Exploring the Truths and Myths of the Harmonic Oscillator Model

In summary, the harmonic oscillator (HO) model does not account for bond dissociation and the bond strength is related to the depth of the potential energy surface, not the steepness of the potential energy curve. The vibrational frequency increases with increasing quantum numbers, which means the energy level is higher up the potential well. This can be seen in a situation where tunneling is applicable, as the increased energy allows particles to tunnel through a potential barrier.
  • #1
adiabatman
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Homework Statement


Which of the following statements about the harmonic oscillator (HO) is true?
a) The depth of the potential energy surface is related to bond strength.
b) The vibrational frequency increases with increasing quantum numbers.
c) The HO model does not account for bond dissociation.
d) The bond strength is related to the steepness of the potential energy curve.
e) The tunneling probability increases with the increasing quantum numbers.


The Attempt at a Solution


a) True: The depth of the potential energy surface is related to bond length therefore it is related to bond strength.
b) True: Vibrational frequency is proportional to the increasing quantum numbers
c) True: There is no information about bond dissociation in the HO model
d) False: The steepness of the potential energy curve is not related to the bond strength
e) not sure about this one

any help or direction is appreciated. thanks!
 
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  • #2
Review tunneling ... draw a sketch of a situation where tunneling would apply and work it out?
increased quantum numbers means energy is increased - means the energy level is higher up the potential well ... what does that mean in relation to the barrier?
 
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What is a harmonic oscillator?

A harmonic oscillator is a type of system in which a particle or object undergoes periodic motion around an equilibrium point. This motion is characterized by a restoring force that is directly proportional to the displacement from the equilibrium point.

What is the equation of motion for a harmonic oscillator?

The equation of motion for a harmonic oscillator is given by m(d^2x/dt^2) + kx = 0, where m is the mass of the object, k is the spring constant, and x is the displacement from the equilibrium point.

What are the different types of harmonic oscillators?

The two main types of harmonic oscillators are the simple harmonic oscillator and the damped harmonic oscillator. The simple harmonic oscillator has no external forces acting on it, while the damped harmonic oscillator experiences a damping force that decreases its amplitude over time.

What is the relationship between a harmonic oscillator and energy?

In a harmonic oscillator, the total energy is constant and is divided between kinetic energy (due to motion) and potential energy (due to the restoring force). As the object oscillates, the energy is continuously transferred between these two forms, but the total energy remains constant.

How is a harmonic oscillator used in real life?

Harmonic oscillators are used in many real-life applications, including clocks, musical instruments, and even earthquake-resistant buildings. They are also used in physics experiments to study oscillatory motion and understand the behavior of systems in equilibrium.

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