March 20, 2007

At least get the chemistry right

So I saw the most recent episode of 24 last night. You really have to watch the whole thing with a huge grain of salt and significant suspension of disbelief, but when the writers start ignoring things like fundamental physical facts I start to get annoyed.

I suppose this is where I warn about spoilers, so proceed at your own risk.

The bomb headed for San Francisco was downed in an industrial park on the outskirts of the city. So far so good. In the crash, the bomb itself broke open and allegedly spilled radioactive fuel. Plausible enough, I suppose. At least it isn't downright impossible.

What's annoying is that they're talking as if this is a major catastrophe, and have said that the first responders have almost certainly received fatal doses of radiation. This is nonsense. First, both federal agents and terrorists have been handling these bombs all day with no adverse effects. If mere proximity were sufficient, everyone would be dead. And as Jack Bauer doesn't seem to be killable, that can't be it.

Second, nuclear fuel is heavy. The critical mass for uranium, i.e. the minimum mass required to start a chain reaction, is 52kg. So right off, we're almost certainly looking at a plutonium-based device, as I don't see anyone lugging around a 100+lbs device the way these guys do.

Third, nuclear fuel is dense. I mean really dense. Plutonium has a minimum critical mass of 10kg. That's a far more manageable 20-ish pounds. But plutonium weighs 19.2g/cm^3. So 10kg of plutonium is only 505cm^3. That's 17oz. That'd fit inside a single-serving plastic soda bottle, which fits with the size of the devices portrayed in the show. But even if 100% of the fuel were pulverized and dispersed in the atmosphere - not gonna happen - we're hardly looking at sufficient radioactivity to kill a few dozen firefighters who never came closer than a few dozen feet.

I'm willing to grant them essentially magic programming and networking skills. Fine, that stuff is fuzzy anyways, and just because something isn't current technologically feasible today doesn't mean that it's impossible. But plutonium has always weighed 19.816g/cm^3 and will always weigh 19.816g.cm^3. Check your facts, people. It's not that hard.

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Posted by ryan at March 20, 2007 1:45 PM | TrackBack
Comments

I recognize the changing nature of a wikipedia entry, but seeing as you just put this up, I suspect it claimed 7kg was the minimum amount of U-235 for a bomb 20 minutes ago, the same as it does now. Anyway, I've heard different figures bandied about, but I suspect your 52kg is related to the fact that that was the mass of the "little boy" warhead dropped on Hiroshima.

Anyway, according to actual research done at Los Alomos by scientist Dr. Rene G. Sanchez, the minimum critical mass of U-235 is only 275g (about 10 ounces). That's to get a reactor started. Actually creating a bomb probably does require something on the order of 7kg, as your wikipedia reference claims, though I can't easily cite a confirming source from a more reliable publication.

As to the lethal exposure paradox, there's a huge difference between the amount of radiation present when your bomb is surrounded by its protective casing, versus having the warhead actually exposed and bare. The 24 writers got it completely right Ry-Dogg.

Posted by: Mason at March 20, 2007 7:33 PM

I actually got my info on critical mass from here, which does list U-235 at 52kg. They cite references from the Nuclear Threat Initiative, and indicate that the smallest nuclear device that the US has ever deployed weighed 50 pounds. That's a good 20-ish kg, but as the fuel type isn't specified, this doesn't help much. The abstract you cited said it's possible to get a critical reaction going in "a critical reactor assembly moderated with high-density polyethylene surrounded by a thick-beryllium reflector." We have none of those things here, so a critical mass would take more fuel. Besides, if you simply get the reaction to be critical, that's not enough to generate a nuclear explosion, so you've got to use more than that.

Furthermore, when I was discussing radiation exposure I was assuming - from the conversation in the Situation Room - that they were discussing an actual dispersal of nuclear fuel, which would only be fatal in that short of a time if actually inhaled, like George Mason did in season 2. That will definitely kill you. But I think you would agree that this doesn't seem possible given the amount of fuel involved.

If we're talking about direct radiation exposure, it's my understanding that nuclear fuel only puts out that kind of radiation (absolute bare minimum of 200REM, but for truly fatal doses at least 500+REM) when the mass goes critical. As the bomb didn't explode, this doesn't strike me as being particularly likely. Until the weapon is detonated, the fuel is kept subcritical at all times, and uranium is barely radioactive when subcritical. You can hold it in your hand without danger.

I still say they got it wrong.

Posted by: ryan at March 20, 2007 8:03 PM

I'll concede your points about the bare sphere critical mass of U. I also agree that both U and Pu are safe enough to simply hold in one's hand. That's just documented fact.

However, if the bomb-makers had a little sense and used a neutron source of some sort to coat their warhead (probably a Pu warhead, I agree) and reduce the amount of nuclear fuel necessary, it would be easy to envision a lethal dose being absorbed simply by being near the open bomb casing. Picture a shell of radioactive Be-Po-210 as a neutron source and reflector, and those firefighters will be lucky to survive a week before their organs liquefy!

Posted by: Mason at March 20, 2007 8:18 PM

My only objection there is that the bomb casing would have to be made of lead, which is itself no lightweight (11g/cm^3). Assuming the warhead was capable of putting out that kind of hard radiation before detonation, the sheer amount of lead needed (at least 3cm in every direction) to keep anyone handling the bomb safe would weigh far more than a single man would be able to lift.

If we assume that the casing that the image indicated was breached was the radiation shield, a rough, back-o'-the-napkin weight figure enough lead sufficient to block a lethal dose of radiation would be at least 100 pounds. But an examination of the bomb casing indicates that it's very thin, not nearly 3cm. Which would suggest that the lead is inside the external case, and probably not breached.

