Assertion : A nuclear binding energy per nucleon is in the order `._(4)^(9)Be gt ._(3)^(7)Li gt ._(2)^(4)He`
Reason : Binding energy per nucleon increases linearly with difference in number of neutrons and protons.

Options

A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanantion of the assertion
C. If assertion is true but reason is false
D. If the assertion and reason both are false

Explanation

To analyze the assertion and reason provided in the question, we will break it down step by step.

### Step 1: Understand the Assertion
The assertion states that the nuclear binding energy per nucleon is in the order:
\[ \text{Be} (4, 9) > \text{Li} (3, 7) > \text{He} (2, 4) \]
This means that beryllium has a higher binding energy per nucleon than lithium, and lithium has a higher binding energy per nucleon than helium.

### Step 2: Understand Binding Energy
Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. The binding energy per nucleon is a measure of the stability of a nucleus; the higher the binding energy per nucleon, the more stable the nucleus.

### Step 3: Analyze the Reason
The reason states that binding energy per nucleon increases linearly with the difference in the number of neutrons and protons. This implies that as the number of neutrons and protons increases, the binding energy per nucleon should also increase.

### Step 4: Compare the Nuclei
- **Beryllium (Be)**: Has 4 nucleons (2 protons and 2 neutrons).
- **Lithium (Li)**: Has 7 nucleons (3 protons and 4 neutrons).
- **Helium (He)**: Has 4 nucleons (2 protons and 2 neutrons).

When comparing these nuclei, we need to consider their stability and the ratio of neutrons to protons. Beryllium has a balanced ratio, which contributes to its higher binding energy per nucleon compared to lithium and helium.

### Step 5: Conclusion
The assertion is correct because beryllium does have a higher binding energy per nucleon than lithium, and lithium has a higher binding energy per nucleon than helium. However, the reason provided is not entirely accurate. The binding energy per nucleon does not increase linearly with the difference in the number of neutrons and protons; it is more complex and depends on the overall stability of the nucleus.

### Final Answer
- **Assertion**: True
- **Reason**: False