Mark out the coreect statemnet (s).

Options

A. Higher binding energy per nucleon means the nucleus is more stable.
B. If the binding energy of nucleus can be negative.
C. Binding energy of a nucleus can be negative.
D. Binding energy of a nucleus is always positive.

Explanation

To solve the question of identifying the correct statements regarding binding energy in nuclear physics, we will analyze each statement step by step.

### Step 1: Understanding Binding Energy
Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. A higher binding energy indicates that more energy is needed to break the nucleus apart.

**Hint:** Remember that binding energy reflects the stability of a nucleus; higher values mean greater stability.

### Step 2: Analyzing the First Statement
The first statement claims that higher binding energy per nucleon means the nucleus is more stable. Since a higher binding energy indicates that more energy is required to break the nucleus apart, this statement is correct.

**Hint:** Think about what it means for a nucleus to be stable—if it requires a lot of energy to break it apart, it is stable.

### Step 3: Analyzing the Second Statement
The second statement suggests that the binding energy of a nucleus can be negative. This is incorrect. Binding energy is always a positive value because it represents the energy required to separate the nucleons. A negative binding energy would imply that the nucleus can spontaneously break apart without any energy input, which is not the case.

**Hint:** Consider the implications of negative energy—what would it mean for the stability of a nucleus?

### Step 4: Analyzing the Third Statement
The third statement is similar to the second and also claims that the binding energy of a nucleus can be negative. As established, this statement is also incorrect for the same reasons.

**Hint:** Revisit the definition of binding energy and its implications for nuclear stability.

### Step 5: Analyzing the Fourth Statement
The fourth statement asserts that the binding energy of a nucleus is positive. This is correct because, as previously discussed, binding energy must be positive to indicate that energy is required to break the nucleus apart.

**Hint:** Reflect on the nature of energy in nuclear reactions—what does it mean for energy to be positive in this context?

### Conclusion
Based on the analysis:
- The correct statements are:
- Higher binding energy per nucleon means the nucleus is more stable (Statement 1).
- The binding energy of a nucleus is positive (Statement 4).

**Final Answer:** The correct options are Statement 1 and Statement 4.