Question

Draw the graph showing the variation of binding energy per nucleon with the mass number for a large number of nuclei 2 < A < 240 . What are the main inferences from the graph ? How do you explain the constancy of binding energy in the range 30 < A < 170 using the property that the nuclear force is short-ranged. Explain with the help of this plot the release of energy in the process of nuclear fission and fusion.

Answer 1

The variation of binding energy per nucleon versus mass number is shown in figure. 

Inferences from graph 

1. The nuclei having mass number below 20 and above 180 have relatively small binding energy and hence they are unstable.

2. The nuclei having mass number 56 and about 56 have maximum binding energy – 5.8 MeV and so they are most stable.

3. Some nuclei have peaks, e.g., ₂He⁴ , ₆C¹², ₈O¹⁶ ; this indicates that these nuclei are relatively more stable than their neighbours.

Explanation of constancy of binding energy : Nuclear force is short-ranged, so every nucleon interacts with their neighbours only, therefore binding energy per nucleon remains constant. 

Explanation of Nuclear Fission : When a heavy nucleus (A + 235 say) breaks into two lighter nuclei (nuclear fission), the binding energy per nucleon increases i.e., nucleons get more tightly bound. This implies that energy would be released in nuclear fission.

Explanation of Nuclear Fusion : When two very light nuclei (A ,10) join to form a heavy nucleus, the binding is energy per nucleon of fused heavier nucleus more than the binding energy per nucleon of lighter nuclei, so again energy would be released in nuclear fusion.