Question

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
Assertion (A): The binding energy per nucleon is practically constant for mass number in the range \( 30<A<170 \).
Reason (R): Nuclear forces between the nucleons for mass numbers in the range \( 30<A<170 \) are not short-range.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Binding energy per nucleon remains almost constant for \( 30<A<170 \) due to saturation of short-range nuclear forces, not because the range changes.

Answer 1

The Correct Option is C

Assertion (A) is true: The binding energy per nucleon remains approximately constant (around 8 MeV) for nuclei with mass numbers in the range \( 30<A<170 \). This is because the nuclear forces saturate — each nucleon only interacts significantly with its nearest neighbors. This plateau in binding energy explains the relative stability of medium- and heavy-sized nuclei. Reason (R) is false: The nuclear force is always a short-range force, regardless of mass number. It acts over distances of a few femtometers and drops off rapidly beyond that. The range of the force does not increase with mass number. Therefore, the reason contradicts well-established nuclear physics principles.