Binding Energy and Mass Deficit

[kcodon]

Hi there all,

I'm new at this whole idea of using a forum, but am unfortunately stuck on some of the theory behind my high school nuclear physics teaching. Basically its to do with the mass deficit and E=mc^2. We have learned so far that the uncombined nucleons of an atom have more mass than the combined atom...and this mass deficit is converted into binding energy by E=mc^2, as a result of strong nuclear force. So I get that part i think, its just when you have a nuclear reaction, for example the fusion of deuterium and tritium to make alpha particle and a neutron. I have fiddled around with the numbers, playing with the mass deficit, and it seems to me that the binding energy of tritium and deuterium, plus the energy from the mass deficit, is equal to the binding energy in the helium nucleus. So I am stumped as to how any other energy is thus emitted, as the mass deficit gives the energy for additional binding energy in the helium nucleus...? I know of course that there must be heaps emitted, but to me it appears that it all goes into the binding energy of product...

If anyone could shed some light on this little dilemma of mine it would be greatly appreciated,

Thanks,

Kcodon

 

[Norman]

This post by Astronuc explains it quite well I think. See the middle paragraphs.

 

[Astronuc]

Here is a good explanation of binding energy

http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html

Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference is a measure of the nuclear binding energy which holds the nucleus together. This binding energy can be calculated from the Einstein relationship:

E = $\Delta$mc²

 

[kcodon]

Thanks Astronuc,

I think I've realized the error of my ways...by the nucleons binding together with strong nuclear force to form nucleus, there is a loss in energy, shown by the fact that energy must be put in (binding energy) to separate nucleus back into nucleons. Binding energy is therefore misleading...nucleons are not held together by binding energy, but the nuclear force. The binding energy is the energy required to break strong nuclear force, and the nucleus actually has less energy (equal to binding energy). Therefore the mass deficit is directly related to E=mc^2 and voila we have energy.

 

[Astronuc]

Correct. The binding energy is released during a nuclear reaction. It is the energy that must be put back into the nucleus to separate the nucleons.

When a neutrons combines with a proton to form a deuteron, a gamma ray is given off. That is the binding energy. Similar when a deutron absorbs a neutron, a triton (nucleus of H3 tritium atom) is formed, and binding energy is given off as a gamma ray.

When a deuteron and triton 'fuse', the reaction forms a helium nucleus (alpha particle) and free neutron. The binding energy is then expressed in the kinetic energy of alpha particle and neutron.

 

[johna]

could somebody explain in which field (EM or SNF) this energy released in nuclear FISSION (200MeV) is stored before the fission event. The "binding energy" terminology seems to have introduced some confusion about the nature of this energy source.