JEE MAIN - Physics (2024 - 27th January Morning Shift - No. 25)
Explanation
To determine the energy released in a nuclear fission process, we use the difference in binding energy (BE) before and after the fission. The formula for energy released ($$Q$$ value) in the process is given by:
$$Q = (\text{Total BE of products}) - (\text{Total BE of reactants})$$
In this case, the reactant is a high mass nuclide with atomic mass $A \approx 236$ and a binding energy of $$7.6 \mathrm{MeV}/\mathrm{nucleon}$$. Each of the two middle mass nuclides formed as products has atomic mass $A \approx 118$ and a binding energy of $$8.6 \mathrm{MeV}/\mathrm{nucleon}$$.
Therefore, we calculate the total binding energy of reactant and products as follows:
For reactant:
$$\text{BE}_{\text{reactant}} = 236 \times 7.6 \mathrm{MeV}$$
For products (since there are two identical products):
$$\text{BE}_{\text{products}} = 2 \times (118 \times 8.6) \mathrm{MeV}$$
Thus, the energy released ($$Q$$ value) is:
$$Q = \text{BE}_{\text{products}} - \text{BE}_{\text{reactant}}$$
$$Q = 2(118 \times 8.6) - (236 \times 7.6)$$
$$Q = 236 \times (8.6 - 7.6)$$
$$Q = 236 \times 1$$
$$Q = 236 \mathrm{MeV}$$
This calculation demonstrates how the difference in binding energy per nucleon before and after fission leads to the release of energy, consistent with the mass-energy equivalence principle.
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