I was talking with a friend last night and somehow I mentioned that his body represented more energy than found in the biggest nuclear bombs. If he went BOOM by meeting an equivalent amount of antimatter he would easily take out Chicago. My friend thought this was nonsense. I pointed out that a nuclear weapon usually only carries a few tens of kilos of nuclear fuel…less than he weighs at least. Add to that the fact that nuclear fusion/fission (IIRC) is only around 5% or less efficient at converting its mass to energy. If I got 100% conversion on a larger mass the explosion would be stupendous. He responded by saying that Uranium and other nuclear fuels were heavier elements thus had more energy potential. I said that had nothing to do with it since it is like the old riddle, “What weighs more…a pound of bricks or a pound of feathers?” He didn’t buy into that one either.
So, to settle the matter I figured I’d just pop off a quick equation to prove my point. I’m not good at math but even I can handle E=MC[sup]2[/sup]. Unfortunately for me I always get hung up on my units and how to relate them to something I understand. Basically, I could generate an answer but I had no idea what the answer meant.
So, assuming my friend weighs 75 kilos and I threw him in an equivalently sized pool of antimatter just how big of an explosion would result? (NOTE: Since the antimatter would also be 75 kilos thus getting us 150 kilos total it may be more relevant to say 37.5 kilos each of both antimatter and matter to get an energy equivalent for 75 kilos…I don’t know if that makes sense so I leave it to those smarter than me to decide which way to go.)
If possible please relate your answer to something I can understand. 3.2*10[sup]12[/sup] joules (I just made that number up) doesn’t mean anything to my brain. An answer in megatons of TNT or something else (it’s up to you) would be nice.
Just stick with SI unites (meters, kg, Joules) and you’re all set. c is 3x10[sup]8[/sup] m/s, and your mass is 75kg, so resulting energy is about 10[sup]19[/sup] Joules. If I remember correctly, one megaton TNT equivalent is 10[sup]15[/sup] Joules. So you’d make a 10,000 megaton bomb.
Hmm, I expected it to be more. Did I do that right? (It’s getting late here, sorry)
yeah, scr4, my numbers pretty much agree with yours. I got 6.75x10[sup]18[/sup] joules.
A kiloton is 10[sup]12[/sup] calories, or 4.186x10[sup]12[/sup] joules. So I get that the OP would actually be equivalent to 1,612.5 megatons.
To put it in terms you can fathom (not really, since the numbers are way too big), that’s enough energy to power One Million 100W light bulbs nonstop for over 2100 years. In other words, a shitload of energy.
Whack-a-mole, you are completely right on this one.
My numbers match scr4’s pretty well.
75kg + 75kg anti matter would release 13500 megatons of energy (in TNT equiv). Cut that figure in half if you don’t want to include the energy from the anti-matter.
1kg of matter completely converted would run a 100 Watt light for 28.5 million years.
The largest nuclear test was the Soviet Tsar Bomba. It was on the order of 100 megatons.
So, total conversion of your 75kg body (with the 75kg of anti matter) would yield 135 times more energy.
It just occurred to me that using kilograms may not be appropriate. I mean, if I weighed myself on the moon I’d be around 12 kilos. Is there some other unit for mass and not weight that should be used here?
Yes, there is, and it’s the kilogram. The SI unit of weight (a force) is the newton, which you hardly ever see outside of a physics textbook. Pounds, on the other hand, are a unit of weight.
Generally, when they’re used interchangeably, the gravity at the surface of the Earth is assumed.