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# Binding energy and its calculation

In this article you will learn the concept of binding energy, types of binding energy, mass defect, calculation of binding energy and binding energy curve.

In an atomic nucleus protons and neutrons are bound together by a means of strong attractive nuclear forces. The small amount of energy required to separate protons and neutrons of an atomic nucleus or to separate electrons from an atom is known as binding energy. Binding energy breaks up a nucleus to such an extent that they may not interact with each other. We can understood binding energy in terms of mass-energy equivalence, as they two are connected through Einstein’s famous relationship E = (Δm)c2.  The mass of a stable nucleus is always less than the mass of protons and neutrons in their free state, this difference of mass between nucleus and its constituents is known as mass defect act and this accounts for the energy released when protons and neutrons are brought together to form a nucleus of  certain charge and mass. Therefore, E = (Δm)c2 .

## Types of binding energy

Atomic binding energy: Atomic binding energy is the small amount of energy required to break an atom into free electrons and nucleus, it is the sum of ionisation energies of all the electrons belonging to a specific atom.

Bond dissociation energy: Bond dissociation energy is the binding energy between the atoms of the same chemical bond it is the energy required to break a molecule into its constituent atom. The bond dissociation energy increases as the difference in the electronegativities of the bonded atoms increases. Bond energy depends on the number of bonds between atoms. High bond dissociation energy means the bond is stable and is of low energy.

Ionization energy: Ionization energy or electron binding energy is the energy required to pull a negatively charged electron from an atom which is held in place by the electrostatic pull of a positively charged nucleus. The electron binding energy is measured in electron volt (eV), where 1 eV = 1.6 x 10-19 J. The magnitude of electron binding energy e is directly proportional to atomic number and inversely proportional to the distance from the nucleus.

Nuclear binding energy: It is the energy required to break a nucleus into free protons and neutrons. It is the energy equivalent to mass defect, the difference between the mass number of a nucleus and its measured mass.

## Mass defect

Mass of a stable nucleus is always less than the sum of the masses of its constituent protons and neutrons in their free state. The difference between the rest mass of a nucleus and the sum of rest masses of its constituent nucleons is called its mass defect.

Things we need to calculate mass defect,

• the actual mass of the nucleus
• number of protons and neutrons
• masses of a Proton and of a Neutron

### Nuclear Fission and nuclear fusion

Nuclear Fission reaction is when a heavy nucleus splits up into smaller nuclei of comparable masses, high temperature and pressure and not necessary for its occurrence.

Nuclear fusion is the reaction when nuclei are combined together to form a heavy nucleus nucleus, it needs high pressure and temperature to occur.

### Calculation of binding energy

#### Binding energy curve

The stability of a nucleon depends upon the value of binding energy per nucleon.

### Conclusion

The amount of energy required to break a nucleus into its constituent particles is known as binding energy. We have learnt different types of binding energies: Ionization energy, atomic binding energy, nuclear binding energy, bond energy or bond dissociation energy. Mass defect=∆m=Zmp + ( A – Z )mp – m, it is the difference between an atom and its rest particle. Binding energy curves suggest a second way in which energy could be released in nuclear reactions. Nuclear fusion is the process in which two smaller nuclei fuse into a heavier nucleus with the release of a large amount of energy. Nuclear Fission is the process in which a heavy nucleus splits into smaller nuclei of nearly comparable masses.

## Frequently asked questions

Get answers to the most common queries related to the IIT JEE Examination Preparation.

## Calculate the binding energy per nucleon for an alpha particle whose mass defect is calculated as 0.0292amu.

Ans. Given: mass defect = 0.0292amu Convert the mass d...Read full

## What is mass defect?

Ans. Mass defect is the difference between therest mass of an atom and it constituent particles tha...Read full

## Calculate the binding energy per nucleon of 1735Cl nucleus. Given that: Mass of 1735Cl = 34.980000u,  mass of proton = 1.007825, mass of neutron = 1.008665, 1 atomic mass unit(1u) = 931MeV

Ans. cl has 17 protons and 18 neutrons. mass of 1 prot...Read full

## Calculate the energy equivalence (inMeV) of one twelfth of the mass of one atom of C12.

Ans. Mass of one atom of 12...Read full

## State two characteristics of nuclear forces.

Ans. Nuclear forces at the strongest forces in nature ...Read full