Suppose we build an anti-matter bomb.
If 1 gram of anti-matter were to explode (That is react completely with one gram matter in a mutual anihilation reaction), what would be the yield in TNT tons?
Are we talking the GIGATON range?
Well, using E=mc[sup]2[/sup]:
E = (0.001 kg) * (3.0x10[sup]8[/sup])[sup]2[/sup]
= 9x10[sup]13[/sup] Joules
Now, how many Joules are in a megaton blast? This says it’s 4x10[sup]15[/sup] Joules.
Hence one gram is about 0.02 megatons, or about 2 percent of a megaton.
Well, considering that 1 gram of antimatter would destroy 1 gram of matter, wouldn’t that be 1.8x10[sup]14[/sup] J ?
That’d be 4% of a megaton. So maybe we would need 12.5 g for a megaton, or 12.5 kg for a gigaton.
How much do you have available, enolancooper?
I did those calculations, and got similar answers, but I figured “That’s way to low. I must’ve screwed up.” I guess I didn’t. It looks like you’d need several pounds of antimatter to get a one megaton detonation. I assumed that the total mass would be two grams (the antimatter plus the matter that it annihilates).
This appears to be about correct. Diceman, you are off by an order of magnitude or so, however. If 1 gram is 2 percent of a megaton, 50 grams is one megaton. That’s about 2 ounces, not several pounds as you state.
(28.4 grams per ounce)
You are correct. I didn’t calculate the “several pounds” thing, it was just a WAG.
Careful with your units. If you multiply kg by (m/s)[sup]2[/sup], you get kg*(m/s[sup]2[/sup])*m, or kJ.
So, one gram of matter annhilating one gram of antimatter would yield 1.810[sup]17[/sup] joules (1.810[sup]14[/sup] kJ) of energy… that’s about a 45 megaton explosion.
Okayyy… But, correct me if I’m wrong, isn’t the S.I. unit of mass, when used in equations like the above, given as Kg for some reason?
D’oh!
Yes, 1 kg times 1 m/s[sup]2[/sup] is 1 N, 1 N times 1 m is 1 J.
Sorry about that confusion… I was thinking about engineering thermodynamics, where specific enthalpy and specific energy are given in units of kJ/kg.
Still, it’s a bigger explosion then the Hiroshima bomb.