Spectroscopy hookes law, derivation?

In summary, the conversation is discussing the equation for Hooke's law, which is 1/(2pi*c)*sqrt(k/m_reduced). The speaker is confused about the inclusion of c in the equation and wonders why reduced mass is used. Another person explains that this is not actually Hooke's law, but a result of solving the motion equation for a harmonic oscillator. The use of reduced mass makes calculations easier for systems with two oscillating objects. The inclusion of c comes from the definition of wavenumber as v/c. However, there is a discrepancy as the document states ν as frequency, not wavenumber.
  • #1
popopopd
12
0
hi, i am a lillte confused why the equation for hookes law is

1/(2pi*c)*sqrt(k/m_reduced)?

where does c come from?

http://www.massey.ac.nz/~gjrowlan/intro/lecture5.pdf

- slide 8.
Untitled-1.png


also, is there any particular reason why we use reduced mass?
 
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  • #2
This is not a Hooke's law, rather a result you can get by solving the motion equation for an oscillator assuming it obeys Hooke's law (so it is a harmonic oscillator).

I don't see where the c comes from either. Using reduced mass makes calculations much easier for the system made of two oscillating objects (as compared to the system containing one object oscillating around some equilibrium position).

Moving thread to physics.
 
  • #3
Borek said:
result
Ah I found it. by definition wavenumber is v/c and that gave the equation 'c'
 
  • #4
They stated ν is frequency, not wavenumber.
 
  • #5
Borek said:
They stated ν is frequency, not wavenumber.
yeah thanks, they did. I think they are wrong.
 

FAQ: Spectroscopy hookes law, derivation?

1. What is Hooke's Law in spectroscopy?

Hooke's Law states that the amount of displacement of a molecule from its equilibrium position is directly proportional to the force applied to it.

2. How is Hooke's Law used in spectroscopy?

In spectroscopy, Hooke's Law is used to calculate the bond force constant or spring constant, which is a measure of the stiffness of a chemical bond.

3. What is the equation for Hooke's Law in spectroscopy?

The equation for Hooke's Law in spectroscopy is F = -kx, where F is the force applied, k is the bond force constant, and x is the displacement of the molecule from its equilibrium position.

4. What is the derivation of Hooke's Law in spectroscopy?

The derivation of Hooke's Law in spectroscopy is based on the assumption that the bond force constant remains constant throughout the range of displacement and that the force applied is directly proportional to the change in bond length.

5. How is Hooke's Law used to determine bond lengths in molecules?

By measuring the force applied and the corresponding displacement of a molecule, Hooke's Law can be used to calculate the bond force constant and in turn, determine the bond length in a molecule. This allows for the determination of molecular structures and the study of chemical bonding.

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