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 determine which statement is correct among the given options regarding the binding energy of a nucleus, let's analyze each statement step by step.

### Step 1: Understand Binding Energy
Binding energy is the energy required to disassemble a nucleus into its constituent nucleons (protons and neutrons). It is a measure of the stability of the nucleus; higher binding energy generally indicates a more stable nucleus.

### Step 2: Analyze the First Statement
The first statement claims that "the binding energy of a nucleus is always negative."
- This statement is incorrect. While the binding energy is often described in terms of energy required to remove nucleons (which can be considered negative), it does not mean that the binding energy itself is always negative. In fact, the binding energy is typically expressed as a positive value when discussing the energy required to hold the nucleus together.

### Step 3: Analyze the Second Statement
The second statement suggests that "the binding energy of a nucleus may be positive."
- This statement is somewhat misleading. While it is true that binding energy is often expressed as a positive value, the phrasing "may be positive" is not entirely accurate in the context of nuclear physics. Binding energy is a measure of energy required to break apart the nucleus, and it is conventionally treated as a positive quantity.

### Step 4: Analyze the Third Statement
The third statement claims that "higher the value of binding energy per nucleon means the nucleus is more stable."
- This statement is correct. The binding energy per nucleon is a crucial factor in determining the stability of a nucleus. A higher binding energy per nucleon indicates that each nucleon is held more tightly within the nucleus, thus contributing to greater stability.

### Step 5: Analyze the Fourth Statement
The fourth statement suggests that "higher binding energy means the nucleus is more stable."
- This statement is also correct, but it is important to clarify that it is the binding energy per nucleon that is the more significant measure of stability. A nucleus with a high total binding energy but a low binding energy per nucleon may not be stable.

### Conclusion
Based on the analysis:
- The first statement is incorrect.
- The second statement is misleading.
- The third statement is correct.
- The fourth statement is correct but needs clarification.

Thus, the correct statement among the options is that "higher the value of binding energy per nucleon means the nucleus is more stable."