|Fig. Binding Energy Curve|
The binding energy ranges from 2.23 MeV for heavy hydrogen to about 1800 MeV for Uranium. This shows that binding energy increases with complexity of nucleus.
Therefore in order to compare the stabilities of different nuclie we require the average binding energy per nucleon which is obtained by dividing the total binding energy of nucleus to total number of nucleons.
When the average binding energy per nucleon for various nuclie 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 nuclie are most stable because they have greatest average binding energy ranging from 8.8 to 7.6 MeV.
This means that greatest amount of energy is required to break them in their nucleons.
The light nuclie with A < 20 are least stable except 2He(4) , 6C(12), and O(16) because they are even-tempered even nuclie. i.e. number of protons are even number.
The graph is shown below as :
Packing Fraction :
We observed that atomic mass are not whole number. This divergence of masses of nucleus from whole number was studied by Aston and is expressed in terms of Packing fraction.
Packing fraction is defined as :
where zM(A) is actual mass of nucleus and A is mass number.
Since, zM(A) = Actual mass – mass number
= Mass defect
Eq. (i) can be expressed as :
This is the formula for packing fraction.