Assertion:Nuclear binding energy per nucleon is in the order -`""_(4)^9Be 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 reason is the explaination of assertion.
B. If both assertion and reason are true but reason is not the correct explaination of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the nuclear binding energy per nucleon is in the order:
\[ {}_4^9\text{Be} > {}_3^7\text{Li} > {}_2^4\text{He} \]

### Step 2: Analyze the Binding Energy
Nuclear binding energy is the energy released when nucleons (protons and neutrons) bind together to form a nucleus. Generally, for light nuclei, the binding energy per nucleon tends to be higher, while for heavier nuclei, it tends to decrease due to increased repulsion among protons.

### Step 3: Compare the Elements
- **Helium (He)**: Atomic mass = 4, has a relatively high binding energy per nucleon.
- **Lithium (Li)**: Atomic mass = 7, has a lower binding energy per nucleon than Helium.
- **Beryllium (Be)**: Atomic mass = 9, has an even lower binding energy per nucleon than Lithium.

From this, we can conclude that the correct order of binding energy per nucleon should actually be:
\[ {}_2^4\text{He} > {}_3^7\text{Li} > {}_4^9\text{Be} \]

Thus, the assertion is **false**.

### Step 4: Understand the Reason
The reason states that the binding energy per nucleon increases linearly with the difference in the number of neutrons and protons. This statement is also misleading because the binding energy does not necessarily increase linearly with the difference in neutrons and protons. In fact, the relationship is more complex and does not follow a simple linear trend.

### Step 5: Conclusion
Both the assertion and the reason are false. Therefore, the correct answer is that both the assertion and reason are false.

### Final Answer
Both the assertion and the reason are false.

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