A close-quarter nuclear weapon. Makes *perfect* sense.
Did anyone release a statement, that says it is specifically a close-quarter combat weapon? that is impossible indeed, and senseless if it is in fact what you say it is, but it is a projectile which means that it fires at distances, and considering it is a miniaturized nuclear device, then it depends on it's yield, to determine the blast radius, and at which range it will kill.
Second as I said before, that sort of weapon already exists.
Not that is impossible to do it, but there's no *sense* doing it, because there is a high risk that it'll kill the person using it. Especially a 19 year old kid with no protection from radiation and explosions whatsoever.
How is it impossible to make such a weapons, if it already exists, and was built and put to service by the us army in the early 1960's, and quite a substantial sum of them were manufactured, and instored.
Second, if someone is stupid enought to use it in such an enclosed space, and short range, then he shouldn't wield it, you make sound as if it is the only weapon available in the game, while I'm sure it is not. As for radiation, it is widely known that radiation from nuclear explosions quickly dissipate and does not last quite long (in reference to Nagasaki and Hiroshima), while radiation from nuclear waste, or nuclear fuel leakage, whould last quite a long time, such as the leakage that occures in Chernobyll.