Proving 8Be Ground State Stability vs Nucleon Emission

[Str1k3]

Homework Statement

The question is longer than this but the part I'm stuck on is this - Show that the ground state of 8Be is stable against nucleon emission.

Homework Equations

I'm not sure which ones to use... I used the binding energy formula.

The Attempt at a Solution

what I'm not sure about is that in our textbook it says you need to look at the energy difference between neighboring isobars and if the difference in energy is greater than the nucleon binding energy then you get nucleon emission. So now does this mean I look at 8Be, 8B, 8Li and compare the binding energies? If I do this I see a difference of 17MeV or so, which is greater than the nucleon binding energy of 7MeV. If I instead look at 8Be, 7Li and 7Be I have the same problem - there is a big difference. Now this would indicate to me that there is in face nucleon emission. What am I doing wrong?

 

[Jhero]

Thank you for your question. It seems like you are on the right track with using the binding energy formula to analyze the stability of the ground state of 8Be. However, there are a few things that you may want to consider in your approach.

Firstly, when comparing the binding energies of neighboring isobars, it is important to consider the mass difference between them as well. The energy difference that you calculated may not be a significant factor if the mass difference is also large. In this case, it would be helpful to calculate the binding energy per nucleon for each isobar, as this will give you a better idea of the overall stability of the nuclei.

Secondly, it is important to note that the ground state of 8Be is actually a highly excited state, with a half-life of only about 7x10^-17 seconds. This means that it is not a stable state and will eventually decay through various decay modes, including nucleon emission. However, the question is asking you to show that the ground state is stable against nucleon emission. This means that you need to show that there is a barrier preventing nucleon emission from occurring in this state, at least in the short time that it exists before decaying through other means.

Finally, it may be helpful to consider the nuclear forces at play in 8Be. you are probably aware that the strong nuclear force is responsible for binding nucleons together in the nucleus. In the case of 8Be, there are two alpha particles (each consisting of two protons and two neutrons) bound together by this force. This means that the strong force is acting on a larger scale in this nucleus, potentially providing a stronger barrier against nucleon emission.

I hope this helps guide you in the right direction. Good luck with your analysis!