Nuclear energy is released in fusion reaction, since binding energy per nucleon is

Options

A. Smaller of fusion products than for fusing nuclei
B. same for fusion products as for fusing nuclei
C. Larger for fusion products than for fusion nuclei
D. Sometimes larger and sometimes smaller

Answer

To solve the question regarding the release of nuclear energy in a fusion reaction and the binding energy per nucleon, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Nuclear Fusion**:
- In a fusion reaction, two smaller nuclei combine to form a larger nucleus. For example, if we have nuclei A and B, they fuse to create nucleus C.

2. **Mass Defect**:
- The mass of the resultant nucleus (C) is less than the total mass of the original nuclei (A and B). This difference in mass is known as the mass defect.
- The mass defect can be calculated using the formula:
\[ \text{Mass Defect} = (\text{Mass of A} + \text{Mass of B}) - \text{Mass of C} \]

3. **Energy Released**:
- According to Einstein's mass-energy equivalence principle, the energy released during the fusion can be calculated using the mass defect. The energy (E) released is given by:
\[ E = \text{Mass Defect} \times 931 \text{ MeV} \]
- Here, 931 MeV is the energy equivalent of 1 atomic mass unit (u).

4. **Binding Energy**:
- The binding energy of a nucleus is the energy required to disassemble it into its constituent nucleons (protons and neutrons).
- For nucleus C, the binding energy can be calculated using the mass defect:
\[ \text{Binding Energy} = E \]

5. **Binding Energy per Nucleon**:
- To find the binding energy per nucleon, we divide the total binding energy of nucleus C by the number of nucleons (A + B) in the nucleus:
\[ \text{Binding Energy per Nucleon} = \frac{\text{Binding Energy}}{\text{Total Number of Nucleons}} \]

6. **Conclusion**:
- In fusion reactions, the binding energy per nucleon of the product nucleus (C) is greater than that of the reactant nuclei (A and B). This is why energy is released during the fusion process.

### Final Answer:
Nuclear energy is released in fusion reactions because the binding energy per nucleon of the product nucleus is greater than that of the reactant nuclei.

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