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### Plot of Binding Energy per Nucleon against Mass Number - Important Conclusions

What is Binding Energy?

Binding Energy (BE) is the energy required to break a Nucleus into free neutrons and free protons.

According to Einstein's relative theory, mass of a system bound by energy 'B' is less than mass of its constituents by B/c².

BE/Nucleon(B/A) vs Mass Number (A) Plot

Important Conclusions

a) Approximately for most of Nuclei B/A ~ Constant.
b) B/A falls off at small values of A

Reason: For very light Nuclei a large fraction of their nucleons resides on the surface rather than inside. This reduces the B/A value as a surface nucleon is surrounded by fewer nucleons compared to a nucleon residing in interior and consequently is not so strongly bound.

c) B/A falls off at large values of A. This is clearly a Coulomb effect. Between every pair of Protons, there is a Coulomb repulsion which increases as Z². Notice that for naturally occurring nuclei, Z² increases faster than A and so Coulomb effect cannot adequately compensated by an increase in A.

d) B/A against A plot is peaked about A~50.
Binding Energy can be increased by either breaking a heavy nucleus into parts or fusing light nuclei together.  It is easy to see that when binding energy is increased, energy in other forms can be released , since a decrease in 'M' corresponds to conversion of mass into energy.

e) The peak of the plot corresponds to iron. This explains large abundance of Fe(iron) in nature.

f) The plot indicates that binding becomes strong for a grouping of four particles. This unit is 𝛂 particle (2 neutrons + 2 protons).

The peaks in figure at mass numbers 4,8,12,16,20 & 24 are clear evidence of this effect. This effect is due to a pairing  force which exists  between a pair of neutrons and pair of protons.

g)  On closer inspection, it is found that B/A against A plot shows discontinuities  at neutron or proton number values 2,4,8,20,50,82 & 126. At these values of neutron or proton numbers, the BE is found to be unusually large. Large BE means high stability.

### What is a Nuclear Reactor?

A Nuclear Reactor is a systematic arrangement to convert Nuclear Energy into thermal energy and then to Electrical energy .  Nuclear Reactor uses fissile material, heavy atomic nuclei, called as Nuclear Fuel. Fissile material leads to nuclear fission when the nuclei are hit by suitable energy Neutrons.

Example for Fissile Material is Uranium oxide.

Fission reaction of Uranium is as follows:

The energy evolved is distributed as kinetic energy of fission fragments  and heat.

This heat energy transmitted to a coolant which leads to generation of steam that could drive turbine system for conversion of thermal energy into electrical energy.

There are different types of Nuclear Reactors operating across the world.

a)  Boiling Water Reactors
b)  Pressurized Water Reactors
c)  Pressurized heavy water Reactors
d)  Fast Breeder Reactors