Simulation · Physics · Class 12

Climbing the binding energy curve

From the lesson Binding energy curve in Nuclei. Change the values and watch what happens.

The idea behind it

NCERT §13.4.2

Fig. 13.1 plots the binding energy per nucleon Ebn against the mass number A for many nuclei.
For middle-mass nuclei, 30 < A < 170, Ebn hardly changes with A. The curve peaks at about 8.75 MeV for A = 56 and falls to 7.6 MeV at A = 238.
Ebn is lower for light nuclei (A < 30) and for heavy nuclei (A > 170).
Conclusion (i): the force binding nucleons is attractive and strong enough to give a few MeV per nucleon.
Conclusion (ii): the flat middle means the force is short-ranged. A nucleon deep inside a big nucleus feels only the neighbours within range. If it can have at most p of them, its binding is about pk, k being a constant energy. Adding more nucleons far away does not change it, and most nucleons of a large nucleus are inside, not on the surface.
This is the saturation property of the nuclear force: each nucleon affects only nucleons close to it.
Conclusion (iii): a nucleus of A = 240 has lower Ebn than one of A = 120. If it splits into two A = 120 nuclei, the nucleons end up more tightly bound and energy is released: fission.
Conclusion (iv): two very light nuclei (A ≤ 10) joining into a heavier one also end up with higher Ebn, again releasing energy: fusion, the energy source of the sun.
The curve is smooth, but it shows peaks at nuclides such as ⁴He and ¹⁶O, which is taken as evidence of an atom-like shell structure in nuclei.

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