Calculate the energies of the first three energy levels of an electron that is constrained to move in a sphere of radius 50 pm. Indicate the degeneracy of each rotational level.
6) For a certain quantum harmonic oscillator of effective mass 1.33 x 10^-25 kg, the difference in adjacent energy levels is 4.82 x 10^-21 J. Calculate the force constant of the quantum harmonic oscillator.
c) To first approximation, a diatomic molecule can be represented by a harmonic oscillator. However, we learned that the Morse oscillator provides a better representation of a diatomic molecule. The figure below shows the harmonic and Morse potential energy curves for a diatomic molecule, along with the corresponding vibrational wavefunctions. How do you expect the average bond length of a diatomic molecule would change if the molecule transitions from the ground to any of the excited vibrational levels when: 1) the molecule is represented by the harmonic potential, and 2) the molecule is represented by the Morse potential? Explain your reasoning.
Harmonic potential
Morse potential