Which is Greater: Binding Energy Per Nucleon of Parent or Daughter Nucleus?

[kihr]

Homework Statement

A nucleus of mass M + m1 is at rest and decays into two daughter nuclei of equal mass M/2 each. The binding energy per nucleon for the parent nucleus is A and that for the daughter nucleus is B. Which is greater A or B?

Homework Equations

Binding energy per nucleon= Mass defect of nucleus / mass number

The Attempt at a Solution

I am unable to link the given masses of nuclei (parent and daughters) with their mass defect in the absence of data on A and Z. I need a few hints on how to proceed with tackling this problem.

 

[lanedance]

think about rest masses & conservation of energy

and remember, all up, there's likely to be the same number of nucleons before and after the decay...

 

[kihr]

Yes I do understand that in this case there would be a generation of energy because of the difference in rest masses between the parent and daughters. Also I am aware that energy would be conserved, and that this information would help in finding out, for instance, the kinetic energy of the two daughter nuclei. But how does this get linked up with the binding energy per nucleon when I do not know the values of A? Also the concept of binding energy per nucleon is relevant for individual nuclei, the data for which does not appear to be available in the problem. I would request for a few more tips. Thanks.

 

[lanedance]

if you need to, make some assumptions

first assume N nucleons in the parent, each daughter can be assumed to have N/2. Each daughter will have the same BEPN of B, whilst the parent has B.

also decays generally move to a more stable low energy configuration...

If you want to get right down into, make some assumption about the type of decay & put some limits on numbers...

 

[kihr]

OK. Let me try out the way you have suggested.

 

[kihr]

Going by the BEPN versus A (mass number) graph, in the case of fission (to which this problem appears to relate) the BEPN for the fission products is less than that of the parent nucleus. If this logic is to be applied A > B should be the correct answer. However, I understand that it is to be the reverse. This is what I am unable to understand. I would appreciate some further guidance. Thanks.