If the nuclei of masess `X` and `Y` are fused together to form a nucleus of mass `m` and some energy is released, then

Options

A. `X+Y gt m`
B. `X-Y=m`
C. `X+Y=m`
D. `X+Y lt m`

Answer

To solve the problem, we need to analyze the fusion of two nuclei with masses \(X\) and \(Y\) to form a new nucleus of mass \(m\), while also considering the energy released during this process.

### Step-by-Step Solution:

1. **Understanding Fusion and Mass Defect**:
When two nuclei fuse, they combine to form a heavier nucleus. In this process, some mass is converted into energy, which is released. This phenomenon is known as mass defect.

2. **Mass of Reactants and Products**:
Let the mass of the first nucleus be \(X\) and the mass of the second nucleus be \(Y\). The mass of the resulting nucleus after fusion is \(m\). According to the law of conservation of mass-energy, the mass of the reactants must be greater than the mass of the products if energy is released.

3. **Setting Up the Inequality**:
Since energy is released, we can express this relationship mathematically:
\[ X + Y > m \]
This inequality indicates that the total mass of the reactants (the original nuclei) is greater than the mass of the resulting nucleus.

4. **Understanding Binding Energy**:
The energy released during the fusion process is related to the mass defect. The binding energy can be calculated using the mass defect (\(\Delta m\)):
\[ \text{Binding Energy} = \Delta m \times 931 \, \text{MeV} \]
where \(\Delta m = (X + Y - m)\).

5. **Conclusion**:
Since we established that \(X + Y > m\), it confirms that energy is released during the fusion process. Thus, the correct interpretation of the problem is that the sum of the masses of the original nuclei is greater than the mass of the resulting nucleus.

### Final Answer:
The correct conclusion is that:
\[ X + Y > m \]