Nuclear Physics

Step 1: Binding energy per nucleon curve.
- The binding energy per nucleon ( ) is a measure of nuclear stability.
- It increases sharply for light nuclei, reaches a maximum around iron ( ), and then decreases gradually for heavy nuclei.

Step 2: Fusion of light nuclei.
- Light nuclei (H, He, Li) lie on the left side of the curve.
- When two light nuclei fuse, the product nucleus has a higher .
- Example:
- The increase in binding energy per nucleon means the product is more stable. The difference in energy is released as kinetic energy and radiation.
Step 3: Fission of heavy nuclei.
- Very heavy nuclei (U, Th) lie on the right side of the curve where decreases with .
- Splitting them into two medium nuclei (Ba, Kr) increases the .
- Example:
- Since products are more stable, the mass defect appears as released energy.
Step 4: Why energy is released in both.
- In both fusion and fission, the system moves toward greater stability (higher binding energy per nucleon).
- Energy released is given by Einstein’s relation: - In fusion, is positive because a heavy nucleus formed is more stable.
- In fission, is positive because medium nuclei are more stable than very heavy ones.
Step 5: Conclusion.
(i) Light nuclei fuse to reach higher and become stable.
(ii) Heavy nuclei split for the same reason.
(iii) Both processes release energy because the final nuclei lie closer to the peak (iron region) of the binding energy curve.

Step 1: Definition of -value.
The -value of a nuclear reaction is the difference between the total binding energy of products and reactants: If , the reaction is exothermic; if , it is endothermic.
Step 2: Binding energy of reactants.
Deuterium ( ) has 2 nucleons and B.E. per nucleon . Since two deuterium nuclei are involved:
Step 3: Binding energy of product helium.
Helium-4 has 4 nucleons and B.E. per nucleon . So,
Step 4: Calculate -value.
(approx considering significant figures).
Step 5: Nature of reaction.
Since , the reaction is exothermic (energy releasing).
Step 6: Mass defect.
Energy released . In atomic mass units ( ),
Step 7: Conclusion.
- The reaction is exothermic.
- -value .
- Mass defect .

Step 1: Recall definition.
Isotones are atoms of different elements that have the same number of neutrons but different numbers of protons.
Step 2: Calculate neutrons.
- : Neutrons .
- : Neutrons .
So, they are isotones.
For others:
- : neutrons , : neutrons (not isotones).
- : neutrons , : neutrons (not isotones).
- : neutrons , : neutrons (not isotones).

Step 3: Conclusion.
Correct isotone pair is and .

Step 1: Write expression for volume of nucleus.

Step 2: Write expression for mass of nucleus.
Mass of nucleus (where is mass of one nucleon, nearly proton/neutron mass).
Step 3: Density of nucleus.

Step 4: Conclusion.
Since cancels out, is independent of mass number .