[QUE/CM-07010] Small Ocillations and He molecule

Assuming that the van der Waals force between two He  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  \(\epsilon_0=1.42\times10^{15} \text{erg},\qquad r_0= 2.87\times10^{-8}\text{cm}\).

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 above and quanum mechanical expression for vibrational energy of He molecule, determine whether or not two He atoms canform a molecule He\(_2\). ( Note that these results are only approximate  (and can in fact lead to the worng conclusion!) but nevetheless they are instructive. Can you guess why the result might be wrong?

Atlee Jackson*