Anti-matter bomb yield?

[Enola Straight]

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?

[emarkp]

Well, using E=mc2:

E = (0.001 kg) * (3.0x108)2

= 9x1013 Joules

Now, how many Joules are in a megaton blast? This (http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/explosions.html) says it's 4x1015 Joules.

Hence one gram is about 0.02 megatons, or about 2 percent of a megaton.

[Dev Null]

Originally posted by emarkp
Well, using E=mc2:

E = (0.001 kg) * (3.0x108)2

= 9x1013 Joules

Now, how many Joules are in a megaton blast? This (http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/explosions.html) says it's 4x1015 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 1.8x1014 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?

[Diceman]

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).

[douglips]

Originally posted by emarkp
Well, using E=mc2:

E = (0.001 kg) * (3.0x108)2

= 9x1013 Joules

Now, how many Joules are in a megaton blast? This (http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/explosions.html) says it's 4x1015 Joules.

Hence one gram is about 0.02 megatons, or about 2 percent of a megaton.

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)

[Diceman]

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.

You are correct. I didn't calculate the "several pounds" thing, it was just a WAG.

[KeithT]

Well, using E=mc2:

E = (0.001 kg) * (3.0x108)2

= 9x1013 Joules

Now, how many Joules are in a megaton blast? This says it's 4x1015 Joules.

Hence one gram is about 0.02 megatons, or about 2 percent of a megaton.


Careful with your units. If you multiply kg by (m/s)2, you get kg*(m/s2)*m, or kJ.

So, one gram of matter annhilating one gram of antimatter would yield 1.8*1017 joules (1.8*1014 kJ) of energy... that's about a 45 megaton explosion.

[superdenseprotohippy]

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?

[KeithT]

D'oh!

Yes, 1 kg times 1 m/s2 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.