Let's be clear: while it may not be difficult to make explosives with radioactive
components, which will spread radiation, it isn't quite that easy to build a device which causes an atomic detonation
. At least, not unless you have a fairly large chunk of fissile
material. If you have a lot
of it, you can certainly build something that you can be reasonably sure will work; after all, the Manhattan Project
scientists and engineers did just that. The uranium
gun-type weapon dropped on Hiroshima
) was an untested design of a type of weapon that had never been made - and yet, despite being designed with chalk, pencils and slide rule
s, worked fine. The caveat
was that it required a (relatively) enormous amount of fissile material
s to work; the reason the implosion
weapon (Fat Man
) became the standard is that while being more complicated it required a smaller amount of material.
In any case, getting enough fissionables to build a gun-type bomb would be really, really hard. Getting enough to build an implosion weapon wouldn't be easy; plus, the technology required isn't trivial. It can be done; however, doing it in a backyard is stretching credibility unless that backyard has some pretty high-quality machine tools, electronic components and explosives experts in it with the facilities to handle and cast radioactive metal.
Finally, while it's true that low-level radioactives can be found in everyday life, none of these are suitable for fission or even decent contamination levels.
Note: niaporte noted, quite properly, that I had misidentified Little Boy's target as Nagasaki. It was, in fact, Hiroshima. My error.