HCl is a diatomic molecule that can be modeled as two balls connected by a spring, i.e. a quantum oscillator. Experiments indicate that the spring constant k of the bond is 480 N/m. Assume the reduced mass of the molecule to be about . Treat the molecule as a quantum oscillator of stiffness and mass .
- Determine the energies of the two lowest-energy vibrational states, in units of eV. (That's the ground state and first excited state.)
- For each energy state, determine the amplitude of vibration of the oscillator if you treat it classically with an energy .
- What energy photon, in units of eV, is emitted if the molecule transitions from the first excited vibrational state to the ground state?
- What is the change in the amplitude of vibration if the molecule transitions from the first excited vibrational state to the ground state?
- After the molecule emits the photon, it loses energy. Does its frequency of oscillation increase, decrease, or remain constant? Explain your answer.