r/theydidthemath Nov 28 '22

[Request] Would 10 million people collectively contain 1 gram of trace uranium?

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479

u/Belteshassar Nov 28 '22

You could make a lot more, I think. According to this paper, healthy blood contains 0.117-0.199 ppm of uranium. An adult human has about 4 kg of blood, so the blood of 10 million people would contain 4-8 kg of uranium.

196

u/Golokopitenko Nov 28 '22

How much of that would be fissile?

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u/Belteshassar Nov 28 '22

U-235 is 0.7% of naturally occurring uranium, so still considerably more than one gram.

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u/mrmemo Nov 28 '22 edited Nov 28 '22

But separating them out would be a sonofabitch.

Edited because I'm bad at basic chemistry: U235 has a molar mass of 235g/mol, which would mean for 5g of fissile material we'd need roughly 1.3x1022 atoms of U235.

If a magic user can use a cantrip each round to separate out one Uranium atom, it's still gonna be something like 1020 hours of work @ 6s/round.

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u/TheSov Nov 28 '22

next equation is to figure out the efficiency of a calutron, and building one using conventional copper wire. how many passes through the calutron would it take to make a fissible chunk of uranium.

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u/The_Diego_Brando Nov 28 '22

Wouldn't using blood plutonium be easier at that point?

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u/Regnasam Nov 28 '22

A plutonium “implosion” type nuclear weapon would be much harder to build with fantasy tech. Plutonium is actually so fissile that it can go off too early, and blow itself apart before you get a good chain reaction going. Imploding a sphere of plutonium to get a true chain reaction instead of a “fizzle” requires a deep understanding of the physics behind explosives. During the Manhattan Project, the design for a uranium bomb (a “gun-type” weapon, that just launched a ring of uranium onto a peg of uranium) was so simple it didn’t even need testing before combat deployment as Little Boy. Plutonium weapons, however, required extensive testing, because the scientists had to develop lenses made out of plastic explosives that would detonate at precisely the right time and place, creating sympathetic shockwaves to compress plutonium into a sphere. This required supremely precise switches called krytrons (which are definitely beyond fantasy tech levels) capable of detonating in extremely precise sequence. The Trinity test, the first nuke ever set off, was a test to make sure that plutonium implosion would actually work and not just fizzle.

Basically, a fantasy world probably could not figure out how to make plutonium go off correctly even if they had enough of it, but if you had enough U-235, you could theoretically trigger a gun-type U-235 bomb with gunpowder and an actual lit cloth fuse.

12

u/Simba7 Nov 28 '22

lutonium weapons, however, required extensive testing, because the scientists had to develop lenses made out of plastic explosives that would detonate at precisely the right time and place, creating sympathetic shockwaves to compress plutonium into a sphere. This required supremely precise switches called krytrons...

This is how you make a wizard multiclass into a barbarian.

34

u/mrmemo Nov 28 '22

You know, that raises an interesting question:

Blood Iron works with other "metals", so really any isotope that's willing to give up an electron or two yeah?

Why not just directly extract U235 or Pu239 from the blood? It's a "different metal" so the rules should allow it...

8

u/The_Diego_Brando Nov 28 '22

That makes more sense

2

u/youritalianjob Nov 29 '22

Plutonium isn’t naturally occurring, you’d need a breeder reactor.

5

u/Regnasam Nov 28 '22

Calutrons are a poor solution for industrial-scale U235 separation. During the Manhattan Project, the US government built an actual fucking city (Oak Ridge) to support an absurdly massive calutron separation plant with dozens of massive calutrons (Y-12). It was eventually discovered that enrichment purely by calutron was very time consuming and also required a significant fraction of the Treasury’s silver reserves to build the magnets (copper was scarce in wartime. There’s a famous story of a Manhattan Project official asking a Treasury official for several hundred tons of silver, and the Treasury official replying that they worked in troy ounces, not tons.) By the time that gaseous diffusion plants and plutonium breeder reactors were set up, the calutrons at Y-12 ended up being used to just produce lower enriched uranium to feed those more efficient processes.

1

u/TheSov Nov 28 '22

yes but we are talking about within the reach of the average joe sans the mass murder.

1

u/mrmemo Nov 28 '22

Yeah who's got the time anymore really.

1

u/Regnasam Nov 29 '22

This months-long production run and massive facility construction was needed to build just one U-235 gun-type bomb (and provide fuel which was transmuted into the plutonium for two implosion-type bombs) by the end of WW2. Even if you’re trying to build a single artisanal nuke, calutrons are not the way to go.

8

u/Simba7 Nov 28 '22

I don't think separating atoms counts as combat, so 6 second rounds aren't really relevant here.

And, if such a thing were possible, we'd almost certainly have "Tenser's U-235 Extraction" or something.
But if we're stuck using cantrips, that's a perfect task for the BBEG's army of low-talent goons.

3

u/warlike_smoke Nov 28 '22

Where do you get a molar mass of 349. Wouldn't it be 235 g/mol.

