JEE Main 2023 · 13 April · evening · Single correct · +4 / −1
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 practically independent of the atomic number for nuclei of mass number in the range 30 to 170 .
Reason R : Nuclear force is short ranged.
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 and solution
Answer (c) Both A and R are true and R is the correct explanation of A
Solution
Physics sir · 4 steps
A nucleon feels only its nearest neighbours, so its binding energy stops growing in a big nucleus.
- Check A. On the binding energy curve, B/A rises quickly for light nuclei and then flattens at about 8 MeV per nucleon. From mass number 30 to 170 it stays between about 8.0 and 8.8 MeV, so A is true.
- Check R. The nuclear force is strong only over about 2 to 3 fm and drops almost to zero beyond that. So R is true.
- Link them. Because the force is short ranged, a nucleon binds only to the few nucleons right next to it. Once the nucleus is wider than this range, adding more nucleons does not give any one nucleon more neighbours. So each nucleon adds about the same energy and B/A stays nearly constant, which is called saturation of the nuclear force.
- So. Both statements are true, and the short range of the nuclear force is exactly why B/A levels off. The answer is (c).
The idea to keep. Short range means saturation: each nucleon bonds only with its nearest neighbours, so B/A stays nearly constant for medium-sized nuclei.
Answer from the NTA final answer key. Solution by PrepWiser.