OT - Physics Question on Anti-Matter

[Tnargversion2]

I am curious to know what an estimated force in kt that an ounce of Anti-Matter mixing with an ounce of Matter would be.

Lets compare that to say a standard 20kt nuclear weapon.

I realize this is hypothetical, as this has never been done before, but in theory I am just curious how much energy can be realized from an anti-matter/matter contact.

[Ed Kolis]

OK, let's see... You have 2 ounces of matter and antimatter, that's about 57 grams or 0.057kg, and the speed of light is 300 million meters per second... thus using E=m*c^2, the energy produced in the detonation is 5.7*10^-2kg * (3.00*10^8m/s)^2 = 5.1*10^15 kg*m^2/s^2, or 5.1 quadrillion (the American kind, a thousand million million) joules. What that is in kT I don't know, but I'll try looking it up...

edit: OK, a "ton of TNT", according to Wikipedia, is defined as 1 gigacalorie, which equals 4.184 billion (thousand million) joules (it also happens to equal a million dietary calories - think of THAT next time you sit down to dinner, since there are a million grams in a metric ton, you are eating the energy equivalent of hundreds of grams of TNT! Don't let your food a splode! )... anyway, since the antimatter explosion produces 5.1 quadrillion joules and a ton of TNT is 4.184 billion, that means that the antimatter explosion is equivalent to... 1.2 *billion* tons of TNT (1,200,000 kT) - which is about 10 times more powerful than any bomb mankind has ever devised! (The most powerful bomb was developed by the Russians during the Cold War and it had an estimated output of 100,000 to 150,000 kT...)
(SJ or some other mathematically inclined person, could you stop by and make sure I didn't horribly screw up the math? )

[capnq]

Assuming the matter and antimatter can be combined perfectly to cause total annihilation (which is actually a huge assumption), you just have to plug the numbers into Einstein's equation:

E=mc^2

=(1 ounce matter+1 ounce antimatter)(186000 miles/sec)^2

= 6.9192E10 ounce-miles/(sec^2)

Unfortunately, college physics was too long ago for me to remember the conversion factors to change that mess of units to kilotons. Converting ounces to tons gives an order of magnitude around two megaton-miles/sec^2.

Edit: and Ed posted while I was trying to look up the conversion factor before I submitted the post.

[Ed Kolis]

A ton of mass or weight is not the same as a ton of explosive force, so that conversion would have been misleading anyway

[capnq]

Well, there's got to be some conversion factor between the two. Whatever that number is, you've still got a big BOOM.

[Baron Munchausen]

Wow, here we have the resources to figure out what it really takes to blow up a planet. The 'death star' beam is stoopid, of course. It takes enough energy to accelerate the planet's entire mass to its own escape velocity to make it explode. For an earth-sized planet this is equivalent to several months output by our sun. (!) A simple 'beam' cannot possibly deliver this much energy. And anyway, if it's delivered from outside, it just burns away one side of the planet, sending the rest spinning away somewhere. The only practical way to really explode a planet is to deliver enough anti-matter to the core to make an explosion big enough to shatter the planet.

So, if someone can figure out how much energy is needed to accelerate the earth's mass to it's own escape velocity, then back-convert that to matter/anti-matter reaction, we would then know how much anti-matter a super-high-tech ablative delivery device (the 'bunker buster' is a toy compared to this problem... ) has to deliver to the planet's core.

[PvK]

E = mass x C^2 is valid to give the energy for total conversion from matter to energy. But ya, assuming that's what you can get from an anti-matter bomb is an assumption.

Nuclear weapons kilotons are in terms of equivalent explosive force compared to a certain mass of T.N.T., which of course has its own conversion factor involved. I bet it's not too hard to google up.

There is of course another web page with lots of discussion about what it takes to destroy a planet in various ways.

[Will]

Well, it's a bit more complicated than that. First, it's gonna be a nasty volume integral, since the gravity will be different along points from the surface to the core. Then, there isn't an easy way to tell how much of the energy from the annihilation will be converted to kinetic energy instead of heating up bits of former-earth. And it would probably not be the case that the annihilation happens all at once, or that the energy flux would be uniform across the unit sphere, so you cannot be certain where the center of gravity will be.

Anyway, with all that, I would say that it is safe to assume that the amount of anti-matter needed is bounded by the mass of the Earth.

[Thy_Reaper]

All my data is from Google, so ask it to back me up

Earth has a mass of 5.9742 x 10^24 kg.
Escape velocity is 11 km/s approx.
7.228782 × 10^32 (72,278,200,000,000,000,000,000,000,000,000) Joules are needed to blow the planet up.
Based on e = mc^2, 8.0431047 × 10^15 kilograms of a matter/anti-matter mix is needed to detonate the planet, so just inject 4.02155235 x 10^15 kg of anti-matter into the core.
That's 4,021,552,350 million kilograms of anti-matter... ouch.

Well, good luck on getting that

[Tnargversion2]

Ed Kolis said:
OK, let's see... You have 2 ounces of matter and antimatter, that's about 57 grams or 0.057kg, and the speed of light is 300 million meters per second... thus using E=m*c^2, the energy produced in the detonation is 5.7*10^-2kg * (3.00*10^8m/s)^2 = 5.1*10^15 kg*m^2/s^2, or 5.1 quadrillion (the American kind, a thousand million million) joules. What that is in kT I don't know, but I'll try looking it up...

edit: OK, a "ton of TNT", according to Wikipedia, is defined as 1 gigacalorie, which equals 4.184 billion (thousand million) joules (it also happens to equal a million dietary calories - think of THAT next time you sit down to dinner, since there are a million grams in a metric ton, you are eating the energy equivalent of hundreds of grams of TNT! Don't let your food a splode! )... anyway, since the antimatter explosion produces 5.1 quadrillion joules and a ton of TNT is 4.184 billion, that means that the antimatter explosion is equivalent to... 1.2 *billion* tons of TNT (1,200,000 kT) - which is about 10 times more powerful than any bomb mankind has ever devised! (The most powerful bomb was developed by the Russians during the Cold War and it had an estimated output of 100,000 to 150,000 kT...)
(SJ or some other mathematically inclined person, could you stop by and make sure I didn't horribly screw up the math? )

Well regardless of how close you are, that still paints a pretty picture. I guess if an Anti-Matter research center proposal comes up in your next city counsel meeting, it would be a safe bet to say no!

Whoops, the magnetic containment field surrounding the pebble sized bit of Anti-Matter failed and wham there goes the county.