Suppose we have reason to suspect that a certain quantum object has only three quantum states. When we excite a collection
of such objects we observe that they emit electromagnetic radiation of three different energies: 0.3 eV (infrared), 2.0 eV
(visible), and 2.3 eV (visible).
(a) Draw a possible energy-level diagram for one of the quantum objects, which has three bound states. On the diagram,
indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the
observed photons and no others. Label the energies of each level (K + U, which is negative). The energy K + U of
the ground state is −4 eV.
(b) The material is now cooled down to a very low temperature, and the photon detector stops detecting photon
emissions. Next a beam of light with a continuous range of energies from infrared through ultraviolet shines on the
material, and the photon detector observes the beam of light after it passes through the material. What photon
energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)?
(c) There exists another possible set of energy levels for these objects that produces the same photon emission spectrum.
On an alternative energy-level diagram, different from the one you drew in part (a), indicate the transitions
corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no
others. Label the energies of each level (K + U, which is negative).
(d) For your second proposed energy-level scheme, what photon energies would be observed to be significantly reduced
in intensity in an absorption experiment (“dark absorption lines”)? (Given the differences from part (b), you can see
that an absorption measurement can be used to tell which of your two energy-level schemes is correct.)