Calculating Binding Energy of 24 Mg

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Discussion Overview

The discussion revolves around calculating the binding energy of the isotope 24 Mg, which consists of 12 protons and 12 neutrons. Participants explore different approaches to determine the binding energy, including the mass defect method and an alternative equation that accounts for various nuclear interactions.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion over obtaining a negative mass defect when calculating the binding energy using the equation Eb (MeV) = (ZMp + NMn - Ma)931.494 MeV/u.
  • Another participant suggests that the issue may stem from incorrect input values, asserting that the binding energy should be positive since the combined mass of protons and neutrons exceeds the mass of the nucleus.
  • A participant later indicates that they resolved their issue by considering the coulomb repulsion effect and found a different equation for binding energy that incorporates various constants related to nuclear interactions.
  • There is a question raised about the proper definition of binding energy and whether it is synonymous with negative potential energy.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of binding energy, and there are differing views on the calculations and factors influencing the binding energy of 24 Mg.

Contextual Notes

Some participants mention the importance of considering the coulomb repulsion effect and the interactions between nucleons, but the discussion does not resolve how these factors definitively affect the binding energy calculations.

Who May Find This Useful

This discussion may be useful for students and enthusiasts interested in nuclear physics, particularly those seeking to understand binding energy calculations and the factors influencing them.

rogersj
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I'm trying to figure out the binding energy of 24 Mg. That is (12 protons and 12 neutrons. I keep getting a negative number. Using the equation:
Eb (MeV) = (ZMp + NMn - Ma)931.494 MeV/u I should be able to get the right answer but my mass defect ( delta m) is negative. What am I missing?
Thank you very much.
 
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You must be plugging in the wrong numbers. Your equation is correct. Since the proton and neutron massess are greater than 1u, and the mass of Mg is less than 24u, the binding energy is positive (as it better be).

Show the us the numbers.

And welcome to Physics Forums, by the way! :smile:
 
Last edited:
got it

thanks!
yeah I got the answer, apparently I wasn't taking into account the coulomb repulsion effect. I did a little reading and found this equation:

Eb = C1(A) - C2(A^2/3) - C3 Z(Z-1)/A^1/3 - C4(N-Z)^2/ A

where C1 = 15.7 MeV, C2 = 17.8 MeV, C3 = 0.71 MeV, C4 = 23.6 MeV

I don't quite understand it, but it worked to find the right answer. Thanks for your reply.
 
rogersj said:
thanks!
yeah I got the answer, apparently I wasn't taking into account the coulomb repulsion effect. I did a little reading and found this equation:

Eb = C1(A) - C2(A^2/3) - C3 Z(Z-1)/A^1/3 - C4(N-Z)^2/ A

where C1 = 15.7 MeV, C2 = 17.8 MeV, C3 = 0.71 MeV, C4 = 23.6 MeV

I don't quite understand it, but it worked to find the right answer. Thanks for your reply.

You should get the same answer using the mass defect, as Doc Al said. It takes into account all of the interactions without modeling them; it's just a direct measurement of the energy difference.
 
what is the proper definition of binding energy? Is it also called negative potential energy?
 

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