Binding Energy per Nucleon (Fission)

[NotoriousNick]

Homework Statement

By analyzing the Binding Energy per Nucleon Curve, and using the equivalence factor 1amu=931.4 MeV, show that a U fission frees energy equivalent to 0.2 AMU.

Homework Equations

E=mc^2

A fission I picked: U-235 + slow neutron ---> 141/56 Ba + 93/36 Kr + 2n

The Attempt at a Solution

I am understanding that the binding energy per nucleon shown in this chart is essentially the mass defect, or in other words, the difference between the sum of the rest masses of the constituent nucleons VS the actual experimental mass of that nucleus.


I would imagine, that if we had a Fission, we break this U-235 nucleus into other nucleus types, like the fission into Ba and Kr and 2n shown above.

Then if we take the sum of:

[the mass defect or binding energy of resultant Ba] +
[the mass of resultant Ba nucleus in amu] +
[the mass defect or binding energy of resultant Kr]
[the mass of resultant Kr nucleus in amu]
[the mass of 2n in amu]

and Subtract

The Actual experimental measured mass of these by products

You are left with:

The energy released from the binding energy, as now kinetic energy of the fast neutrons.




I'm sure I'm making it more complicated.
What I don't understand is, if in the graph of Binding Energies per Nucleon, if the ones in the middle have Higher binding energies per nucleon, than wouldn't it make sense that the energy release would be in a process that resulted in nucleus's with less binding energies per nucleon?

Thanks

 

[Jhero]

for your post! You are correct in your understanding of the binding energy per nucleon curve and its relationship to the mass defect. In the case of a fission reaction, the binding energy of the products is greater than the binding energy of the original nucleus, resulting in a release of energy. This release of energy is equivalent to the mass defect, which is why we use the equivalence factor of 1amu=931.4 MeV.

In the specific fission reaction you have chosen, U-235, the total mass of the products (Ba, Kr, and 2n) is less than the mass of the original U-235 nucleus. This difference in mass, when multiplied by the equivalence factor, gives us the energy released in the fission reaction.

To calculate this, we would use the equation E=mc^2, where E is the energy released, m is the mass difference, and c is the speed of light. In this case, the mass difference would be the mass of the products (Ba, Kr, and 2n) minus the mass of the original U-235 nucleus. This difference would then be multiplied by the equivalence factor to give us the energy released.

As for your question about the binding energies of the products, it is important to remember that the binding energy per nucleon curve is a general trend and does not apply to every single nucleus. In the case of fission reactions, the products may have lower binding energies per nucleon, but the overall binding energy is still greater than that of the original nucleus, resulting in a release of energy.

I hope this helps clarify the concept for you! Let me know if you have any further questions or need any additional explanation.