diff --git a/src/6_bonds_and_spectra.md b/src/6_bonds_and_spectra.md index 052d463ee128fbfcda237e654bf097a7bf15a8ad..194b3c9f5e087e1fcb15ff3820536c2a08086db9 100644 --- a/src/6_bonds_and_spectra.md +++ b/src/6_bonds_and_spectra.md @@ -604,9 +604,9 @@ where $r$ is the distance between two atoms, $\epsilon$ is the depth of the pote 3. Expand $U(r)$ in a Taylor series around $r_0$ up to second order. By considering a second-order (=harmonic) potential approximation around the minimum ($r_0$), find an expression for the spring constant, $\kappa$, in terms of $\epsilon$ and $\sigma$. 4. Using the spring constant $\kappa$ you found earlier, find the ground state energy of the molecule by comparing the molecule to a quantum harmonic oscillator. What is the energy required to break the molecule apart? -??? hint + ??? hint - Because the diatomic molecule is modeled as a one-body problem (in the center of mass rest frame of the molecule), the mass should be replaced by the [reduced mass](https://en.wikipedia.org/wiki/Reduced_mass). + Because the diatomic molecule is modeled as a one-body problem (in the center of mass rest frame of the molecule), the mass should be replaced by the [reduced mass](https://en.wikipedia.org/wiki/Reduced_mass). 5. What is the approximate number of phonons that can occupy this mode before the potential becomes anharmonic?