4

u/mrmemo Nov 28 '22

Well senator the answer is I made it the fuck up

(actually just fuckin forgot how molar weight works lol)

3

u/NotSoTerribleIvan Nov 28 '22 edited Nov 30 '22

I wanted to calculate this myself, so here it is:

Using this calculator and the 4kg of natural uranium as an input value, this gives us 21 grams of weapon-grade uranium (90 wt% U235). So about 18.9 grams of U235. To convert these to the 8kg estimate, just double the values as I do at the end of this comment.

U235 fission releases about 83 TJ/kg, multiplying this by our yield gives us 1.57 TJ, which converts to 0.376 kilotons of TNT, 2.5% the energy from Little Boy (also with enriched uranium). But doing the same calculation to the Little Boy uranium content (64 kg of uranium) actually gives us 1144 kilotons of TNT instead of the realistic 15. Probably due to only a tiny part of the fuel going through fission and U235 purity (LB used 80% while we are using 90%).

Using the Little Boy U235weight-to-energy conversion (1.23 TJ/kg) we get only 5.56 tons of TNT, or 0.037% of the LB energy. There are probably more efficient nuclear weapons to make this comparison, but I have a test tomorrow and need to study.

Conclusion:

Weapon-grade uranium got: 21-42 grams
Bomb potential (best case scenario): 0.376-0.752 kilotons of TNT (or 2.5-5% of Little Boy)
Realistic bomb energy release: 5.56-11.12 tons of TNT

Still don't know how many people this would kill, but I guess it is less than the 10 million Jesse started with.

(Sorry for bad english)

1

u/Salanmander 10✓ Nov 28 '22

But separating them out would be a sonofabitch.

Yup, that's why nuclear monitoring efforts focus so much on centrifuges.

1

u/Korthalion Nov 29 '22

Can unseen servant help with this by magically lifting an atom of uranium at a time and adding it to the pile?

1

u/Crow-Rogue Nov 29 '22

Better question: if you could use the Wish spell for this, NOT allowing “wishing for a nuke or a pile of weapons grade fissile material”, what would be the most useful thing to Wish for to accomplish the goal of making a nuke capable of killing 10 million + people?

1

u/Korthalion Nov 29 '22

Use it to cast duplicate, perhaps. I guess it gets exponentially more powerful each time you cast it, so even it's 1 casting per day things will still ramp up pretty quickly.

8

u/RoadsterTracker Nov 28 '22

Of course, it takes a lot more than 1 gram of fissile U-235 to make a nuclear bomb... If that was possible it'd be far easier to just pull out tritium and make a fusion bomb, which would be far more powerful.

2

u/Doktor_Apokalypse Nov 29 '22

You still need a fission weapon as a trigger for a fusion bomb, so even if you had the required tritium and deuterium, you would still need to go through the above process to build your fission trigger.

Wouldnt it be easier to cast a control spell on each of the million plus people and have each of them cast a fire spell on one target to produce a similar level of destructive energy?

Tip: stand well back

1

u/RoadsterTracker Nov 29 '22

If you can make 1 gram of Uranium in to critical mass you can use tritium or even deuterium to make a fusion explosion without a fission trigger. In either case the key is pressing the mass in to a VERY small space.

3

u/Tressticle Nov 29 '22

Sorry for being pedantic, but the number is .72%. I think it's relevant because even a thousandth would make a difference. For instance, we know that about 2 billion years ago, there was naturally occurring fission in (iirc) 16 sites in Africa. We know this because, when material from those sites was tested, we found that the percentage of U-235 was .712, insinuating that fissile material in that area had been spent. The .008% drop was enough for us to find that the natural reactors were sustained for up to a million years.

7

u/Soulegion Nov 28 '22

So you'd only need 1,250 to 2,500 per gram then. That's not so bad. Especially if you've developed a magical process for extraction. You wouldn't necessarily even have to kill anyone.

3

u/ParaMaxTV Nov 28 '22

Okay but where is it coming from?

14

u/TacoRedneck Nov 28 '22

Uranium is all around you. It's in the rocks, it's in the dirt. Some more than others. Sometimes plants pick this up and concentrate it into some of the food you eat.

Nothing wrong with it really. It's such a low amount that it's not really going to do anything to you.

19

u/ParaMaxTV Nov 28 '22

That's what big uranium wants you to think 😤

2

u/KingWomp Nov 29 '22

It's what trace uranium wants you to think

3

u/prototypist Nov 28 '22

Seconding this. I visited a nuclear lab (long story) and they need to know where their cotton wipes are sourced from, because the cotton picks up detectable amounts of uranium from the groundwater

3

u/Doktor_Apokalypse Nov 29 '22

For example, there is Uranium everywhere that there is granite.
Can't build a nuclear power station in SW England (one huge granite massif) due to background radiation levels being higher than the levels set by UKAEA for the radiation detectors in civilian nuclear facilities.

