In the options given below, let E denote the mass energy of a nucleus and E(n) that of a neutron. The correct option is

Options

A. `E(""_(92)^(236)U)gtE(""_(53)^(137)I)+E(""_(39)^(97)Y)+2E(n)`
B. `E(""_(92)^(236)U)ltE(""_(53)^(137)I)+E(""_(39)^(97)Y)+2E(n)`
C. `E(""_(92)^(236)U)ltE(""_(56)^(140)Ba)+E(""_(36)^(94)Kr)+2E(n)`
D. `E(""_(92)^(236)U)gtE(""_(56)^(140)Ba)+E(""_(36)^(94)Kr)+2E(n)`

Answer

To solve the question regarding the mass energy of a nucleus (E) and that of a neutron (E(n)), we need to analyze the given nuclear fusion reactions and determine which options are correct based on the conservation of nucleons and energy. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Conservation Laws
In any nuclear reaction, the total number of nucleons (protons + neutrons) must be conserved. This means that the mass number on the left-hand side (LHS) of the reaction must equal the mass number on the right-hand side (RHS).

### Step 2: Analyze Each Option
We will analyze the options provided to check for conservation of nucleons and energy.

1. **Option A:** Check the mass numbers on both sides of the equation.
- LHS: Mass number of nucleus X.
- RHS: Mass numbers of daughter nuclei Y and Z plus any released neutrons.
- Ensure that the total mass number on LHS equals the total on RHS.

2. **Option B:** Repeat the same analysis as in Option A.
- Check if the mass numbers balance.

3. **Option C:** Again, check the mass numbers.
- Ensure that the nucleon count is conserved.

4. **Option D:** Perform the same checks as above.
- Confirm that the mass numbers are balanced.

### Step 3: Evaluate Energy Considerations
In a nuclear reaction, the energy released is due to the difference in mass-energy between the reactants and products. The mass-energy of the nucleus (E) must be greater than the sum of the energies of the products (E(Y) + E(Z)) plus any energy released.

### Step 4: Identify Correct Options
From the analysis:
- If the mass numbers are balanced in Options A and D, and they also satisfy the energy conservation principle, then these options are correct.
- If Options B and C do not balance the mass numbers or violate energy conservation, they are incorrect.

### Conclusion
Based on the analysis, the correct options will be those that maintain both nucleon and energy conservation.