Let `E_(1)` and `E_(2)` be the binding energies of two nuclei `A` and `B`. it is observed that nuclei of `A` combine together to form a `B` nuclus. This observation is correct only if .

Options

A. `E_(1) gt E_(2)`
B. `E_(2) gt E_(1)`
C. `E_(2) gt 2E_(1)`
D. nothing can be said

Explanation

To solve the problem, we need to analyze the conditions under which two nuclei A can combine to form a nucleus B. The key concept here is the binding energy of the nuclei involved in the reaction.

### Step-by-Step Solution:

1. **Understanding Binding Energy**:
- The binding energy of a nucleus is the energy required to disassemble it into its constituent protons and neutrons. A higher binding energy indicates a more stable nucleus.

2. **Formation of Nucleus B from Nuclei A**:
- When two nuclei of type A combine to form one nucleus of type B, we need to consider the binding energies involved. Let \( E_1 \) be the binding energy of nucleus A and \( E_2 \) be the binding energy of nucleus B.

3. **Energy Considerations**:
- For the reaction to be energetically favorable (i.e., for it to occur spontaneously), the total energy of the products must be less than the total energy of the reactants. This means that energy must be released during the formation of nucleus B.

4. **Setting Up the Equation**:
- The total binding energy of the reactants (two nuclei of A) is \( 2E_1 \).
- The binding energy of the product (nucleus B) is \( E_2 \).
- For the reaction to be possible, the energy released must be positive, which can be expressed mathematically as:
\[ E_2 > 2E_1 \]

5. **Conclusion**:
- Therefore, the observation that nuclei of A combine to form a nucleus B is correct only if the binding energy of nucleus B is greater than twice the binding energy of nucleus A.

### Final Answer:
The observation is correct only if \( E_2 > 2E_1 \).

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