Final answer:
Isotopes used as stable neutron sources are generally located above the band of stability on the isotope stability curve and undergo beta decay, releasing excess neutrons. These isotopes have too many neutrons with respect to protons and decay consistently at a rate that makes them useful sources of free neutrons.
Step-by-step explanation:
A stable neutron source is an isotope that undergoes consistent decay to release excess neutrons. These isotopes are typically located away from the band of stability on the isotope stability curve, which is a graph that plots neutron number (N) versus proton number (Z). The band of stability represents the combination of protons and neutrons which make a nucleus stable. Isotopes with too many neutrons compared to protons are found above the band of stability. A stable neutron source would therefore be located in this region, where radioactive decay can result in the emission of neutrons. These isotopes will typically undergo beta minus (\(\beta^{-}\)) decay, where a neutron is converted into a proton, releasing a beta particle (an electron) and an antineutrino, along with the free neutron in question. It should be noted that not all unstable isotopes quickly release neutrons. Some may have relatively long half-lives despite being radioactive. However, those that are used as neutron sources have a suitable half-life that allows for a steady rate of neutron emission.