels". Finally, using your energy state
lines as individual axis, draw the wave functions for the ground and first two excited states.
Consider the standard one-dimensional Harmonic oscillator centered about x = 0.
physical chemistry
4. Sketch the shape of the ground state wavefunction for a harmonic oscillator, and the
wavefunction for the next highest energy. Be sure to include the potential energy curve on the
graph. What are the corresponding vibrational quantum numbers and the energies in terms of v,
the classical vibrational frequency?
a. A diatomic molecule with a reduced mass of 5.00 amu has a force constant of 1000 N m¹.
What is the vibrational frequency in cm¹?
Carbon dioxide is a linear molecule. The carbon-oxygen
bonds in this molecule act very much like springs.
Figure 11–58 shows one possible way the oxygen atoms
in this molecule can oscillate: the oxygen atoms oscillate
symmetrically in and out, while the central carbon atom
remains at rest. Hence each oxygen atom acts like a simple
harmonic oscillator with a mass equal to the mass of an
oxygen atom. It is observed that this oscillation occurs
at a frequency ƒ = 2.83 × 1013 Hz. What is the spring
constant of the C-O bond?
Chapter 14 Solutions
Physical Chemistry
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