Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1740001     Energy and amplitude of vibration of HCl     1740001
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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 .

  1. Determine the energies of the two lowest-energy vibrational states, in units of eV. (That's the ground state and first excited state.)
  2. For each energy state, determine the amplitude of vibration of the oscillator if you treat it classically with an energy .
  3. What energy photon, in units of eV, is emitted if the molecule transitions from the first excited vibrational state to the ground state?
  4. What is the change in the amplitude of vibration if the molecule transitions from the first excited vibrational state to the ground state?
  5. After the molecule emits the photon, it loses energy. Does its frequency of oscillation increase, decrease, or remain constant? Explain your answer.

 

1710001     Infrared photons absorbed by hydrogen     1710001
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Suppose that you shine continuous IR light in the range 0.5 eV - 1.6 eV on atomic hydrogen gas and study the light that gets absorbed by the gas. What are the two lowest energy photons that will be absorbed by atoms and what are the initial and final states of the hydrogen atoms that absorb these photons?

 


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