A few questions about Chernobyl's Elephants Foot and criticality.

Couple questions for the Doper physicists:

  1. Why is the elephants foot at Chernobyl so dangerous if it only has trace amounts of uranium and is mostly silicon dioxide? Is it the sheer quantity?

  2. If U235 has a half-life of 700 mil years, how is it the elephants foot can be so much safer than it was a few years ago?

  3. I’ve read a bit on criticality but I have a hard time wrapping my head around how 2 subcritical halves of a supercritical sphere can be safe separately but deadly apart. I’d think it’s the type of thing you’d want to split into more pieces. If I throw a ping pong ball into a room filled with 50 mousetraps there’s still a good chance of a bunch going off vs a room with a 100 mousetraps. What am I missing? Note that I do get that it’s an exponential process and if the neutrons escape, etc, etc.

  4. What would happen if I brought two halves of a supercritical u235 sphere together? I’ve read that it can fizzle, but how big a reaction is that?

Thanks!

Daughter elements. Decay product - Wikipedia

U-235, and I don’t believe an RBMK was enriched much above 3-5% -235, isn’t that radioactive when not prompt critical. The daughter elements from its fission chains are. They have much shorter halflifes, which is usually inversely proportional to how radioactive they are. Half life of a few hours like Xe-135, the isotope of Xenon responsible for the ‘reactor poisoning’ mentioned in the movie? Very radioactive.

For #4, ask the poor bastards who were around the Tokaimura criticality accident, in 1999. Tokaimura nuclear accident - Wikipedia

If the sub critical masses of U-235 are large enough and pure enough, the speed necessary to combine them and get a bang, isn’t that fast. Like drop them off a building fast. IIRC, it’s at the Nuclear Weapon Archive, but Dr. Sublette showed the speed was something like 50 m/s or so. It’s going to depend on the size of your blocks, and their geometry, but I wouldn’t be surprised to see a yield of a few hundred tons or so, even without an initiator.

Oh and for #3, go take a look at the terms for the neutron transport equation. Its complicated. But it’s basically a question of neutron flux, cross-section available to capture a neutron, and speed of the neutron.

Pure uranium is not that radioactive (don’t swallow any, though); it’s all the nasty highly radioactive fission products that you have to worry about. But the thing about short-lived to medium-lived isotopes is, if you wait a while, they decay. I still wouldn’t get close to that Elephant’s Foot, but evidently its radioactivity has decayed somewhat since people have.

If there is not a critical mass, not enough neutrons are released to sustain a chain reaction and it will die down. If, on the other hand, all the uranium atoms are bunched up together then a lot of the neutrons go on to hit other atoms which in turn split and release even more neutrons, etc.

If you split a minimal critical mass into two pieces like you describe, neutrons will be more likely to escape instead of causing further fissions.

Such things have been done accidentally with U235 (and also other materials such as plutonium). What would happen is, there would be a fatal burst of radiation that will kill you sooner or later, and a lot of energy will be instantaneously released. This energy may be the equivalent of however many pounds of high explosive, but the effects are not the same as setting off that much TNT, since most of the energy will be in the form of heat rather than kinetic energy. The heat will melt/destroy your uranium sphere, so it won’t stay supercritical for very long. In gun-type weapons like the original Little Boy they fired one piece into another using cordite; I don’t know what’s the best you could do trying to smash pieces of uranium together by hand. Note that uranium basically weighs as much as gold; it’s not that easy to juggle huge chunks of it around. Those Japanese workers managed to kill themselves by pouring liquid uranium solution from a bucket.

You may be missing the Law of Large Numbers. Suppose you’re hoping for five events, each a one-in-a-thousand chance, so you throw in 5000 ping-pong balls. You’ll probably get about five events but there’s uncertainty: more than 8% of the time you’ll see two events or fewer and there’s a 0.7% chance you’ll get no events at all.

Try the same experiment with 10[sup]24[/sup] ping-pong balls. Now it is virtually certain that the number of events will be 1.000000000×10[sup]21[/sup], to that precision. Reactions involving very large numbers of atoms are predictable.

It’s not like there is a sharp criticality dividing line between N atoms of uranium and N+1 atoms. And remember that it’s not just one value of ‘critical mass’ It’s a particular value for whatever particulr mixture and purity and desnity you have.

Even if it’s a super-critical mass, it still takes time for the reaction to build. If it’s only slightly supercritical, it starts to build slowly. If it’s slightly less than critical, it dies down slowly. If it’s inbetween, it can run for years.

I understand the law of large numbers but I’m not sure how it applies. I’ve read a bunch about the factors affecting criticality - temperature, density, shape of mass, etc. The part I have trouble understanding is how splitting the mass in just two pieces is considered enough of a safe guard. Ok so maybe you can’t as many fission generations but I’d think you could get enough to make it dangerous.

Or to put it another way: If you have a sub-critical mass, sometimes a neutron will in fact hit another nucleus in the mass and cause another fission event. But the key is that this will happen on average less than once per fission event. If you’re very close to criticality, then maybe it’ll happen on average to .9 of the initial fission events: So if you have 100 spontaneous (or outside-induced) fission events, those will trigger 90 more, which will in turn trigger 81 more, and so on, but it’ll die out. On the other hand, if you’re just a little bit above critical mass, then maybe it’ll happen on average 1.1 times per initial fission event: So if you start with 100, then you’ll get 110 the next round, then 121 after that, and it eventually (pretty quickly) grows very large.

