AIIMS 2006 Physics Binding Energy Assertion Reason Question

To analyze the given question effectively, let's break down the assertion and the reason, and see how they relate to nuclear physics concepts.

Assertion (A):

The binding energy per nucleon, for nuclei with atomic mass number $A > 100$, decreases with $A$.

Explanation: The binding energy per nucleon is defined as the total binding energy of a nucleus divided by the number of nucleons (protons and neutrons) in that nucleus. It is given by:

$$\text{Binding Energy per Nucleon} = \frac{B}{A}$$

where $B$ is the total binding energy and $A$ is the atomic mass number.

For heavier nuclei (those with $A > 100$), the binding energy per nucleon tends to decrease. This phenomenon can be explained by the fact that as nuclei get larger, the overall stability is affected by the balance between the attractive nuclear forces and the repulsive electrostatic forces between protons. The attractive nuclear force, while strong, acts over very short ranges and becomes less effective in holding larger nuclei together, leading to a relatively lower binding energy per nucleon.

Reason (R):

The nuclear forces are weak for heavier nuclei.

Explanation: This statement is partially correct. While it is true that the effective nuclear force does not hold heavier nuclei as effectively as it does for lighter nuclei, it is not entirely accurate to say that nuclear forces are "weak." The nuclear force is indeed strong, but as the number of nucleons increases, the repulsive forces between protons (due to electrostatic repulsion) start to dominate, which leads to instability. Hence, while nuclear forces still exist, they are less effective in keeping the nucleus stable or tightly bound for larger nuclei.

Correct Answer: B

A is true, R is true but R is not the correct explanation of A.

• The assertion (A) is true, as the binding energy per nucleon decreases with increasing $A$ for heavy nuclei.
• The reason (R) is also true, but it does not correctly explain the assertion. The decrease in binding energy per nucleon is more about the balance of forces rather than the strength of the nuclear force itself.

Why Other Options Are Incorrect:

• Option A: Incorrect because although both A and R are true, R does not explain A correctly.
• Option C: Incorrect because while A is true, R is also true.
• Option D: Incorrect because both A and R are true.

Summary:

In conclusion, the assertion regarding the binding energy per nucleon for heavy nuclei is accurate, reflecting the nature of nuclear stability and forces. The reason provided, while true, does not adequately explain the assertion, leading us to select option B as the correct answer.

This analysis helps clarify key concepts in nuclear physics, particularly regarding binding energy and the roles of nuclear forces in larger nuclei.