I still say they got it wrong.

Posted by: ryan at March 20, 2007 9:23 PM

Who uses lead for radiation shielding on bombs anymore? I mean sure, maybe in the 1950's. But personally, if I were building a nuke with a highly radioactive neutron reflector, I'd opt for depleted Uranium if I could get my hands on it. And if these terrorists can attain Plutonium, the Uranium should be piece of cake. I can achieve the same shielding effect of your 3cm of lead with barely .5 cm of depleted U.

Posted by: Mason at March 20, 2007 11:15 PM

Yeah, but U being almost 50% denser than lead, that's still a few dozen pounds of shielding. But you don't construct the actual housing for the device out of depleted U. You'd build a tiny shield around the warhead itself, meaning that a mere plane crash isn't going to rupture the shielding in any significant way. So no radiation either way.

Posted by: ryan at March 21, 2007 1:10 AM

So how are things up in Harrisburg, Ryan? Arguing like this was reminiscent of old times, wasn't it?

I don't actually watch 24, so I didn't see what the ruptured bomb looked like. Without conceding your point necessarily (after all, I've always considered plane crashes sufficiently destructive events for most purposes), I will at least concede you have access to information that I am unable to either verify or refute in this matter, so I'm letting it go.

I was originally attracted to this post by the fact that you'd written it and that you were complaining that someone had gotten their Chemistry wrong. How could I resist something like that? Thanks for the stimulating discussion, and perhaps we'll do it again sometime.

Peace brother,

Posted by: Mason at March 21, 2007 9:41 AM

Yeah, that was fun. Actually, I'm not in Harrisburg anymore. I'm at Notre Dame Law School, mostly finished my first year.

Posted by: ryan at March 21, 2007 10:18 AM

But not watching the show would really change the debate here. The bomb in question is a "suitcase nuke", consisting of a cylinder approximately 18 inches long and 4-5 inches in diameter. This is a little bomb, and we see several characters carry the thing with little effort. They're admittedly quite fit, but a man of normal size will have a problem carrying anything that weighs more than 100 lbs in one hand. I'm not going to quibble with the fact that the prop they used does not in fact weigh as much as it's supposed to. This is television after all. But if an object is supposed to be too heavy to lift, they should at least act as if it were, even if the prop in question is just a prop.

From all appearances, the manufacturers (the Russian military, not terrorists) used as few components and as little material as possible to create a device that is capable of a nuclear explosion. I think if you were to watch the episode in question, I think you'd probably agree with me that the situation described is not remotely plausible, if even possible.

Posted by: ryan at March 21, 2007 10:46 AM

Well Ryan, one thing I do not claim to be, though I find the science behind it fascinating, is an engineer capable of designing a suitcase nuke. I don't know what materials the Russians used for actual suitcase nukes, but I do know that such materials exist which are capable of producing lethal doses of radiation even within the volume their nuke uses, and also that materials exist capable of shielding such radiation, even in the volume they claim to be using.

However, now that I know it's supposedly a suitcase nuke, I have to agree with you about the unlikeliness of the radiation by simple exposure. For something that small to be that radioactive, it needs to be fresh. Otherwise it will have expended so much of its radiation energy as to be nearly completely converted into whatever component elements it decays into. A Russian suitcase nuke isn't going to be fresh, since I believe they were only built during the Cold War (of course, it's not like Moscow would keep me in the loop if they were still making them today). So if they had such a radioactive component when originally built, they probably wouldn't still be all that radioactive 20 years later.

If, as I'd assumed previously, the terrorists had built the bomb themselves, then it's fairly plausible to imagine they have fresh radioactive material in use, and that's why I came to my original conclusions. Apparently that's not what the writers are claiming.

All the same, even plain old nuclear fuel has an extremely small lethal dosage if inhaled. Pulverize some Pu into dust and combust it, and you'll have some plutonium oxide flying around... very, very deadly (see 'The Sum of All Fears' by Tom Clancy). A spill is not enough to kill your first responders, but inhaling Plutonium would be. It's just a question of whether the crash was bad enough to do that. Was it?

Posted by: Mason at March 21, 2007 12:40 PM

The writers claim that the bomb was made during the 1980s as part of the last round of Soviet nuke construction. They were supposed to have been destroyed, but various parties thought they were worth keeping. So they're at least 25 years old.

True, the inhalation dosage is very low. That clearly will kill everybody. But as we're talking about a very small amount of fuel (a soda bottle's worth), which didn't suffer any kind of explosive trauma, there isn't any way to get enough radioactive dust in the air. If 100% of the stuff was pulverized, we're talking about two handfuls of dust. That's not enough to poison a whole first-responder team that didn't approach within yards of the device. Everybody is gonna get sick, but no one's gonna die.

But there isn't really reason to think that any of the fuel was pulverized. The bomb is materially intact, just fractured. It isn't even in two pieces. The bomb itself is bent and the casing has broken open, but you could still pick it up in one piece.

Posted by: ryan at March 21, 2007 4:02 PM

ok, the writers got it wrong. :)

Posted by: Mason at March 21, 2007 4:16 PM

Maybe you should just stop dicking around with 24 and focus all attention on Battlestar Galactica. Holding out until 2008 will be tragic indeed, but I'd like to hear your (Ryan) thoughts on the season finale. Dad, Dave and I all have somewhat different opinions on what exactly happened, and where the season is heading. Since I don't really blog much anymore, I'll let you post first, then add my comments :)

Posted by: Daniel at March 26, 2007 1:23 AM

My roommate's cable package doesn't have Scifi, so I always have to download and watch 'em a day or so later. Planning on watching it tonight.

Posted by: ryan at March 26, 2007 8:39 AM
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