# Anti-matter bomb yield? **URL:** \ **Category:** Factual Questions\ **Created:** [March 13, 2001, 8:12pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842 "2001-03-13T20:12:53Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [March 13, 2001, 8:12pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/1 "2001-03-13T20:12:53Z")
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? ---
**Author:** ![emarkp](https://avatars.discourse-cdn.com/v4/letter/e/3be4f8/32.png) [@emarkp](https://boards.straightdope.com/u/emarkp)\ **Post date:** [March 13, 2001, 9:03pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/2 "2001-03-13T21:03:43Z")
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](http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/explosions.html) says it’s 4x10[sup]15[/sup] Joules. Hence one gram is about 0.02 megatons, or about 2 percent of a megaton. ---
**Author:** ![Dev\_Null](https://avatars.discourse-cdn.com/v4/letter/d/46a35a/32.png) [@Dev\_Null](https://boards.straightdope.com/u/Dev_Null)\ **Post date:** [March 13, 2001, 9:22pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/3 "2001-03-13T21:22:57Z")
> [@](#): > > \*Originally posted by emarkp \* > \*\*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](http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/explosions.html) 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? ---
**Author:** ![Diceman](https://avatars.discourse-cdn.com/v4/letter/d/22d042/32.png) [@Diceman](https://boards.straightdope.com/u/Diceman)\ **Post date:** [March 16, 2001, 10:29pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/4 "2001-03-16T22:29:02Z")
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). ---
**Author:** ![douglips](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@douglips](https://boards.straightdope.com/u/douglips)\ **Post date:** [March 17, 2001, 12:45am UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/5 "2001-03-17T00:45:56Z")
> [@](#): > > \*Originally posted by emarkp \* > \*\*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](http://muller.lbl.gov/teaching/Physics10/physics%2010%20notes/explosions.html) says it’s 4x10[sup]15[/sup] 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) ---
**Author:** ![Diceman](https://avatars.discourse-cdn.com/v4/letter/d/22d042/32.png) [@Diceman](https://boards.straightdope.com/u/Diceman)\ **Post date:** [March 17, 2001, 2:44pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/6 "2001-03-17T14:44:11Z")
> [@](#): > > 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. ---
**Author:** ![KeithT](https://avatars.discourse-cdn.com/v4/letter/k/e47774/32.png) [@KeithT](https://boards.straightdope.com/u/KeithT)\ **Post date:** [March 17, 2001, 8:59pm UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/7 "2001-03-17T20:59:28Z")
> [@](#): > > Well, using E=mc2: > > 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 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)[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 1.8_10[sup]17[/sup] joules (1.8_10[sup]14[/sup] kJ) of energy… that’s about a 45 megaton explosion. ---
**Author:** ![superdenseprotohippy](https://avatars.discourse-cdn.com/v4/letter/s/dbc845/32.png) [@superdenseprotohippy](https://boards.straightdope.com/u/superdenseprotohippy)\ **Post date:** [March 21, 2001, 6:47am UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/8 "2001-03-21T06:47:17Z")
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? ---
**Author:** ![KeithT](https://avatars.discourse-cdn.com/v4/letter/k/e47774/32.png) [@KeithT](https://boards.straightdope.com/u/KeithT)\ **Post date:** [March 21, 2001, 7:11am UTC](https://boards.straightdope.com/t/anti-matter-bomb-yield/57842/9 "2001-03-21T07:11:42Z")
**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.