Put yourself in their coveralls: just another day at the nuclear slurry lab, some idiot took all the good vessels, so you get Orlav to help you pour the day's plutonium solution into a smaller one. But after only a beer's worth is transferred, you feel a flash of heat and watch spectacularly radioactive liquid hose your coworkers. Oh man. Which one of you was closest to the gusher? That is to say, which one of you will die a painful death within within the day, the week, the month?
I'm betting only nuclear workers and biosafety level 4 lab techs have these "dead man walking" accidents. It's not like being clobbered by a girder. There's a mess, but usually no blood or explosion. Everything's mostly as it was before, but for everyone wracking their terror-flayed minds for how, exactly, the inverse-square law works. If we in general expire on a calendar, the recently irradiated die on the stopwatch.
These "criticality accidents" are dissected in the pdf linked above. Well, what precisely is a a criticality accident? Let's start with just criticality: we're talking nuclear fission, whereby a neutron hits an atomic nucleus and breaks it apart, releasing at least one other neutron among the resulting new elements. This doesn't happen with most of the stuff around you; the nuclei are comfortable with themselves. Shoot neutrons at iron or nitrogen all day, they shrug it off. But oh man did you see when Janet tossed a neutron at Uranium-235, not even that fast, like as a joke? Uranium just went to pieces. I don't think he'll show up tomorrow.
These sensitive, unstable atoms are mega-useful for extracting a lot of energy out a little matter. Pack enough of them close together, surround them with materials that neutrons like to bounce off of, and if you did your math right you'll reach criticality or critical mass: for every neutron tossed into this system you'll release, on average, another neutron. That ensures enough neutrons are hitting nuclei, knocking them to pieces, which releases more neutrons, which hit more nuclei, and so on in a chain reaction. This nuclei cracking fest releases energy in the form of heat. Say you were to use that heat to boil water, and maybe pipe the steam over to a turbine, and great gallopin' Greenpeace you got yourself a nuclear reactor.
These terms are a spooky-sounding menagerie, evoking mushrooom clouds and evaporated houses, but it's more helpful to think of criticality as a kind of equilibrium. You can be below equilibrium, subcritical, where neutrons die off like flies in a freezer and you're left with a heavy chunk that can't go in either the blue or the green bin. Or you can be above equilibrium, supercritical, where each neutron release begets a big stankin' load of them and the massive rate of atom splitting gets you an immolated city. But a critical mass, properly controlled, likes to hum along quietly.
That utilitarian-looking pdf, however, collects the dark teachable moments that come out of underestimating criticality. It's not inordinately difficult to handle nuclear materials, but there's a lot of factors to keep track of. The common term critical mass implies it's as simple as controlling the amount of "stuff" you're moving around, but shape matters too. For fissionable materials dissolved into liquids, a container's shape will affect reactions. Pull on your toque and pour that Uranium juice into a baking dish; no problem. Funnel it into a mason jar, however, and you might have one hot mess and an entry in "Criticality Incidents 20XX: All Goofuses, No Gallants."
"A Review of Criticality Accidents," a standout of the "technocratic summaries of awful things" genre, details a bunch of these messes. Legions of hapless (mostly east bloc) nuclear workers dropping, overfilling, and corner-cutting themselves to death. It's the written, murderous equivalent of infomercial goobers staining their homes. The totem of this PDF is "unfavorable geometry." Remember the shape stuff I mentioned before? That's what Los Alamos is trying to scare you away from. Unfavorable geometry apparently translates from the safety argot as "container that definitely wasn't supposed to have this much fissile material in this chain-reaction-friendly shape, as evinced by the dead people." Half the tales lay blame on these most disagreeable angles and forms. It comes up so often you'd think it'd be a menace even outside the nuclear engineering realm.
Tragic, but I think the Waltons are off the hook for that one.