The binding energies of two nuclei `P^n` and `Q^(2n)` and x and y joules. If `2x gt y` then the energy released in the reaction `P^n + P^n to Q^(2n)`, will be

Options

A. 2x+y
B. 2x-y
C. `-(2x-y)`
D. x+y

Answer

To solve the problem, we need to determine the energy released in the nuclear reaction \( P^n + P^n \rightarrow Q^{2n} \) given the binding energies of the nuclei involved.

### Step-by-Step Solution:

1. **Identify the Binding Energies**:
- The binding energy of nucleus \( P^n \) is given as \( x \) joules.
- The binding energy of nucleus \( Q^{2n} \) is given as \( y \) joules.

2. **Calculate the Total Binding Energy of Reactants**:
- Since we have two nuclei \( P^n \) in the reaction, the total binding energy of the reactants is:
\[ \text{Total Binding Energy of Reactants} = x + x = 2x \]

3. **Calculate the Total Binding Energy of Products**:
- There is one nucleus \( Q^{2n} \) in the products, so the total binding energy of the products is:
\[ \text{Total Binding Energy of Products} = y \]

4. **Determine the Energy Released in the Reaction**:
- The energy released in the reaction can be calculated using the formula:
\[ \text{Energy Released} = \text{Binding Energy of Products} - \text{Binding Energy of Reactants} \]
- Substituting the values we calculated:
\[ \text{Energy Released} = y - 2x \]

5. **Rearranging the Expression**:
- To express this in a more standard form:
\[ \text{Energy Released} = - (2x - y) \]

6. **Final Result**:
- Therefore, the energy released in the reaction \( P^n + P^n \rightarrow Q^{2n} \) is:
\[ \text{Energy Released} = - (2x - y) \]

### Conclusion:
The energy released in the reaction is \( - (2x - y) \).