Energy content of fissile material?

[cosmicalstorm]

I was talking to a friend of mine about sci-fi, the question of antimatter came up. I mentioned that the energy content of one kilogram of antimatter was the equivalent of roughly 43 megatons of TNT. But none of us have any real physical education (I'm in dental school and he's an artsy) and he wasn't very impressed.

I tried explaining that it was really a lot, it struck me that it would be good if I could give him the same number of megatons or kilotons per kilo of top grade fissile material (plutonium or uranium).

I tried some Googling on the subject but I couldn't find any easy answers (because, again, I lack the necessary competence to make sense of the numbers).

So my question is this; If you took ten kilo's of the purest fissionable/fusionable material that can be produced right* now and used it in an optimal way to build a nuclear device, how many Mt's or Kt's of energy would you get out of that?

(*I assume there is such a thing, but I admit that my knowledge of the production of nuclear weapons is limited to the very basics)

[adam_grif]

I can't tell you the exact numbers, but I can give you some very rough calculations. The Critical Mass of Pu 239 is 10 KG, and Fat Man used a Sub-critical ball. If they wanted to get as close to Critical Mass as possible before detonating to get maximum bang in the first stage (no clue whether or not they did), lets call it 9.8 KG's of Pu (this will be wrong because they use neutron reflectors and other things that will throw the mass estimates off most likely). Please note that this is ignoring all of the impurities that would have brought the real mass up to several times higher.

Divide yield (21 kt) by mass (9.8 kg) to give you ~2.14 KT per KG.

Compare with 43, 000 kt per KG of antimatter.

Best guestimate I can give you.

[Sea Skimmer]

The thing is that when you set off a modern nuclear device, it’s just not possible to release all the energy in the fissile material at once. Some of that energy will be converted into unstable radioactive elements, which then rain down as our friend nuclear fallout and release the energy as radiation latter. Most is gone in days or weeks (about 99% after two weeks), but some will be slowly released over millions of years.

The ratio of instantaneous energy released, creating the immediate blast-thermal pulse and hard radiation effects of a nuclear weapon as compared to the energy of the fallout is the efficiency of the nuclear device. Early nukes were very inefficient at instantaneous energy release to the tune of 10% or so; modern ones can be in the 90%+ ranges. But never 100%.

Likewise, no reason exists to assume that 100% efficient anti matter bomb is possible either. That’d require every last anti matter atom to find another normal atom to annihilate with while the whole mass is blowing itself apart… unlikely to say the least. It’s more likely that efficiency would be very low in any realistic anti matter based weapon, and it may not be possible to use any tricks to raise it significantly.

One of the main ways we increase the efficiency of nuclear devices is by adding a second or even third source of nuclear fuel, and making the device into a boosted fission or fission-fusion bomb, collectively known as thermonuclear weapons. So what this means is, you really couldn’t have a high efficiency nuclear device that is only using one fission material. The weapon will blow itself apart before all the nuclear material can be consumed and be fairly inefficient.
So anyway, I’m lazy and wikipedia isn’t always wrong, so I used them for this. The energy density of one kilogram of uranium enriched to 99.3% U-235 content is about 88,250,000,000,000 joules. The content of one kilogram split between anti matter and matter should be around 90,000,000,000,000,000 joules. One Megaton is around 4,180,000,000,000,000 joules.

That would mean with 100% efficiency the one kg of anti matter and matter is about 21.5 megatons (after all, its worthless without the equal mass of matter to annihilate with but your 43 megaton figure is still right too), and one kg of nearly pure U-235 is about 211 kilotons.

However as a I was pointing out above, if you want a close too 100% efficient nuclear weapon you are going to need other nuclear materials to use that uranium in conjunction with, and god only knows what for the anti matter bomb to work right.

Also, nuclear weapons and anti matter reactions don’t release energy in the same way, so even when total energy is equal, the actual damage inflicted onto a target will be different. This is further affected by if the weapons are set off inside an atmosphere (when a lot of radiation turns into heat, and then heats the air to make a shockwave) or if it’s in a vacuumed like space when the radiation is not converted.

[cosmicalstorm]

Well I think I get the gist of it now, those numbers are a bit easier to use than the ones I found elsewhere. Thanks for the very informative answers!

[Starglider]

Likewise, no reason exists to assume that 100% efficient anti matter bomb is possible either. That’d require every last anti matter atom to find another normal atom to annihilate with while the whole mass is blowing itself apart… unlikely to say the least.

Only true for a bomb going off in hard vacuum. In an atmosphere, every last antiparticle will get mopped up pretty quickly; even extremely high energy antiprotons / antineutrons that manage to leak out of the initial fireball won't get more than a few hundred meters and will still contribute to the overall blast. Remember that antimatter has opposite charge to normal matter; particularly in an ionised plasma particles will find their antiparticles and anhiliate pretty quickly.

That would mean with 100% efficiency the one kg of anti matter and matter is about 21.5 megatons (after all, its worthless without the equal mass of matter to annihilate with but your 43 megaton figure is still right too), and one kg of nearly pure U-235 is about 211 kilotons.

Although again, if you're in an atmosphere, or expect to penetrate into a solid target normal matter reaction mass is a moot point. In fact the only reason for carrying it at all is because using the bomb/missile casing alone might allow too much antimatter to escape without reacting in a deep space blast.

The primary problem with antimatter weapons is not reaction mass or antimatter leakage, it's neutrino losses, which can easily turn 30% of your yield into useless non-interacting particles.

[Shroom Man 777]

So a kilo of AM is 43MTs of TNT? Then maybe he should see what real-life nuclear weapons nearing, or slightly exceeding, 43MTs in yield would be. The Tsar Bomba yields at 50MTs, show him pictures of the Tsar Bomba, how it's so fucking huge that it can't even fit inside a Tu-95 bomber, and show him material on the effects of the Tsar Bomba explosion.

Then tell him that a kilo of AM can do just about that much damage. Mang.

[Simon_Jester]

So a kilo of AM is 43MTs of TNT? Then maybe he should see what real-life nuclear weapons nearing, or slightly exceeding, 43MTs in yield would be. The Tsar Bomba yields at 50MTs, show him pictures of the Tsar Bomba, how it's so fucking huge that it can't even fit inside a Tu-95 bomber, and show him material on the effects of the Tsar Bomba explosion.

Then tell him that a kilo of AM can do just about that much damage. Mang.

Well... subtract 30% for the neutrinos, since there's no way around that; call it 30 MT. Which is still insanely huge, of course. Or show him the Tsar Bomba blast and tell him that's 1.5 kg worth of antimatter.

[Winston Blake]

Cosmicalstorm, if you want a different 'tangible' way to look at raw energy densities, other than looking at bombs, a quick and dirty calculation is to look at one reaction. E.g. copy the following into Google:

Uranium-235 fission: "203 MeV / (235 amu) in terajoules/kg" = 83 TJ/kg
D-T fusion: "17.6 MeV / (5*amu) in terajoules/kg" (3 amu for tritium, 2 amu for deuterium) = 340 TJ/kg

This makes it easy to see why fusion is so much more energetic than fission, despite having a much smaller energy release per reaction. These results are about the same as given on Wikipedia's page for energy density.

Now, antimatter: "2*1kg*c^2*0.7 in terajoules" (1kg AM + 1kg matter, ~30% neutrino waste) => 130 000 TJ/kg.

Significant.