They have a half-life of about 10.4 minutes. Neutrons in nuclei however are usually not unstable, unless the nucleus itself is unstable.
The question of what is and is not radioactive is an interesting question. People often speak of uranium as being "dangerous radioactive waste," for instance, without recognizing that uranium is a naturally occurring element that is quite ubiquitous and not particularly radioactive when compared with many other radioactive substances. In fact, uranium, at least when it is separated from its radioactive daughters, is a much more powerful chemical toxin than it is a radiotoxin. Potassium is also radioactive, owing to the presence of potassium-40 which has a half-life of 1.227 billion years. People eat bananas quite happily, because without potassium, its radioactivity aside, they would die.
People often focus their attention on the elements in so called "nuclear waste" that will persist for long periods, things like Cs-135, for instance, which has a half-life of 2.3 million years. However, cesium-135 is
far less radioactive than its sister nucleus, cesium-137, which will completely decay to back ground levels over a few centuries. Cesium-137 is dangerous; cesium-135 is not particularly so.
In fact when life first appeared on earth, potassium was about 12 times more radioactive than it was now, about twice as much uranium-238, and about 84 times as much radioactive uranium-235. In fact there was so much U-235 in ancient times that naturally occurring nuclear reactors are known to have formed at Oklo, in Africa.
http://www.ocrwm.doe.gov/factsheets/doeymp0010.shtmlIn fact, it can be shown that under certain circumstances, the use of nuclear power - public perception aside - will make the world
less radioactive than it would be otherwise, although a period of about 1000 years is involved. This works because fission changes elements that stay radioactive a very long time, like uranium and thorium, into elements that do not stay radioactive particularly long - they quickly "burn out."
Leaving nuclear power aside, and looking only at natural radioactivity, it happens that nuclear stability theory predicts that no two nuclei of the same mass number can
both be stable, even though such pairs clearly exist in nature. (Three of the "stable" isotopes of Selenium, for instance, Se-74, Se-76 and Se-80 are members of such pairs. Germanium-74 and Ge-76 both exist and are thought "stable" and Kr-80 also exists and is thought "stable.")
Careful examination, now that the instrumentation for the detection of radioactive decay has become so sensitive, of the question has borne theory out in some cases. For instance, the pair Xenon-136 and Barium-136 both exist. For a long time, it was thought that both were "stable nuclei" but recently it was discovered that Xenon-136 is in fact unstable. Like Bismuth it has an extremely long half-life, greater than 9.3 X 10^19 years. Should the universe persist for a very, very, very long time - which it may not do - all of the xenon-136 in the universe will decay to make barium-136 through the intermediary of cesium-136.
The situation is probably very much parallel to the chemical conception of kinetics vs thermodynamics.