Why Is Nuclear Binding Energy Proportional to the Mass Defect?

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SUMMARY

The binding energy of a nucleus is directly proportional to the mass defect, defined as the difference between the total mass of individual protons and neutrons and the actual mass of the nucleus (M). This relationship indicates that the binding energy arises from the mass lost when nucleons combine to form a nucleus. When comparing a nucleus of mass M+1 to one of mass M, the total mass before combination exceeds the mass after, with the mass difference representing the binding energy, often released as gamma radiation.

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  • Understanding of nuclear physics concepts, specifically mass defect
  • Familiarity with binding energy calculations
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  • Basic grasp of nucleon composition (protons and neutrons)
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semc
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lets say the nucleus of the nuclide is M, why is binding energy of the nucleus directly proportional to (mass of proton and neutron)-M ? shldnt it be M-(mass of proton and neutron) ?
 
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Binding energy is the difference between the total mass (before) and the total mass (after) the combination.

If one takes a nucleus of mass M+1 and compares it to the initial nuclear of mass M and the proton or neutron mass, one will find the total mass before is greater than the mass after. The difference in mass is the binding energy, and in many cases the energy is transformed into a gamma ray.

http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/nucbin.html
 

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