Question

Define binding energy per nucleon. Draw and explain the curve between binding energy per nucleon and mass number.

Hint:

Binding energy per nucleon increases with mass number up to iron and then decreases for heavier elements, explaining the energy release in fission and fusion.

Answer 1

Step 1: Definition of binding energy per nucleon.
The binding energy per nucleon is defined as the energy required to separate a nucleus into its individual nucleons (protons and neutrons). It is given by the total binding energy of the nucleus divided by the number of nucleons in the nucleus. The binding energy is a measure of the stability of the nucleus; higher binding energy per nucleon indicates greater stability. \[ \text{Binding energy per nucleon} = \frac{\text{Total binding energy}}{\text{Number of nucleons}} \] Step 2: Curve between binding energy per nucleon and mass number.
The binding energy per nucleon increases with mass number until it reaches a peak at around mass number 56 (for iron and nickel). After this point, the binding energy per nucleon starts to decrease as the mass number increases further. This curve indicates that nuclei with mass numbers around 56 are the most stable. Step 3: Drawing and explanation of the curve.
The curve typically shows the following: - For light nuclei (low mass number), the binding energy per nucleon is relatively low. - As the mass number increases, the binding energy per nucleon increases until it reaches a maximum at around mass number 56. - Beyond mass number 56, the binding energy per nucleon starts to decrease, indicating that heavier nuclei are less stable and more likely to undergo fission.
Step 4: Conclusion.
The curve between binding energy per nucleon and mass number shows that medium-sized nuclei (especially iron) are the most stable, and fission or fusion can release energy by moving to more stable configurations.