# Binding energy after fission and fusion

1. Aug 17, 2010

### v_pino

The total binding energy after fission and fusion decreases.

Does that sound right to you? Can you please give me some explanation also? Or direct me to webpages for further understanding of binding energy in the context of fusion and fission.

Thanks

2. Aug 17, 2010

### fatra2

Hi there,

That sounds right to me. Meaning that each nucleons is less glued after the fission of the heavy nucleus. This is precisely this "excess" energy that is release in the nuclear process (fission or fusion).

I will spare you the whole theory behind binding energy of nucleons. Instead, let's take an example to illustrate the idea. Take the nucleus U-235, which is used in the nuclear fission process. Go on your periodic table of elements, and check the atomic weight of this element. This element, once bombarded with a neutron, will fission into something like Kr-94 and Ba-141, plus a few neutrons. Check again the atomic weight of these two elements, add three neutrons to it. The weight result is not the same as originally.

There was some energy (E=mcÂ˛) lost/gain in the process. This energy is precisely the energy carried away by the different elements of the fission.

Hope this helps a bit.

Cheers

3. Aug 17, 2010

### v_pino

Hmm... I was having a look at the 'binding energy per nucleon versus nucleon number' curve. I've been told that a large nucleus goes through fission to form smaller daughter nuclei and that small nuclei go through fusion to form a large nucleus.

This means that fission is moving from the very right of the curve to the left of the curve (not going beyond the peak); fusion is mvoing from the very left of the curve to the right of the curve (not going beyond the peak).

Doesn't this mean that, for both fission and fusion, binding energy increase?

4. Aug 17, 2010

### HallsofIvy

No, the whole point of "fusion" and "fission" is that they release energy. Energy is removed from the nuceus. Binding energy in the products of both fusion and fission is less than in the inputs, accounting for the energy released.

Yes, fission "moves to the left" and fusion "moves to the right" and both are moving toward minimum binding energy in the periodic table (which is, I think, at lead).

5. Aug 17, 2010

### v_pino

Thanks a lot - I understand that the total binding energy decrease.

But what about the binding energy per nucleon?

6. Aug 17, 2010

### the_house

There may be an issue of semantics here. Usually "binding energy" of a bound system is defined as a positive quantity. So something that is more tightly bound is said to have a larger binding energy, whereas the total energy of the bound system is smaller.

Therefore, when a system spontaneously splits or fuses into a lower energy state, you would say the binding energy has increased.

See, for example, the standard plot for the binding energy per nucleon:

http://en.wikipedia.org/wiki/Nuclear_binding_energy#Fission_and_fusion

where Iron (not lead) has the maximum binding energy per nucleon.

So, at least according to my understanding, the original sentence "the total binding energy after fission and fusion decreases" seems to be backwards from the standard terminology.

Edit: It would, however be correct if you just remove the word "binding". The total energy of the system decreases.