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Nuclear Binding Energy

February 18, 2013

Introduction to nuclear binding energy

As the the resarch in nuclear structure of atoms progressed,it always intrigued the scientists as to how all the positively charged protons could be held in the nucleus and why the nucleus doesn’t burst out due to repulsion among the similar charges of the protons.

In relation to this one more stark observation noted by the scientists was that the mass of the nucleus is always less than the sum of masses of the neutrons and the protons. The shortfall in the mass was called mass defect.

Einsteins contribution to nuclear binding energy

Subsequently it was only during Einstein’s time that a satisfactory explanation to this could be obtained.It was put forth by him that energy and mass were intra-conservable,i.e. mass could be converted to energy .This mathematical wizard also gave the relationship between the two.

He explained that the loss of the mass ,is actually mass converted to energy.This same energy is used to hold the protons together against their natural tendency to repel one another.This energy which is binding the protons was subsequently termed as binding energy.

Binding energy can conversely defined as energy required to disassemble the nucleus into free protons and neutrons.

Einstein’ s famous equation’


where E is the binding energy ,m is mass defect,c is the speed of light.

The unit of energy employed is Mev i.e. 1000000 electron volt.

1 eV = 1.602176487(40)×10−19 J

Practical applications of nuclear binding energy

Let us consider mass defect of 1 amu

1 amu = 1.66054 x 10-7 Kg

Energy produced =931.494 Mev


The mass of nuclei of alpha particle

The masses of protons= 2x 1.00078u

The masses of neutrons=2 x 1.00866u

Total=4.0388 u

Actual mass of the alpha nucleus =4.00153

Mass defect=0.03035

E=28.3 MeV

It is this huge magnitude of binding energy which attracted the attention of the scientist.Thereafter some of the scientists started contemplating  harnessing this energy which was the most concentrated form of energy discovered so far.

This lead to the discovery of nuclear fission reaction wherein a nuclei is broken down to release this energy.

Normally,a Uranium 92 nucleus is bombarded by a neutron,which makes it unstable and results in its fission,releasing tremendous binding energy.

The first application of this was the creation of the atomic bomb which played unprecedented destruction in Hiroshima and Nagasaki.

The fission reaction is used in atomic reactors too to create electricity.


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