There are two nuclei X and Y . |B.E of X | is a and |B.E of Y| is 2a. Also, |B.E per nucleon of X | is 2b and |B.E per nucleon of Y| is b. Then which one of the following is true ?

Options

A. X is always more stable than Y
B. X is more stable than Y if mass number of X is greater than that of Y .
C. Y is always more stable than X
D. none of the above

Answer

To solve the problem, we need to analyze the given data about the two nuclei, X and Y, in terms of their binding energies and binding energies per nucleon.

### Step-by-Step Solution:

1. **Identify the Binding Energies**:
- The binding energy of nucleus X is given as \( B.E_X = a \).
- The binding energy of nucleus Y is given as \( B.E_Y = 2a \).

2. **Identify the Binding Energies per Nucleon**:
- The binding energy per nucleon of nucleus X is given as \( B.E_{per nucleon, X} = 2b \).
- The binding energy per nucleon of nucleus Y is given as \( B.E_{per nucleon, Y} = b \).

3. **Understanding Stability**:
- The stability of a nucleus is generally determined by its binding energy per nucleon. A higher binding energy per nucleon indicates a more stable nucleus.

4. **Compare Binding Energies per Nucleon**:
- For nucleus X: \( B.E_{per nucleon, X} = 2b \).
- For nucleus Y: \( B.E_{per nucleon, Y} = b \).
- Since \( 2b > b \), this means that nucleus X has a higher binding energy per nucleon than nucleus Y.

5. **Conclusion on Stability**:
- Since nucleus X has a higher binding energy per nucleon, it is more stable than nucleus Y.

6. **Final Answer**:
- Therefore, the correct statement is: "X is always more stable than Y."