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Binding Energy Curve & Packing Fraction

The binding energy ranges from 2.23 MeV for heavy hydrogen to about 1800 MeV for Uranium. This shows that binding energy increases with the complexity of the nucleus. In this topic, we will discuss the binding energy curve & packing fraction.
Therefore in order to compare the stabilities of different nuclei, we require the average binding energy per nucleon which is obtained by dividing the total binding energy of the nucleus to the total number of nucleons.
When the average binding energy per nucleon for various nuclei is plotted against the mass number A, the binding energy curve is obtained.
The curve rises first rapidly & then slowly until it reaches a maximum of 8.8 MeV at A = 56, corresponding to Iron nucleus. It then drops very slowly to about  7.6 MeV at A = 238(U).
The intermediate nuclei are most stable because they have greatest average binding energy ranging from 8.8 to 7.6 MeV. This means that the greatest amount of energy is required to break them in their nucleons.
The light nuclei with A < 20 are least stable except  2He(4), 6C(12), and O(16)  because they are even-tempered even nuclei. i.e. the number of protons is even number.
The graph is shown below as :
Binding Energy Curve & Packing Fraction
Fig. Binding Energy Curve
Packing Fraction :
 
We observed that atomic mass are not the whole number. This divergence of masses of the nucleus from the whole number was studied by Aston and is expressed in terms of Packing fraction.
Packing fraction is defined as :
Binding Energy Curve & Packing Fraction
where zM(A) is the actual mass of the nucleus and A is the mass number.
Since, zM(A) = Actual mass – mass number 
                        = Mass defect
Eq. (i) can be expressed as :
Binding Energy Curve & Packing Fraction
This is the formula for packing fraction.

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