Question

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
 Assertion (A): The binding energy per nucleon is found to be practically independent of the atomic number \( A \), for nuclei with mass numbers between 30 and 170. 
Reason (R): Nuclear force is long range. 
In the light of the above statements, choose the correct answer from the options given below:

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

Hint:

The nuclear force is short-range, and while binding energy per nucleon is nearly constant for a wide range of atomic numbers, it is not due to the nuclear force being long-range.

Answer 1

The Correct Option is B

The task requires evaluating two statements: one concerning nuclear binding energy and another concerning nuclear forces.

1. Analysis of Assertion (A):
   • The assertion posits that the binding energy per nucleon remains largely constant for atomic nuclei with mass numbers ranging from 30 to 170.
   • Within this mass range, the binding energy per nucleon exhibits a plateau before declining for more massive nuclei. This observation is consistent with the semi-empirical mass formula, which attributes this stability to the interplay of nuclear forces.
2. Analysis of Reason (R):
   • The reason incorrectly claims that the nuclear force has a long range. Nuclear forces are, in fact, short-range forces, exerting influence only over distances of approximately a few femtometers (\(1 \text{ fm} = 10^{-15} \text{ m}\)).
   • The short-range nature of the nuclear force dictates its strong effect on closely situated nucleons within a nucleus, but its negligible impact on nucleons in distant nuclei.

Therefore, the assertion (A) accurately describes the binding energy per nucleon within the specified mass range. Conversely, the reason (R) provides an inaccurate characterization of nuclear forces. The correct evaluation is:

(A) is true but (R) is false