I have read from my textbook about binding energy but it indicates two completely different ideas.I am listing them below:
"Binding Energy : An atomic nucleus is a stable structure.Inside it,the protons and neutrons are bond together by means of strong attractive nuclear forces.Thus a definite amount o work is required to be done to breakup the nucleus into its constituent particles and to place them at infinite distance from one another.This work gives a measure of the binding energy of the nucleus."
This definition gives the idea that binding energy is needed to overcome the Nuclear force between nucleons.
"It is seen that the mass of a stable nucleus is always less than the sum of the masses of the constituent protons and neutrons in their free state.This mass difference is called 'mass defect which accounts for the $\Delta E_b$' energy released when a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass.
This gives the idea that binding energy is given to nucleus then this energy reflects as extra mass of protons and nucleus.
So what actually is binding energy.Another definition tells it is the Energy required to break up nucleus. This suggests Binding energy should account for both mass defect and Nuclear force potential energy.Then why the formula of binding energy only accounts for mass defect ?
Edit From the given answers till now,what i get is idea that binding energy is required to break up nucleus into constituent particles. So i applied conservation of energy to find this binding energy. Equation that i get is $$E_b+(m-Δm)*C²+NFP=m*C²$$ (NFP Is net nuclear force potential among all nucleons & m is mass of individual protons and neutrons when they are in free state and Δm is mass defect) rearranging we get
And as NFP is negative and very large in magnitude(ie:- NFP "-100MeV" was between two nucleons[data from graph] so for a smaller nucleus also NFP should be" $-100*(N choose 2)$) Please help in clarifying this Edit.
Please help me make out what actually binding energy is.