|Fig. 1: A nucleus emitting a gamma ray. (Source: Wikimedia Commons)|
Analogous to how electrons have energy levels and release a photon when they drop in energy, nuclei also have energy levels and emit photons when they move from an excited state to a less energetic state. The radiation that a nucleus emits when such an event occurs is dubbed gamma radiation, and is not specific to an energy level. Despite this, most nuclear drops in energy are far larger than electron drops, with gamma rays being produced in the 100 keV - 10 MeV range, where electron drops tend to stay in the 1 - 10 eV range (corresponding to visible and UV light). This whole process is called gamma decay and is shown in Fig. 1.
A high energy nucleus does not have to release all of its energy in a single photon. Rather, and more likely, the nucleus will emit several gamma rays over some period of time until it reaches its ground state. Conservation of energy and angular momentum play a role in which emission takes place. Specifically, there exist rare occurrences in which a nucleus has two low energy states with vastly different total angular momenta. One of these states will be slightly lower in energy, so the nucleus will try to drop to it through gamma decay. However, the large difference in angular momentum must be accounted for in the emitted photon by conservation of momentum. It is unlikely for a photon to have such a large angular momentum, so the excited nucleus will remain in this meta-stable state for a much longer time than the average gamma decay, which is about 10-12 seconds. In fact, these so-called isomeric nuclei can live for several days or even longer. The emitted gamma ray must also obey conservation of energy. Specifically, the emitted photon must always have energy Eγ where Eγ = M0c2 - Mfc2 - Knucleus. M0 is the initial rest mass of the nucleus, Mf is the final mass of the nucleus, Knucleus is the kinetic energy of the recoil of the nucleus (which results from conservation of linear momentum), and c is the speed of light. Additionally, energy and angular momentum at this scale are quantized, i.e. they are integer multiples of some fundamental values. Thus, we can see why it is unlikely for a photon to be emitted in such an event - it is difficult to satisfy both conservation of energy and angular momentum simultaneously. 
As mentioned before, chances are that an excited nucleus won't reach its ground state after just one emission. However, once the nucleus is in its ground state, it will either be stable or undergo radioactive decay, depending on its mass and parent nucleus. For example, if the now-grounded nucleus is somewhere along the uranium decay chain (not at the bottom), it will continue to emit radiation, likely alpha and beta particles, until it reaches stability. 
© Aaron Altman. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 K. S. Krane, Introductory Nuclear Physics (Wiley India, 1988).
 E. Segré, An Introduction to Nuclear and Subnuclear Physics (Benjamin, 1964).