The attached image is from Class 12 NCERT Physics Textbook,Chapter13-Nuclei

It is mentioned that the lesser the total mass of the nuclei, greater would be the binding energy per nucleon.

I do not seem to understand this..

As per my understanding of binding energy, it is the energy required to bind the nucleus of any species together. So if the mass of the nucleus is more doesn't it mean, it would require a lot of energy to hold it together?

ii) Because of the above confusion, I am unable to understand the fundamental idea of energy being released during nuclear fission as well..


2 Answers 2


The nuclear binding energy

Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other,Nucleons are attracted to each other by the strong nuclear force.

In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.

italics mine.

The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, E=mc2, where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.

continuing in the article

Mass defect (also called "mass deficit") is the difference between the mass of an object and the sum of the masses of its constituent particles. Discovered by Albert Einstein in 1905, it can be explained using his formula E = mc2, which describes the equivalence of energy and mass. The decrease in mass is equal to the energy given off in the reaction of an atom's creation divided by c2.[7] By this formula, adding energy also increases mass (both weight and inertia), whereas removing energy decreases mass. For example, a helium atom containing four nucleons has a mass about 0.8% less than the total mass of four hydrogen atoms (each containing one nucleon). The helium nucleus has four nucleons bound together, and the binding energy which holds them together is, in effect, the missing 0.8% of mass

This is the binding energy curve for the atoms

enter image description here

so it is the experimental definition, which is useful in order to calculate how much energy will be needed or released if the nucleus is broken up, or, for the elements in on the left of Fe when fused with another light nucleus

So , for getting energy out of nuclear interactions , one has to study the above curve.

  • $\begingroup$ Note that tagging 56Fe in context of the chart of the avg binding energy per nucleon is misleading. As while 56Fe has maximal avg binding energy per nucleus mass, the nuclide with maximal avg binding energy per nucleon is 62Ni. $\endgroup$
    – Poutnik
    May 12, 2022 at 10:16
  • $\begingroup$ @Poutnik here they consider Ni in the "iron group" hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.html $\endgroup$
    – anna v
    May 12, 2022 at 11:04
  • $\begingroup$ from wikipedia "However, nickel-62 is the most tightly bound nucleus in terms of energy of binding per nucleon.[15] (Nickel-62's higher energy of binding does not translate to a larger mean mass loss than 56Fe, because 62Ni has a slightly higher ratio of neutrons/protons than does iron-56, and the presence of the heavier neutrons increases nickel-62's average mass per nucleon). $\endgroup$
    – anna v
    May 12, 2022 at 11:10
  • $\begingroup$ See also Wikipedia pages for iron-56 and nickel-62 $\endgroup$
    – Poutnik
    May 12, 2022 at 11:11

The binding energy should be negative. That is -8 MeV in the middle. For Uranium it is larger (less negative). Hence, fission produces excess energy, which is manifested as heat (the kinetic energy of the products).

  • $\begingroup$ why exactly does fission produce excess energy ?As i had stated in my question if the reason is that a heavier nuclei has lesser energy so when it breaks into lighter nuclei, the process actually releases energy..I'm unable to understand why the reason holds true $\endgroup$ Feb 19, 2022 at 13:56
  • $\begingroup$ could you also explain why heavier nuclei has lesser binding energy? doesn't heavier nuclei require more energy to be held together? $\endgroup$ Feb 19, 2022 at 13:58
  • $\begingroup$ Yes, the bindig energy per nucleus is larger for heavier atoms. But, as I explained the bindig energy is negative. This causes confusion in the book. $\endgroup$
    – wawa
    Feb 19, 2022 at 14:02
  • $\begingroup$ oh okay..so they are not talking about the magnitude..thank you! $\endgroup$ Feb 19, 2022 at 14:03

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