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[QUE/CM-07011] Small Oscillations of Oxygen Molecule

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Assuming that the van der Waals force between two oxygen  atoms is described by Lenard Jones potential \[ V(r) = \epsilon_0 \Big( \frac{r_0^{12}}{r^{12}}- \frac{r^6_0}{r^6}\Big)\]
and that  \(\epsilon_0=16.4\times10^{15}\) \text{erg}, r_0= 3.88\times10^{-8}\text{cm}\) determine

  1. the force constant for small  oscillations
  2. the fequency of oscillations for the vibrational motion of a bound pair of He atoms.
  3. Using the  approximate results obtained comote the numerical value of the vibration of oxygen molecule. How do explain the differences between your answer and the experimenl value \(\nu=6.45\times10^{13}\).

Atlee Jackson*   

 

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