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 question involves evaluating two statements: an assertion about nuclear binding energy and a reason related to nuclear forces.

1. Understanding the Assertion (A):
   • The assertion states that 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. 
   • For nuclei within this mass range, the binding energy per nucleon is relatively constant and then begins to decrease for heavier nuclei. This is validated by the semi-empirical mass formula which indicates this plateau in binding energy values due to competing nuclear forces.
2. Understanding the Reason (R):
   • The reason states that nuclear force is long-range. This is incorrect because nuclear forces are actually short-range forces, effective only over distances on the order of a few femtometers (\(1 \text{ fm} = 10^{-15} \text{ m}\)).
   • Nuclear force being short-range explains why it strongly influences nucleons tightly packed within an atomic nucleus, but not between widely separated nuclei.

In conclusion, the assertion (A) about the nature of binding energy per nucleon for the specified mass range is correct. However, the reason (R) provided is a false statement about the nature of nuclear forces. Thus, the correct answer is:

(A) is true but (R) is false

Answer 2

Assertion (A) is true. The binding energy per nucleon for most nuclei with mass numbers between 30 and 170 remains approximately constant because the nuclear force is nearly the same for all these nuclei. - Reason (R) is false. The nuclear force is actually a short-range force, typically acting over distances of about 1 to 2 femtometers (fm), which is much shorter than the range of electromagnetic forces. Thus, the correct answer is (2), where Assertion (A) is true, but Reason (R) is false.