Why Is Nuclear Binding Energy Proportional to the Mass Defect?

[semc]

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) ?

 

[Astronuc]

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

 

[kyle8921]

The binding energy of a nucleus is a measure of the energy required to break apart the nucleus into its individual protons and neutrons. This energy is directly related to the mass of the nucleus, which is composed of protons and neutrons.

The equation E=mc^2 tells us that energy and mass are equivalent, and that the mass of a system is related to its energy content. In the case of a nucleus, the mass of the nucleus is slightly less than the combined mass of its individual protons and neutrons. This difference in mass is known as the mass defect and is due to the strong nuclear force that binds the protons and neutrons together.

Therefore, the binding energy of a nucleus is proportional to the mass defect, which is the difference between the mass of the nucleus and the mass of its individual protons and neutrons. This is why the binding energy is directly proportional to the sum of the masses of the protons and neutrons, rather than the difference.

In summary, the binding energy of a nucleus is directly proportional to the mass of its constituent particles, taking into account the mass defect caused by the strong nuclear force.