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MCQEasyJEE 2025Atomic Mass & Binding Energy

JEE Physics 2025 Question with Solution

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 AA, for nuclei with mass numbers between 3030 and 170170. 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)

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given:

  • Assertion (A): The binding energy per nucleon is practically independent of atomic number AA for nuclei with mass numbers between 3030 and 170170.
  • Reason (R): Nuclear force is long range.

Find: The correct option among the given statements.

The solution explains that for nuclei in the mass-number range 3030 to 170170, the binding energy per nucleon remains nearly constant over a wide range. This part of the assertion is true.

The reason is false because nuclear force is short-range, not long-range. It is effective only over distances of a few femtometers.

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

Therefore, the correct option is B.

Detailed Explanation

Given:

  • A statement about binding energy per nucleon.
  • A statement about the range of nuclear force.

Find: Whether Assertion (A) and Reason (R) are true or false.

  1. Understanding Assertion (A): The binding energy per nucleon for nuclei with mass numbers roughly between 3030 and 170170 stays nearly constant. This corresponds to the well-known plateau in the binding-energy-per-nucleon curve.

  2. Understanding Reason (R): The statement says nuclear force is long range. This is incorrect.

  3. Nuclear force acts only over a very small distance, of the order of a few femtometers:

1 fm=10−15 m1 \, \text{fm} = 10^{-15} \, \text{m}

So nuclear force is a short-range force.

  1. Hence, the assertion is true, but the reason is false.

Therefore, the correct option is B, that is, (A) is true but (R) is false.

Common mistakes

  • Assuming that nearly constant binding energy per nucleon implies nuclear force is long range. This is wrong because the nuclear force is actually short-range. Use the known property of nuclear forces before linking it to the graph or trend.

  • Confusing atomic number with mass number in the statement. The assertion discusses nuclei with mass numbers between 3030 and 170170, so the conclusion should be based on the binding-energy-per-nucleon trend over that mass range.

  • Treating both Assertion and Reason as true because the assertion sounds familiar. Even if Assertion (A) is correct, Reason (R) must be checked independently. Here the reason fails because the stated nature of nuclear force is incorrect.

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