sr why does that peak occurs at that binding enrgy graph

Dear Student,
The binding energy curve is a curve showing the variation of nuclear binding energy per nucleon versus mass number of the nuclei. The plot is derived out of experimentally obtained values. The curve shows a peak at mass number 56 which corresponds to 26Fe56‚Äč isotope. The theoretical description for such a maximum, as predicted by Liquid drop model, is due to the resultant of all the forces that act on a collection of protons and neutrons. In this model, the nucleus is considered analogous to a drop of a liquid. Just as in case of a liquid drop, the stability of the drop depends on the competition between surface tension which results in attractive cohesive forces and other inertial forces like force due to gravity due to its weight, etc. As the drop grows in size, no. of water molecules at the surface increases which reduces the net cohesive forces and can be realised as a positive increase in the form of repulsive surface energy. With size its weight also increase. All these forces tend to disrupt the drop and when these repulsive forces exceeds the attractive cohesive force the drop break it into two. As all these forces are always present in a system, there will be a particular combination of these forces for which the drop will be most stable. The peak in the curve resembles that. In nuclear physics, the attractive force is:
 attractive forces while forming bonds between p - p, n - p, n - n (corresponds to negative volume energy) and repulsive forces are due to less binding of the surface nucleons (leading to positive surface energy) and coulomb force of repulsion among protons (leading to positive coulomb energy). A proper combination when makes the energy negative, the system behaves as a bound system and needs extra energy to break. There exists a particular combination when this energy value attains a maximum where the nucleus is most stable. The peak in the binding energy curve corresponds to such a nucleus.


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