Comparing Energy of Nuclear Bombs: TNT vs Matter/Anti-Matter

[ziad1985]

Most Days Nuclear weapons have a detonation energy of Megatons of TNT.
How much weight of Uranium/Plutonium We should be looking in Atomic bomb of a One Gigaton Of TNT ?

A Matter/Anti-matter bomb(It have to do with my nuclear physics class) of one Gigaton of tnt , would need about 46.488 Kg of combined Matter/Anti-matter to be used.

I'm trying to compare energy released..

 

[AlphaNumeric]

I'm trying to compare energy released..

Isn't that a bit like asking "Which is heavier, a ton of lead or a ton of feather?". The energy output of a GT explosion will be the same, no matter what the mechanism which produces the explosion. The difference is the mass of material before hand. You'd need a billion tons of TNT if it's chemical or ~23kg of antimatter.

You know from your calculations that you need about 46kg of mass to turn into energy, so find out what percentage of U235 turns into energy when it goes supercritical and then you can work out how much total U235 you'd need.

For instance, if it's 1%, then you'd need 100*23kg. If it's 0.5%, 200*23kg. Etc

 

[ziad1985]

Sorry I didn't meant it like that, I meant "I'm trying to compare energy released by the two procedures in general"

I'm having the problem in the supercritical thing.Can't i Just use the Induced deacy of The U235 by a neutron?
and find out how much enegry is released per reaction? and how much percentage of mass is converted?
And at this point see how much a one gigaton would need of U235 mass?

 

[Meir Achuz]

would need about 46.488 Kg

Please don't say "about 46.488".

 

[ziad1985]

Please don't say "about 46.488".

what's the problem?

 

[Meir Achuz]

That is like saying the population of England is about 22,468,357 people.

 

[DaveFaz]

Interestingly, in parctical terms, it would require a huge amount of Uranium. The high figure is because Atomic bombs are not very efficient. In the first atomic bomb which had more than 50Kg of Uranium, only 0.7g was converted to energy. So a 50Kg Uranium bomb releases the same energy as a 3.5g anti-matter bomb. So one answer would be around 14,000 times as much Uranium as anti-matter. Course, that was not really the question you asked, but there you go...

 

[ziad1985]

Something is wrong, my calculation gave me a number around 1300.
from the mass lost during a fission of a one U nucleus, I got the percentage, and saw how much mass would I need to have that sort of energy..
14,000 would be a very big number, I understand from this, that the A-bomb design is poor, we have about magnitude of 10 difference in answer..

 

[Janus]

Most Days Nuclear weapons have a detonation energy of Megatons of TNT.
How much weight of Uranium/Plutonium We should be looking in Atomic bomb of a One Gigaton Of TNT ?

A Matter/Anti-matter bomb(It have to do with my nuclear physics class) of one Gigaton of tnt , would need about 46.488 Kg of combined Matter/Anti-matter to be used.

I'm trying to compare energy released..

You aren't going to do it with just Uranium/Plutonium. The maximum yield for a pure fission bomb is around 500kt.

For fusion bombs, the practical yield is 5.2t/mt, so you would need a 192 tonne bomb to produce a 1gt explosion.

 

[DaveFaz]

Something is wrong, my calculation gave me a number around 1300.
from the mass lost during a fission of a one U nucleus, I got the percentage, and saw how much mass would I need to have that sort of energy..
14,000 would be a very big number, I understand from this, that the A-bomb design is poor, we have about magnitude of 10 difference in answer..

I remember that the efficiency of an atomic bomb is low. All we need is 10% for our answers to agree. Actually, that sounds too high to me. I think I remember a figure of 4% for the first atomic bomb.

 

[DaveFaz]

By the way, the largest Plutonium bomb ever built was British with a yield of 750Kt

 

[QuantumPion]

A bomb of such magnitude would have to be a multi-stage fusion bomb. I don't know what the proportional weight of plutonium is in such devices, the specifics might still be highly classified.

The largest bomb ever detonated was a Russian device called Tsar Bomba, it was 50 Mt, and most of its energy was due to fusion. It was originally designed to be 100 Mt, but the designers changed the last stage material to lead from U-238 to minimize fallout over their own territory. The bomb was delivered by an aircraft and weighed ~30 tons.

If you wanted to just calculate how much uranium you would need to release that much energy, you can calculate a rough estimate using 200 MeV released per fission. A Gt of TNT is about 4.2*10^18 J. So that would be 1.31*10^29 fissions. If you assume 10% bomb efficiency, you would need 1.31*10^30 U-235 atoms. One atom of U-235 weighs about 3.9*10^-25 kg, so that is something like 511,000 kg o U-235.

For perspective, the known world reserves of uranium are around 3 million metric tons. Of this, only 0.6% is U-235, or ~18,000,000 kg. So such a bomb would require a significant fraction of the entire world's uranium reserves to make. :)