# BINDING ENERGY OR BINDING ENERGY PER NEUCLEON REMAINS CONSTANT [duplicate]

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Which one is constant BINDING ENERGY or BINDING ENERGY PER NEUCLEON? I GOT LOTS OF ANS. BUT I CAN`T UNDERSTAND. IS NEITHER OF THE IS CONSTANT?

## marked as duplicate by John Rennie, Danu, tom, Kyle Kanos, NeuneckMay 5 '15 at 12:09

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• Neither of them is constant, but binding energy per nucleon is closer to being constant. – John Rennie May 5 '15 at 5:08
• possible duplicate of Peaks in binding energy per nucleon – John Rennie May 5 '15 at 5:12
• I've linked one of the many many posts on this site that discuss this question – John Rennie May 5 '15 at 5:13
• CAN WE PLEASE NOT TYPE EVERYTHING IN ALL-CAPS BECAUSE IT COMES ACROSS AS SHOUTING?! – Danu May 5 '15 at 5:26
• my eyes, my ears... my cerebral cortex!!!! – user77400 May 5 '15 at 6:27

## 2 Answers

1) There are four vectors and a system of particles has an invariant mass according to the addition of its four vectors.

2) each nucleus has a rest mass, M, when it is not moving.

3) each nucleus has a fixed number of protons and neutrons, protons are Z in the table, and neutrons are A-Z

4) Each proton and each neutron has a fixed mass in its center of mass

From the above, multiplying the number of protons with the mass of the proton and multiplying the mass of the neutron with the number of neutrons and adding the quantities will give a mass M'. This would be the mass if all nucleons were at rest . It was observed that M' was bigger than M, i.e. the bound protons and neutrons into a nucleus have less mass than if they were not bound in a nucleus. The difference in the two values, M'-M is the total binding energy of the nucleus. Divided by [Z+(A-Z)] (the number of protons and neutrons one gets the binding energy per nucleon . So both are constant attributes of a specific nucleus. A simple division by a constant .

Inao Shyamananda, Binding Energy of a nucleus normally increases with increasing mass number. In the liquid drop model of the nucleus, when a person talks about constant binding energy, he/she means constant binding energy per nucleon. More precisely neither is a constant.