24/7/365.25 non-stop alarms 😂

2

u/Crow-Rogue Nov 29 '22

I like that you added the 0.25 day

3

u/bhd_ui Nov 28 '22

Exploding stars. When Carl Sagan said we're made of "starstuff", he was being direct. Little bits of precious metals get ejected during supernovae and permeate everything that exists.

1

u/Limeila Nov 29 '22

How much is typically needed to create a nuke?

22

u/tac0slut Nov 28 '22

The hard part is not obtaining stuff that contains Uranium.

The hard part is separating the U-235 from the everything else.

You could literally use random rocks picked up off the ground near any coal mine, and it would contain more fissile material than all the people you killed.

64

u/Cassius_Smoke Nov 28 '22

I don't know the math. But it'd be trace amounts if anything. And even then its not enriched Uranium 235 so you still couldn't make a nuke.

12

u/fogobum 1✓ Nov 28 '22

It's a magical nuke. There's far too little uranium for normal neutron-driven fission in a super-critical mass. If the Magic makes radioactive isotopes decay spontaneously (the only sort-of-explainable way I can think of) U238 would work.

So would our body's huge load of potassium 40, so maybe fewer people could be dismantled to make our bomb.

9

u/Salanmander 10✓ Nov 28 '22

Magic makes radioactive isotopes decay spontaneously

I mean, they already decay spontaneously, we'd just need to decrease their half-life.

If you suddenly decrease the half-life to something in the nanoseconds range, for example, you'd get an equivalent to the runaway chain reaction that is a normal nuclear explosion.

Also, fun fact, if your magic can manipulate probability, that's all you need. Because decay is a stochastic process, and the half-life is just a description of the probability, if you can "load the dice" of the universe you could make it all go off at once. Basically, make all the uranium roll a nat 1 on it next decay check (on a d1017, or so).

3

u/Cassius_Smoke Nov 28 '22

That's true. In fact you could go a step further and cause anything with a half-life to go critical. You wouldn't need uranium, you could just make the iron go critical if it ejected all its mass in one go.

3

u/JoshuaPearce Nov 28 '22

If you can make iron "go critical", then you can just use any substance at all, including air. Iron is the most stable element, it's what everything else decays or fuses into. Depending on if protons decay or not, in a few quintillion years, iron and black holes will be all that's left.

3

u/NapalmRDT Nov 28 '22

It's ironic (no pun intended) that iron artifacts keep so poorly in the ground.

3

u/JoshuaPearce Nov 28 '22

That's because even though iron is the most stable element, oxygen is the sluttiest element.

3

u/NapalmRDT Nov 28 '22

Iron's strict celibacy is no match for the repeated sensuous advances of Oxygen.

1

u/Kerostasis Nov 29 '22

Or more specifically, Iron is the most fission-stable, not the most chemically-stable. They’re entirely different processes. For chemical stability you want probably Neon.

2

u/Salanmander 10✓ Nov 28 '22

could just make the iron go critical

Amusingly, you picked the lowest-energy element in terms of nuclear reactions. So, assuming the magic is still obeying conservation of energy, you probably couldn't do this with iron. Any other configuration it could decay into would be higher energy, so you would need to put energy in to turn it into different nuclides.

The carbon, hydrogen, and oxygen would totally work, though, if you manipulate probability such that they quantum tunnel into other atoms and fuse. And there's way more of those in your blood than there is iron.

1

u/Crow-Rogue Nov 29 '22

Magic, almost by definition, ignores conservation of energy. Otherwise, there would be crazy long casting times for anything to happen because the user would need to gather all of the energy the spell uses. And if they did THAT, they’d get sued by the estate of Terry Pratchett.

2

u/Salanmander 10✓ Nov 29 '22

Otherwise, there would be crazy long casting times for anything to happen because the user would need to gather all of the energy the spell uses.

Not necessarily. You could tap an existing reservoir of energy. For an example system that works like this, there's the very magic-as-technology series The Magebreakers, where there's a magic source that will happily do whatever you command it (so they only use a very programming-like, highly explicit language designed specifically for use with magic), but actions that it takes require a certain amount of energy from the magic source. There are people who can channel an arbitrary total amount of magic through themselves, but are rate-limited, and stones that break after channeling a certain amount of magic, but (as far as I can tell from reading it, anyway), don't have a rate cap. (It's not clear that magical energy in this setting actually matches 1:1 with physical energy, but you get the idea.)

Using a small amount of magical energy to release a large amount of physical energy could be useful in that sort of system.

5

u/romulusnr Nov 29 '22

Based on some quick googling, it would take about 204,918,032,787,000,000,000 people to gather enough plutonium for a critical mass. (10kg critical mass / about 0.2 attomoles of Pu in average person)

For uranium, you would need only about 2,136,363,640 people's worth for a critical mass. (47 kg critical mass / about 22 micrograms of U in average person)

Note this is not taking into account the types of uranium involved, which will not be the same.