Incidentally, the reason that it’s possible to control this process is because not all fission events happen immediately. Some do, but some have a delay of a few seconds or so. If conditions are such that the prompt fission all by itself is enough to maintain criticality (i.e., the reactor is “prompt critical”), then something really big and dramatic that you don’t want is going to happen. If, however, the reactor is subcritical with respect to the prompt fission, but critical when you also include the delayed fission (“delayed critical”), then you’ve got time to wiggle the control rods or whatever.

Ok the daughter elements make a lot of sense- strange that not a single description of the foot explains that.

So the criticality incident you linked to reads a lot like the others I’ve read - blue light and puking. But in the incident you linked, the water just boiled for 20 hours before going subcritical and that even had water to moderate the neutrons (I suppose it just had less uranium then). Where’s the explosion (or enough of one to send it subcritical)? 20 hours seems like a long time for an exponential process to occur without things getting ugly. I suppose it was critical and not supercritical?

So 50m/s is enough speed with subcritical masses to create the brief density and perhaps temp to get an explosion of some measure?

Thanks btw. I know my questions come in barrages, so I appreciate your patience.

Do we have any sense of how many atoms (or some measure of distance) of u235 at normal density a typical neutron from a fission event “misses” before hitting the nucleus of another atom? I ask because if the answer isn’t “alot” it seems strange that a fission event at the center of a critical mass/2 sphere wouldn’t have enough material to, I don’t know, at least melt the thing.

The answer is “a lot”. Put a pea in the middle of the 50-yard-line in an NFL stadium. That’s how big a target the nucleus is. Now pack a bunch of stadiums together, and draw a straight line. You’re going to pass through a heck of a lot of stadiums before you hit one of the peas.

For some subcritical masses. Tokaimura involved a uranyl nitrate solution with 18 or so percent U-235, mixed by hand. Slow, and not that pure. A total amount of U-235 that wasn’t probably that much in excess of a critical mass either. Not too many doublings are going to occur before the mass heats and expands. Enough to change the geometry where one fission neutron leads to less than one fission neutron produced on average. Then of course, the solution cooled, its density increased, steam voids were eliminated with accompanying increase in neutron moderation, and the whole mess started again.

Compare with a hypothetical set of ultra-pure U-235 masses, individually barely subcritical, being combined by gravity or rudimentary explosives. Maybe, as was the case for Little Boy, elements with high neutron capture cross-section are used to shield the masses until the exact instant they’re to be combined. Now the geometry permits plenty of doublings, before heat and expansion alters the geometry into a non-critical configuration. It’ll suffer though, without a tamper or case to confine the masses as long as possible, and reflect otherwise lost fission neutrons back at the now critical mass. How big a boom? I don’t know.

Go read the Nuclear Weapon Archive I’ve mentioned here before, especially sections 3 and 4 of the FAQ. Lots of physics on why and how a nuclear device does what it does.

Thanks everyone - this is starting to make a little more sense. Is there a particular daughter element/isotope of uraniun 235 that is considered the biggest killer in these meltdown/fallout events? I’m only on episode 2 of the HBO show but they’re already concerned for areas awfully far from ground zero. Given the ppm at those distances this stuff is that much more radioactive/deadly?

Radioactive elements that are isotopes of or close cousins to elements your body uses, are really dangerous. You remember Emily Watson’s character talking about Potassium Iodide pills? That was to saturate one’s thyroid gland with non-radioactive iodine, so that it wouldn’t absorb radioactive I-131. Similarly, cesium-137 and strontium-90 are nasty because they are easily absorbed by the body. Where they’ll be happily disintegrating away, battering DNA.

Plutonium and uranium aren’t terribly dangerous in their already oxidized forms. IIRC, I’ve read that one could swallow a lump of the metal, which would pass through the digestive tract largely unchanged. Inhaled plutonium fine particles are a different story. Heavy metals in chemical combinations that facilitate bodily absorption, can be incredibly dangerous. OTOH, the LD 50 for many uranium isotopes and methods of administration, can be rather high. See, e.g.: Acute chemical toxicity of uranium | Request PDF

As noted, the U235 isn’t that radioactive, and your sphere has a chance to cool down. Compare OTOH this nice glowing piece of Pu238

Sigh. So many questions. My curiosity is a plague on me and the SDMB.

So how is it that they needed to evacuate a 30km radius around the Chernobyl plant but the vast majority of the workers on site right after the accident lived? Something like only 28 out of 600 workers died and some of those deaths were from the steam explosion. Hell, even Dyatalov lived another 10 years. How did they all not get lethal doses on site but it could still be lethal many km away?

For one thing, it depends on how long you stay in the contaminated area. There may have been workers on site, but they got off site as quickly as they could. You wouldn’t want to live there.

Because the people on site weren’t going about there daily lives - eating and drinking contaminated items. The one thing you absolutely don’t want to do is to ingest alpha emitters. So, you don’t want to be living in an area where radioactive dust has contaminated.

The explosion of the reactor and subsequent fire sent huge amounts of radioactive smoke and dust over the surrounding area. It’s that fallout that’s so dangerous and widespread. Much of that didn’t get inside the rest of the plant though, and there’s concrete walls and other barriers shielding many of the rooms from the core’s radiation.

Exactly. The workers were exposed to radiation for a short time. The residents, if they didn’t evacuate, would be exposed to radioactive contamination in the air (dust), water and food for years and years.

Also, a danger level can be much lower than lethal and still be high enough to justify evacuation.

So in episode three of Chernobyl, the nurse asks the wife of someone with radiation poisoning if she’s pregnant before allowing her in the room. Presumably the person would been cleansed of any radioactive dust at that point(at least on the outside of his body). Was the nurse concerned with inhaled particles, ignorant of how radiation works, or rightly concerned for some other reason? I suppose dramatic effect is another possibility but wanted to hear from you all.