Question: 1. Treating a diatomic molecule as a harmonic oscillator, derive the expression for the average potential energy for its ground state 2. Consider HCl in

1. Treating a diatomic molecule as a harmonic oscillator, derive the expression for the average potential energy for its ground state 2. Consider HCl in its first excited vibrational state. Search online for the HCl bond length and bond force constant. Calculate the molecule's vibrational energy. Compare with the value obtained from the equipartition of energy theorem. 3. Calculate the separation between energy levels for an anharmonic quantum oscillator. 4. How many electrons can occupy the system with l=0, l=2 and l=4 assuming 2e in each energy state. What are the number of possible orientations of the orbital angular momentum for each state? 5. Based on the model for the hydrogenic atom, calculate the ionization energy in eV for one more of oxygen. 6. Calculate the most probable radius at which an electron will be found when it occupies the 2pz orbital in the hydrogenic atom. 7. Write down the hydrogenic wavefunction for the 3S orbital of Nitrogen. Calculate the values of r

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