# Mass converted to energy in fission of U-235?

1. Jan 15, 2005

### NanakiXIII

I'm looking to find out about how much mass is converted to energy during the fission of a U-235 atom. I know that it can differ, depending on how the nucleus is split, but an estimated average would be good. I don't know if it matters, but I'm talking about the fission in a nuclear bomb.

2. Jan 15, 2005

### dextercioby

Obviously the order of magnitude is MeV*c^{-2},but if u don't give me a reaction,i can't give an exact (not even an approximate) value.

Daniel.

3. Jan 15, 2005

### NanakiXIII

Well I don't know which reactions can occur, if you could tell me just one possible reaction, that would be helpful too.

4. Jan 15, 2005

### Chronos

U235 fission weapons yield about 17.5 kilotons per kilogram.

5. Jan 15, 2005

### NanakiXIII

I'm not really sure how much a kiloton is (well, a thousand tons obviously, but I'm not sure what the unit ton is).

I need to demonstrate E=mc^2 for a school project, and it has to be about U-235 fission. Really, any reaction would do, I just need to have an example.

6. Jan 15, 2005

### Chronos

This is all textbook stuff, so I am not in abeyance of the nuclear non-proliferation treaty. A U235 fissile reaction works like this. A neutron is fired into a U-235 atom creating a U-236 atom. U236 is unstable and immediately decays into atoms of Ba-141 (barium), Kr-92 (krypton), three neutrons, and energy [a repectable amount]. U236 has an atomic mass of 236.05. The combined mass of the decay products total 233.85. The mass difference (2.20) is converted to energy per the usual E = mc^2 rule [about 200MeV per atom].

Last edited: Jan 15, 2005
7. Jan 15, 2005

### kirovman

I'm a physist and I think I'm just having a slow brained day today, been learning Medical Imaging for an exam. But I had a sudden query, how do you get kilotons of energy from ~1 kg of plutonium? Surely that's 1 million times more energy than is available in mass? Would the energy required from this be liberated from elsewhere, ie mass from outside of the bomb.

I know, it's probably an obvious explaination, but can someone please enlighten me?
(I just did a Nuclear Physics exam couple of days ago, but it was mainly about quantum scattering, and an introduction to advanced particle phyics more than anything.)

8. Jan 15, 2005

### Chronos

c^2 is a really big number.

9. Jan 15, 2005

### NanakiXIII

I'm not sure what you meant by the first sentence, Chronos, but that's what I needed. Thanks. Just one more question, the mass units you used are atomic mass units, right? 1.660538 * 10^-27 kilograms?

10. Jan 15, 2005

### kirovman

Yes, but 1kg is a mass. 1 kiloton, well that value is 1 millon times larger than a kiloton. So surely 1kg corresponds to 9E16 J of energy?
But 1 kiloton corresponds to 9E22 J of energy.

So, what have I overlooked?
Or maybe I've misinterpreted the meaning of kiloton explosion?

Oh wait, I think I have misinterpreted.... The explosion is EQUIVILANT to a kiloton of TNT exploding. As we know the explosion of TNT is terribly inefficient in terms of energy liberated. That accounts for the discrepancy, I believe.

Sorry, getting confused there. Problem solved I think. :rofl:

11. Jan 15, 2005

### vincentchan

Chronos:
Please don't confuse him.. the U236 is not neccessary decays into Ba-141 and Kr-92.... there are hundreds ways for U236 to decay... NanakiXIII has already showed that he knew this point already....

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kirovman:
Chronos was right this time..However, his statement is not clear.. that's where the confusion came from.. he said one kilogram of mass will yield about 17.5 kilotons of TNT.. not (17.5kilotons) c^2 joules of energy.. surely 1 kilogram of mass doesn't contain 17500 tons of energy (this is seriously violent the Conservation Law of Mass-Energy).
Just wanna add 1 ton of TNT has energy of 4.1*10^9 joules.

NanakiXIII:
I think you can get from here.. how much mass is actually converted into energy per kilogram of U235 in a nuclear explosion.. don't surprise if your answer is less than 1%.. mc^2 is a big number as Chronos said..

12. Jan 15, 2005

### dextercioby

WRONG!! 1 Kiloton of ANY SUBSTANCE has the energy of:
$$\sim 10^6Kg\cdot (3\cdot 10^{8}ms^{-1})^{2}= 9\cdot 10^{22}J$$

That's physics.

However,the energy released in this chemical reaction:
$$TNT+O_{2}\rightarrow CO_{2}+H_{2}O_{(v)}+NO_{2}$$

by 10^{6} Kg of TNT is what Chronos said...

Daniel.

PS.IIRC the structural formula for TNT is $CH_{3}-C_{6}H_{2}-(NO_{2})_{3} [/tex] 13. Jan 15, 2005 ### vincentchan I was saying if a ton of TNT explodes , it will release 4.1*10^9 joules of energy... If I confused you... sry... next time, I will say it like this: When 1 ton of TNT (which official named Trinitrotoluene, is a pale yellow crystalline aromatic hydrocarbon compound, has a chemical formula of [itex]C_{6}H_{2}(NO_{2})_{3}CH_{3}$, and IUPAC name 2,4,6-trinitromethylbenzene.) explodes chemically, (disintegrate itself violently under heat influence).it will release $4.1 \times 10^9$ joules of energy. (assume the explosion takes place under 1atm and normal room temperatur)

dex:
don't play this kind of word games with me.. English is not my first language, at least conceptually I am right, not like you, YOU DONT EVEN KNOW WHAT TNT IS.. TAKE A LOOK AT WHAT YOU SAID....
TNT contains their oxidant as well as the fuel, it doesn't react with oxygen in air....Do you know the different between dynamite and normal fuel?

Last edited: Jan 15, 2005
14. Jan 15, 2005

### vincentchan

Here is the chemical formulas for TNT explosion:
$$2TNT \rightarrow 3N_{2} + 7 CO + 5 H_{2}O + 7C$$

the H2O is in gas form.....