Nuclear binding energy problem

In summary, the conversation is discussing a calculation for a collision between 2 helium-3 nuclei that produces 1 helium-4 nucleus and 2 protons. The numbers used are taken from Wikipedia. The conversation reveals that the discrepancy in the calculated energy output is due to using atomic masses instead of nuclear masses, which include the electrons accompanying the nucleus. The conversation ends with a clarification on the use of nuclear masses in nuclear reactions.
  • #1
JeWiSh
3
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
Ahhhh I understand. The protons that are emitted are actually hydrogen nuclei, complete with electrons. It adds up now. Thanks.
 
  • #5
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.
 
  • #6
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
 

1. What is nuclear binding energy?

Nuclear binding energy is the amount of energy needed to hold the nucleus of an atom together. It is the result of the strong nuclear force, which is responsible for binding protons and neutrons together in the nucleus.

2. Why is the nuclear binding energy problem important?

The nuclear binding energy problem is important because it helps us understand the stability of atoms and how they are formed. It also plays a crucial role in nuclear reactions and energy production.

3. How is nuclear binding energy calculated?

Nuclear binding energy is calculated by subtracting the total mass of the individual protons and neutrons in an atom from the mass of the atom itself. The difference in mass is converted to energy using Einstein's famous equation, E=mc².

4. What is the significance of the nuclear binding energy curve?

The nuclear binding energy curve is a graph that shows the relationship between the number of protons and neutrons in a nucleus and the amount of binding energy needed to hold them together. It helps us understand the stability of different isotopes and the process of nuclear fusion and fission.

5. What challenges are associated with the nuclear binding energy problem?

One of the main challenges is accurately predicting the exact amount of binding energy for a given nucleus. This is due to the complex interactions between protons and neutrons and the difficulty in measuring their masses precisely. Another challenge is understanding the effects of nuclear forces at extremely high energies, which is important for nuclear reactions and particle accelerators.

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