Question

Show the variation of binding energy per nucleon with mass number. Write the significance of the binding energy curve.
(b) Two nuclei with lower binding energy per nucleon form a nuclei with more binding energy per nucleon.
(i) What type of nuclear reaction is it ?
(ii) Whether the total mass of nuclei increases, decreases or remains unchanged ?
(iii) Does the process require energy or produce energy ?

Hint:

(a) BE per nucleon rises, peaks near A = 56 and then falls slowly; it explains stability, fission and fusion. (b) Fusion; mass decreases; energy is released.

Answer 1

Step 1: The binding energy curve (part a):
Plot the binding energy per nucleon (\(BE/A\), in MeV) on the vertical axis and the mass number A on the horizontal axis.
Curve in words: for very light nuclei the value is small (about 1.1 MeV for deuterium). It rises steeply to about 7 MeV for helium-4 (with a small bump there), then goes up slowly. It is nearly flat at about 8 MeV for A between about 30 and 170.
The peak is about 8.75 MeV at A around 56 (iron). After that the curve falls slowly to about 7.6 MeV at A = 238 (uranium).

Step 2: Significance of the curve (part a):
The flat part, about 8 MeV per nucleon for 30 < A < 170, shows that nuclear forces are short-range and saturated. Each nucleon interacts only with its near neighbours.
Nuclei near the peak (around iron) are the most tightly bound and the most stable.
Heavy nuclei have lower \(BE/A\). When a heavy nucleus splits into medium ones (fission), the products are more tightly bound, so energy is released.
Very light nuclei also have lower \(BE/A\). When they join to form a heavier nucleus (fusion), the product is more tightly bound, so energy is released.

Step 3: Part (b):
(i) Two light nuclei with lower \(BE/A\) join to form one nucleus with higher \(BE/A\). This is nuclear fusion.
(ii) The product is more tightly bound, so it has a larger mass defect. The total mass of the nucleus formed is less than the sum of the masses of the two nuclei. The total mass decreases.
(iii) The lost mass appears as energy, \(Q = \Delta m\,c^{2}\). The process produces (releases) energy.

Final Answer:
(a) Curve rises, peaks at about 8.75 MeV near A = 56 and then falls slowly; it explains stability, fission and fusion. (b) (i) Nuclear fusion, (ii) mass decreases, (iii) energy is produced.