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Q.

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 :

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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)

answer is B.

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Detailed Solution

Step 1: Understanding the Statements

Assertion (A): The binding energy per nucleon (BE/A) is the average energy required to remove a nucleon from the nucleus.

It is observed that for nuclei with mass numbers between 30 and 170, the binding energy per nucleon is nearly constant (~8 MeV).

This happens because, in this range, nuclear forces reach saturation, meaning each nucleon interacts with only its closest neighbors.

Assertion (A) is correct.

Reason (R): The nuclear force is a short-range force, acting significantly only within distances of about 1–2 femtometers (fm).

Unlike gravitational and electrostatic forces (which are long-range), nuclear forces do not act over large distances.

Since the reason states that nuclear force is long-range, which is incorrect, Reason (R) is false.

Step 2: Choose the Correct Option

The correct choice is:

(A) is true, but (R) is false.

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