What is Nuclear Binding Energy ?| Binding Energy Formula| Mass-defect

Definition of Nuclear Binding Energy:

Binding energy is the minimum energy compulsory to disassembled or break the nucleus of an atom into its constituent part. This is particularly pertinent to sub-atomic elements in atomic nuclei, to electrons bound to nuclei in atom.

Facts about Binding Energy:

Binding Energy (BE/A) Curve :

Binding Energy (BE/A) Curve
Binding Energy (BE/A) Curve
Binding Energy (BE/A) Curve
Image Credit: Roderich KahnNuclear binding energy RK01CC BY-SA 4.0


The mass of an atomic nucleus is usually less than the sum of the individual masses of the constituent protons and neutrons and this difference of mass is acknowledged as the mass defect, and signifies the energy that is to be released if a nucleus form.


Binding Energy Formula :

The binding energy for a nucleus is given by the equation

Patterns in the binding energy per nucleon, BE/A. if the BE/A is higher, the more stability of the nucleus will become higher too.

Critical Energy :

The minimum excitation energy required for fission to occur is known as the critical energy (EC) or threshold energy.

In principle, a nucleus, if energize sufficiently high excited state, can be parted into constituent parts. For ideal fission condition, the excitation energy must be more than a specific value for that nuclide. The min excitation energy requires for fission to occur is identified as the critical energy (E critical) or threshold energy. This critical energy be subject to nuclear structures also as it is dependent on various nucleus characteristics. This value may be significantly higher for light nuclei with Z < 90. For heavier nuclei with Z > 90, this may in the range of 4 to 6 MeV for A-even nuclei, and this value is considerably lesser for A-odd nuclei

Nuclear Stability peak in BE/A Curve
Nuclear Stability peak in BE/A Curve
WincenzoBinding energyCC BY-SA 3.0

Negative Binding Energy per Nucleon Curve

Negative Binding Energy per Nucleon Curve
Image Credit: BdushawBinding energy curve – common isotopes2CC BY-SA 4.0

The negative of binding energy per nucleon for stable isotopes along the valley of stability.

Dissociation Energy:

The dissociation energy Ed is equivalent to the diff. in-between the binding energy of the compound nucleus going thru fission and the sum of the binding energy of the fission fragments. The min activation energy Ea that has to be supplementary to a nucleus to go thru fission reaction is therefore Ec – Ed.

Nuclear Mass:

Mass of a Neutron ; Mass of a Proton and Mass of an electron in kg and amu

Nuclear mass and unit conversion in kg, amu and energy

Nuclear mass and unit conversion in a.m.u and energy
Nuclear Mass of electron, Proton and Neutron

Atomic mass unit (amu)

Atomic mass unit: Abbreviated as “amu.” A mass equal to one twelfth the mass of an atom of carbon-12.

amu to kg

1 amu = 1.66053873 x 10 -27 kilogram

1 amu= 1.66053873 x 10 -24 gram.

Table of critical energies and binding energies of radioactive fuels:

Table of critical energies and binding energies of radioactive fuels and their difference
Critical energies and binding energies of radioactive fuels and their difference

Spontaneous fission:

This is generally found for heavy elements; A radioactive decay occurs. The nuclear binding energy of the elements reaches its maximum; spontaneous breakdown into lesser mass nucleus and some isolated particle with more atomic mass numbers might also generate.

Spontaneous Fission Halflife (in ms) of Radionulides depending on Z²/A ratio of their nuclei
Spontaneous Fission Halflife (in ms) of Radionulides depending on Z²/A ratio of their nuclei
Frank Klemm(SF) Halflife of Radionulides depending on Z² to A ratioCC BY-SA 4.0

The nuclear binding energy is maximum for an atomic mass number of 56

Spontaneous fission half-life of various nuclides in reliant on their Z2/A ratio. In above figure Nuclides of the same element are linked with a red line. The green line illustrates the upper limit of half-life.

Valley of Stability Parabola

Semi empirical mass formula discrepancy

The discrepancy between experimentally-obtained binding energies and those predicted by the SEMF, alongside nuclear shell lines.

About Dr. Subrata Jana

I am Subrata, Ph.D. in Engineering, more specifically interested in Nuclear and Energy science related domains. I have multi-domain experience starting from Service Engineer for electronics drives and micro-controller to specialized R&D work. I have worked on various projects, including nuclear fission, fusion to solar photovoltaics, heater design, and other projects. I have a keen interest in the science domain, energy, electronics and instrumentation, and industrial automation, primarily because of the wide range of stimulating problems inherited to this field, and every day it’s changing with industrial demand. Our aim here is to exemplify these unconventional, complex science subjects in an easy and understandable to the point manner.
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