Question

Draw a graph showing variation of binding energy per nucleon as a function of mass number $A$. The binding energy per nucleon for heavy nuclei $(A > 170)$ decreases with increase in mass number. Explain its significance.

Hint:

Describe the curve rising to a peak near A = 56 and then falling slowly. Lower BE per nucleon for heavy nuclei means they release energy on fission.

Answer 1

Step 1: Understanding the Concept:
Binding energy per nucleon is the average energy needed to remove one nucleon from the nucleus.
A higher value means the nucleus is held more tightly, so it is more stable.

Step 2: Draw the graph:
Take mass number \(A\) on the x-axis and binding energy per nucleon (in MeV) on the y-axis.
Description of the graph:
1. The curve starts low for light nuclei. For \(_1^2\mathrm{H}\) it is about 1.1 MeV.
2. It rises steeply, with small peaks at \(_2^4\mathrm{He}\), \(_6^{12}\mathrm{C}\) and \(_8^{16}\mathrm{O}\).
3. It reaches a broad maximum of about 8.75 MeV near \(A \approx 56\) (iron).
4. For the region \(30 < A < 170\) the curve is nearly flat at about 8 MeV.
5. For \(A > 170\) it falls slowly. For \(_{92}^{238}\mathrm{U}\) the value is about 7.6 MeV.

Step 3: Explain the significance:
For heavy nuclei the binding energy per nucleon is less than for medium-mass nuclei. This means heavy nuclei are less tightly bound and less stable.
If a heavy nucleus splits into two medium-mass nuclei, the products have a higher binding energy per nucleon.
The extra binding energy is released as energy. For example, for uranium the gain is about \((8.5 - 7.6)\) MeV per nucleon.
This is the basis of nuclear fission in reactors and in nuclear weapons.

Final Answer:
The binding energy per nucleon peaks near \(A = 56\) and falls for \(A > 170\). So heavy nuclei are less stable, and their fission into medium nuclei releases energy.