Assertion Positive value of packing fraction implies a large value of binding energy.
Reason The ratio of the difference between the atomic mass of nucleus and the mass number of the nucleus to that of atomic mass is called packing fraction.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

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

### Step 1: Understand the Assertion
The assertion states: "Positive value of packing fraction implies a large value of binding energy."

- The packing fraction is defined as the mass defect per nucleon. A positive packing fraction indicates that the mass defect is positive, which means that the actual mass of the nucleus is less than the sum of the individual masses of its constituent protons and neutrons.

### Step 2: Understand the Binding Energy
Binding energy is related to the mass defect by the equation:
\[ E_b = \Delta m \cdot c^2 \]
where \(E_b\) is the binding energy, \(\Delta m\) is the mass defect, and \(c\) is the speed of light.

### Step 3: Analyze the Relationship
If the packing fraction is positive, it indicates that the mass defect is positive. However, the assertion claims that this implies a large value of binding energy.

- While a positive packing fraction does indicate that the nucleus is bound, it does not necessarily mean that the binding energy is large. The binding energy depends on the magnitude of the mass defect. A small positive packing fraction could correspond to a small mass defect, leading to a small binding energy.

### Step 4: Evaluate the Reason
The reason states: "The ratio of the difference between the atomic mass of nucleus and the mass number of the nucleus to that of atomic mass is called packing fraction."

- This statement is true. The packing fraction is indeed defined based on the mass defect, which is the difference between the mass of the nucleus and the mass number (in atomic mass units).

### Step 5: Conclusion
Based on the analysis:
- The assertion is **false** because a positive packing fraction does not necessarily imply a large binding energy.
- The reason is **true** as it correctly describes the definition of packing fraction.

Thus, the correct answer is that the assertion is false and the reason is true.

### Final Answer
Assertion: False
Reason: True
Correct Option: D

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