Assume that a hypothetical object has just four quantum states, with the following energies:
−1.0 eV (third excited state)
−1.8 eV (second excited state)
−2.9 eV (first excited state)
−4.8 eV (ground state)
(a) Suppose that material containing many such objects is hit with a beam of energetic electrons, which ensures that there
are always some objects in all of these states. What are the six energies of photons that could be strongly emitted by
the material? (In actual quantum objects there are often “selection rules” that forbid certain emissions even though
there is enough energy; assume that there are no such restrictions here.) List the photon emission energies.
(b) Next, suppose that the beam of electrons is shut off so that all of the objects are in the ground state almost all the
time. If electromagnetic radiation with a wide range of energies is passed through the material, what will be the three
energies of photons corresponding to missing (“dark”) lines in the spectrum? Remember that there is hardly any
absorption from excited states, because emission from an excited state happens very quickly, so there is never a
significant number of objects in an excited state. Assume that the detector is sensitive to a wide range of photon
energies, not just energies in the visible region. List the dark-line energies.
(c) At high enough temperatures, in a collection of these molecules there will be at all times some molecules in each of
these states, and light will be emitted. What are the energies in electron volts of the emitted light?
(d) The “inertial” mass of the molecule is the mass that appears in Newton's second law, and it determines how much
acceleration will result from applying a given force. Compare the inertial mass of a molecule in the top energy state
and the inertial mass of a molecule in the ground state. If there is a difference, briefly explain why and calculate the
difference. If there isn't a difference, briefly explain why not.