Binding Energy curve in nuclear physics

Variation of Binding Energy per Nucleon with Mass Number and Main Features of B.E. Curve

The graph between binding energy per nucleon and mass number of different nuclei is shown in Fig. below

Following are the main features of binding energy curve.

1. The binding energy per nucleon for light nuclei (i.e., ¹H₈) is very small.
2. The binding energy per nucleon increases rapidly for nuclei up to mass number 20. The curve possesses peaks corresponding to nuclei ²He₄, ⁴Be₅, ⁶C₁₂, ⁸O₁₆ and ¹⁰N₂₀.

• The peaks indicate that these nuclei are more stable than other nuclei in their neighbourhood. This confirms the extraordinary stability of α-particle as shown in Fig. (1.6).
• 3. After mass number 20 binding energy per nucleon increases gradually.
• 4. The curve has average value of binding energy per nucleon of about 8.5 MeV for a very considerable range of mass number 40 to 120. In this range the curve is more or less flat.
• 5. For mass number A = 56 (i.e. ₂₆Fe⁵⁶), the binding energy per nucleon is maximum and is equal to 8.8 MeV.
• 6. After mass number A = 120, binding energy per nucleon decreases and drops to 7.6 MeV for uranium. Due to this low value of binding energy per nucleon, the heavy nuclei are unstable. These heavy nuclei are unable to overcome the Coulomb's force of repulsion between the protons inside the nucleus. Hence heavy nuclei split into lighter nuclei by process of fission and a large amount of energy is released.
• 7. ₁₀Ne²⁰ and ₈O¹⁶ both have nearly same value for binding energy per nucleon though they lie almost at the extreme of the mass number scale.
• 8. The smallest binding energy per nucleon is in the case of deuteron.
• 9. The nuclei of intermediate masses (i.e. A = 40 to 120) are the most stable and a very large amount of energy has to be supplied to liberate each of their nucleons.
• 10. The binding energy per nucleon has a low value for both light very light and very heavy nuclei. In order to attain higher value of binding energy per nucleon, the lighter nuclei may unite to form a heavier nucleus (process of nuclear fusion) or a heavier nucleus may split into medium weight nuclei (process of fission). In both these nuclear processes, the resulting nucleus acquires greater value of binding energy per nucleon and large amount of energy is released.