(Solved): The restoring force constant \( \mathrm{C} \) for the vibrations of the interatomic spacing of a t ...

The restoring force constant \( \mathrm{C} \) for the vibrations of the interatomic spacing of a typical molecule is about \( 10^{3} \) Joules \( / \mathrm{m}^{2} \). Use this value to estimate the zero-point energy of the molecular vibrations. The mass of the molecule is \( 4.1 \times 10^{-26} \mathrm{~kg} \). a. For the problem above: a. Estimate the difference in energy between the ground state and the first excited state of the vibrating molecule. b. From your answer in (a) determine the energy of the photon emitted by the vibrations in the charge distribution when the system makes a transition between the first excited state and the ground state. c. Determine the frequency of the photon and compare it with the classical oscillation frequency of the system. d. In what range of the EM spectrum is it?