Which, among the following, is a correct statement?

Options

A. binding energy of a nucleus is always negative
B. binding energy of a nucleus may be positive
C. higher value of binding energy per nucleon means the nucleus is more unustable
D. higher value of binding energy per nucleon means the nucleus is more stable

Answer

To solve the question regarding which statement about binding energy of a nucleus is correct, we will analyze each option step by step.

### Step 1: Analyze the first statement
The first statement claims that "the binding energy of a nucleus is always negative."

- **Explanation**: Binding energy is defined as the energy required to separate a nucleus into its individual nucleons (protons and neutrons). If the binding energy were negative, it would imply that energy is released when the nucleons are separated, which contradicts the definition of binding energy. Therefore, this statement is incorrect.

### Step 2: Analyze the second statement
The second statement claims that "the binding energy of the nucleus may be positive."

- **Explanation**: While it is true that binding energy is positive, the phrase "may be positive" introduces uncertainty. Binding energy is always a positive quantity because it indicates the stability of the nucleus. Thus, this statement is misleading and incorrect.

### Step 3: Analyze the third statement
The third statement claims that "a higher value of binding energy per nucleon means our nucleus is more unstable."

- **Explanation**: A higher binding energy per nucleon indicates that the nucleons are held together more tightly, which means the nucleus is more stable. Therefore, this statement is also incorrect.

### Step 4: Analyze the fourth statement
The fourth statement claims that "a higher value of binding energy per nucleon means the nucleus is more stable."

- **Explanation**: This statement is accurate. A higher binding energy per nucleon signifies that the nucleons are more strongly bound together, leading to greater stability of the nucleus. Thus, this statement is correct.

### Conclusion
The only correct statement among the options provided is that a higher value of binding energy per nucleon means the nucleus is more stable.

### Final Answer
The correct statement is: "A higher value of binding energy per nucleon means the nucleus is more stable."

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