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 exhibits a plateau, approximating 8 MeV, for nuclei with mass numbers \( 30 < A < 170 \). This phenomenon is attributed to the saturation of nuclear forces, wherein each nucleon interacts primarily with its immediate neighbours. This nearly constant binding energy per nucleon explains the high stability of medium and heavy nuclei.

Reason (R) is false: The nuclear force inherently possesses a short range, independent of the mass number of the nucleus. Its influence extends only over a few femtometres and decreases rapidly beyond that range. The effective range of nuclear force does not depend on the mass number.

Conclusion: Assertion (A) is true, but Reason (R) is false.