Nuclear binding energy problem

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Discussion Overview

The discussion revolves around the calculation of nuclear binding energy in a reaction involving helium-3 nuclei, specifically the discrepancy between the calculated binding energy and the value reported in external sources. Participants explore the implications of using atomic versus nuclear masses in these calculations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a calculation for the reaction of two helium-3 nuclei producing one helium-4 nucleus and two protons, noting a discrepancy in the calculated binding energy compared to a source.
  • Another participant points out that the masses used are atomic masses, which include electrons, rather than nuclear masses, which do not.
  • Some participants clarify that the emitted protons are actually hydrogen nuclei, which include electrons, affecting the mass calculations.
  • A later reply emphasizes that nuclear reactions should only consider bare nuclei, thus suggesting that the initial calculations need to be adjusted to reflect nuclear mass instead of atomic mass.

Areas of Agreement / Disagreement

Participants generally agree that the distinction between atomic and nuclear masses is crucial for accurate calculations. However, the discussion remains unresolved regarding the specific adjustments needed to reconcile the calculated and reported binding energies.

Contextual Notes

Limitations include the reliance on atomic versus nuclear mass definitions and the potential confusion arising from including electrons in mass calculations for nuclear reactions.

JeWiSh
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Hi, could someone please try and figure out where I'm going wrong here.
This is a calculation for a collision between 2 helium-3 nuclei which produces 1 helium-4 nucleus and 2 protons. The numbers are taken from wikipedia.
Mass before = 2(3.0160293 u) = 6.0320586 u
Mass after = 1 helium-4 nucleus + 2 protons = 4.002602 + 2(1.00727646677) = 6.017154932 u

6.0320586 - 6.017154932 = 0.014903668 u
1 u = 931.494 MeV
0.014903668 * 931.494 = 13.88267732 MeV, and yet wiki says it's just 12.9 MeV. Can anyone see the problem? I tried another calculation similar to this for another equation on wikipedia and got almost the exact answer that they had, but this is just a bit off.
 
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The masses that you find in tables are atomic masses, not nuclear masses. They include the electrons that accompany the nucleus in an un-ionized atom.
 
jtbell said:
The masses that you find in tables are atomic masses, not nuclear masses. They include the electrons that accompany the nucleus in an un-ionized atom.

Thanks for the help but I don't fully understand. What can be done to correctly modify my calculation?
 
Ahhhh I understand. The protons that are emitted are actually hydrogen nuclei, complete with electrons. It adds up now. Thanks.
 
JeWiSh said:
Mass before = 2(3.0160293 u) = 6.0320586 u

This includes the four electrons that two helium-3 atoms contain.

Mass after = 1 helium-4 nucleus [actually atom] + 2 protons = 4.002602 + 2(1.00727646677) = 6.017154932 u

Your proton mass really is the "bare" proton mass (i.e. not the mass of a hydrogen-1 atom). Therefore this total includes only two electrons from the helium-4 atom.
 
Hi there,

Into a reaction like you mention above, you never take into account the electrons. You are talking about NUCLEAR reactions, which from the name of it implies only the bare nuclei. Therefore, like jtbell said, your calculations need to take into account the nuclear mass and not the atomic mass. Cheers
 

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