Question

The binding energy of deuteron is 2.2 MeV and that of $^4_2$He is 28 MeV. If two deuterons are fused to form one $^4_2He$ then the energy released is :-

• A. 30.2 MeV
• B. 25.8MeV
• C. 23.6 MeV
• D. 19.2MeV

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the energy released when two deuterons fuse to form one helium-4 nucleus. This involves understanding the concept of binding energy and using it to find the total energy released in the fusion process.

1. Binding Energy Concept:
   • The binding energy is the energy required to break a nucleus into its constituent protons and neutrons. Higher binding energy means a more stable nucleus.
   • The energy released during a nuclear reaction, such as fusion, is due to the difference in the binding energies of the reactants and products.
2. Given Data:
   • Binding energy of a deuteron (^2_1\text{H}) = 2.2 MeV
   • Binding energy of a helium-4 nucleus (^4_2\text{He}) = 28 MeV
3. Calculate the Total Binding Energy of the Reactants:
   • Since we have two deuterons, the total binding energy for the deuterons is:
     2 \times 2.2 \text{ MeV} = 4.4 \text{ MeV}
4. Energy Released Calculation:
   • The energy released during the fusion of two deuterons to form one helium-4 nucleus is given by the difference in the total binding energy before and after the reaction:
     \text{Energy Released} = \text{BE}(^4_2\text{He}) - \left(\text{BE of two } ^2_1\text{H}\right)
   • Substitute the values:
     \text{Energy Released} = 28 \text{ MeV} - 4.4 \text{ MeV} = 23.6 \text{ MeV}
5. Conclusion:
   • The energy released when two deuterons are fused to form one helium-4 nucleus is 23.6 MeV.
   • Therefore, the correct answer is 23.6 MeV.