Chemists use infrared absorption spectra to identify chemicals in a sample. In one sample, a chemist finds that light of wavelength 5.8 mm is absorbed when a molecule makes a transition from its ground harmonic oscillator level to its first excited level. (a) Find the energy of this transition. (b) If the molecule can be treated as a harmonic oscillator with mass                       5.6 * 10-26 kg, find the force constant.

What is the energy in eV and wavelength in µm of a photon that, when absorbed by a hydrogen atom, could cause a transition from the n = 4 to the n = 6 energy level? (a) energy in eV?   (b) wavelength in µm?

A free electron moving along the x-direction (one for which V(x) = 0) would have a wave function of the form f(x) = A eikx + B e−ikx where A and B are constants. (a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm¯¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by p² ħ² d² Ĥ 2me 2me dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using Â, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity?

Consider photons incident on a hydrogen atom. (a) A transition from the n = 4 to the n = 7 excited-state requires the absorption of a photon of what minimum energy? eV(b) A transition from the n = 1 ground state to the n = 6 excited state requires the absorption of a photon of what minimum energy?  eV