# Nuclear Fusion and Fission

472
I am currently studying A level Physics. I understand that, in a nuclear fusion reaction, the mass of the nucleus we end up with is smaller than that of its constituent nuclei, so Δm is negative and so energy is lost in huge amounts. But what about a nuclear fission reaction? The mass of the products is bigger than that of the nucleus we started with, so there is no mass defect, but a mass gain instead. Keeping this in mind, how is energy released in nuclear fission? Where have I misunderstood?

2. ### ChrisVer

2,403
Because fission happens in chains,some parts of which are energetically disfavoured ,while other pay this back- so you gave net energy emission.
See for example the procedures of Hyrogen to Hellium (pp chains)...
Also why you say that the mass defect is non negative in fission? You cannot say that until you test it out.

3. ### dauto

The OP is just mistaken. Spontaneous fission is also associated with a mass defect. No mass is gained.

4. ### mathman

6,750
Atom bombs and nuclear reactors get their energy from fission, where mass of fission products is less than that of original material (usually U235 or Pu239).

5. ### SteamKing

10,946
Staff Emeritus
The energy released in both fusion and fission reactions comes from excess nuclear binding energy which is left over after the nuclei have fused or fissioned.

Fusion reactions occur in lighter nuclei, while fission reactions occur in heavy nuclei. To take fission reactions first, a heavy nucleus like U-235 is bombarded typically with neutrons, which can penetrate to the nucleus without being affected by the electrons surrounding the nucleus, due to the neutral charge of the neutron. When a neutron strikes the uranium nucleus, it sets up an unstable situation, and the nucleus splits into two roughly equal parts, emitting more single neutrons in the process. As long as at least 2 additional neutrons are produced during every fission, a 'chain-reaction' phenomenon is established, where fission of a critical mass of uranium can proceed until either all of the uranium splits, or the critical mass dissipates due to the high temperatures which result.

http://en.wikipedia.org/wiki/Nuclear_fission

Because there is less binding energy for the fission products (including the neutrons) than for the original uranium nucleus, the difference in binding energy is emitted as gamma rays and in the form of kinetic energy, as the fission product nuclei physically fly away from the spot where the nucleus was originally struck by the neutron.

The fusion reaction works in reverse: two lighter nuclei, like isotopes of hydrogen H-2 and H-3, join together to make a heavier nuclei, like He-3 or He-4. The heavier nuclei take less binding energy than the lighter nuclei, so there is a release of this excess energy into the environment.

http://en.wikipedia.org/wiki/Nuclear_fusion

Typically, fusion reactions occur only when certain conditions of temperature or density are achieved in the original material. Once those conditions no longer exist, the fusion reactions stop. In order to achieve these conditions for fusion on earth in a nuclear weapon, first a fission bomb is detonated, which produces the high temperature and which compresses the hydrogen fuel to the density required to initiate fusion. These conditions exist for only a fraction of a second, during which the fusion reactions take place to spectacular effect.

472
What about E = mc^2 and the mass defect?

### Staff: Mentor

In both fission and fusion reactions, the mass of the products is less than the initial mass and you apply ##E=mc^2## to this mass defect to calculate the energy released.

Generally energy is released by fusing things lighter than iron-56 and fissioning things heavier than iron-56; google for "curve of binding energy" for more detail.

8. ### SteamKing

10,946
Staff Emeritus
If you read the two cited articles, they will tell you.

In the fission of a uranium nuclei, about 0.1% of the mass of the nucleus is converted to energy, the amount of which is given by Einstein's formula. (See the section titled 'Output'). There is also energy derived in several other different forms, since the fission fragments do not remain stationary after the reaction occurs.

In the fusion reaction, the physics of energy generation are more complex, but if you read the 'Overview' and 'Requirements' sections of the Fusion article, these will describe the amount of energy and its source in a typical D-D reaction.

472
I understood now. Apparently, I have a lot of misconceptions (although my physics teacher has a masters degree in nuclear physics).
But how is energy released if the binding energy of the products is bigger? I mean, doesn't that mean there is an increase in E, not s decrease?

10. ### SteamKing

10,946
Staff Emeritus
I'm not sure what you mean. Which products?

472
The products of fission/fusion.

### Staff: Mentor

If the binding energy of the products of a reaction is greater than the initial binding energy, then the reaction does not release energy. It consumes energy, and that energy must be added from outside before the reaction will even happen.

On a small scale, we do this when transuranic elements are produced in particle accelerators by colliding heavy nuclei together. On a vastly larger scale, every nucleus heavier than iron-56 in our solar system was originally produced in a supernova explosion; some tiny fraction of the energy released by the supernova went to forming heavy elements.

13. ### Jilang

648
I thought binding energy is always negative. When you say it is "bigger" I think you mean more negative. So energy can be released.

14. ### PAllen

5,890
I assume it's covered in the wiki articles, but it doesn't seem to have been mentions explicitly in the thread so far:

The binding energy per nucleon is greatest for iron and nickel. It gets smaller for heavier nuclei and also for lighter nuclei. Thus, for light nuclei, fusion (by producing a result closer to iron) will produce a result with more binding energy (thus less mass) than the starting ingredients. For heavy nucleii fission will produce a result with more binding energy (thus less total mass) than the starting nucleus. Both results are consistent with the idea that if the weight of the products is less than the weight of the starting ingredients, there is a release of energy.

15. ### ChrisVer

2,403
you must be careful. In general, we have the semi-empirical formula to calculate binding energies of nuclei. Once you calculate for the initial bodies and final products, you can see whether the process is energetically favored or disfavored.

Also, there is also a threshold for $B^{8}$ which is subject to alpha decay and which kept the after the Big Bang nuclei light... (if I recall well)

16. ### PAllen

5,890
I was just giving a general rule for how to understand that both fusion of light nuclei and fission of heavy nuclei can both be exothermic. Obviously, you can't conclude from this that any nucleus more that 2xiron can energetically fission, or that any nucleus < 1/2 iron can energetically fuse.

17. ### ChrisVer

2,403
I didn't say you didn't, you also said "in general".. I just wanted to complete it by giving an example where this generality doesn't hold. I agree on the rest...